condition monitoring acoustic emission

1. INTRODUCTION INTRODUCTION TO CONDITION MONITORING Productivity is a key weapon for manufacturing companies to stay competitive in a continuous growing global market. Increased productivity can be achieved through increased availability. Managing industries into the 21st century is a challenging task. Increasing global competition, fast technological change, consumer’s perceptions towards total quality, reliability, health and safety, environmental considerations and changes in management structure not only provides many companies with considerable opportunities to improve their performance but also the much needed competitive edge to those firms that strategically plan for the future and exploit fully the advantages of modern manufacturing techniques and methods. Manufacturing productivity is found to be influenced by following major factors: i) Greater availability of physical resources ii) Improvements in the quality of the human resources iii) Improved manufacturing methods and techniques. It is the later sector of manufacturing, to which condition monitoring contributes significantly. Today, most maintenance actions are carried out by either the predetermined preventive- or the corrective approach. The predetermined preventive approach has fixed maintenance intervals in order to prevent components, sub-systems or systems to degrade. The concept of condition monitoring is to select measurable parameters on the machines, which will change as the health or condition of a machine. Regular monitoring is done and the change is detected. Once a change is detected it is possible to make a more detailed analysis of the measurements to determine what the problem is, and hence arrive at a diagnosis of the problem. The parameters most often chosen to detect this change in conditions are either vibration, which tends to increase as a machine moves away from a smooth running condition into a rough mode with development of a fault, or an analysis of machine noise or acoustics, or machine lubricants where samples are tested for items such as wear debris from a developing fault. There are various sensors to detect and monitor the early signals of electrical, mechanical, electronic, pneumatic, hydraulic, etc. and provide an aid to fault diagnosis and to establish an effective maintenance management procedure to predict and prevent system failure just in time. A well-designed condition monitoring strategy reduces production costs, operating costs and labour costs. The International Standardization Organization (ISO) has recently set up a subcommittee 9ISO/TC/108/SC5, “Condition Monitoring and Diagnostics of Machines”. The scope of this committee is to standardize the procedure, equipments etc. so that a unique procedure can be set. The cost of people involved in condition monitoring, is an important factor to consider when looking at the total cost of the system, and it often outweighs the cost of technology involved. It is also important to remember that the investment in the system is largely a single, one off cost at the beginning of the program. The amount of time that takes to walk around the plant with such a device, fixing a transducer, or reading a meter cannot substantially be reduced. However software now a day, are helping hands to reduce this time. It allows the reduction of the vast array of often complex measurements into a list of those machines needing maintenance attention, as well as listing the nature of the problem, in a completely automated way. [1] 1.2 CONDITION MONITORING TOOLS The architecture of condition monitoring systems today has largely been dictated by the technical focus. There are several different types of measurements commonly used to determine condition and the technical requirements.[1] Gearboxes are often critical components of machine requiring the application of condition monitoring techniques. Condition monitoring of Gearboxes implies determination of condition of gears and its change with respect to time. The condition of these gears may be determined by the physical parameters like vibration, noise, temperature, wear debris, oil contamination, etc. A change in any of these parameters called ‘signatures’ would thus indicate the change in the condition or health of the gears. The major measurement techniques are: 1.2.1 Sound and Vibration The most established and tangible technology is sound and vibration analysis. Almost all the machines vibrate and produce sound, and the link between this sound and the machine condition is both easily measured and the results easily interpreted. Transducers can be easily attached on a temporary basis to a machine, most often with a strong magnet, so that collection of data is quick and efficient. A major benefit of vibration however, is that different mechanical processes within the machine (e.g. imbalance, gear mesh, bearing faults) will produce energy at different frequencies. If the different frequencies are separate from one another through analyzer, the whole new level of detail may be seen, with more advanced warning of development of faults. 1.2.2 Lubricant Analysis The second most common technique is testing of lubricant samples. This can have the major benefits as it can detect the root cause of a problem. Viscosity checks, moisture content as well as detection of contaminants all fall into this category of test. The technique can also look for the effects of wear site with the lubricant. But this technique relies on the samples being taken away from machinery to a laboratory for full analysis to be performed. 1.2.3 Thermography Electrical departments were the first to benefit from the user of thermal imaging cameras to obtain the temperature distribution maps, looking for a hot spot from the loose connection. The technique is being widely used to look at the pipe work vessels, as well as bearing and couplings. The cameras are getting smaller, lighter and the quality is better all the time. 1.2.4 Ultrasonics, Acoustic Emission and High Frequency Vibration Various techniques, using simpler approaches to vibration analysis, are used to detect friction and presence of bursts of energy resulting from defects in rolling element bearings, where a rolling element may be impacting defects in a race creating shocks and spikes of energy. Whilst having merits of their own, the uses of these techniques often use simpler transducers, mounted in the same locations as vibration analysis. The combination of vibration with these techniques can therefore create economies in the time and manpower needed to collect the data. 1.2.5 Wear Debris Monitoring The condition of critical component surfaces subject to loading and relative movement is assessed from wear debris, which they generate. They are usually oil washed components, and the collection and analysis of debris is done via lubricating oil. Available condition monitoring and diagnostic techniques are listed in Table 1.1 and the selection of the condition monitoring technique is given in Table 1.2 Table 1.1: Available condition monitoring and diagnostic techniques A. ACOUSTIC MONITORING B. VIBRATION MONITORING a) Microphone a) Overall monitor b) Spectral analysis b) Spectral analysis c) FFT/ Zoom FFT c) Discrete frequency monitoring d) Shock pulse monitoring e) Signal averaging C. WEAR DEBRIS ANALYSIS D. VISUAL INSPECTION a) Ferrography a) Radiography b) Inductive sensors b) Eddy current c) Capacitive sensors c) Ultrasonics d) Spectrography Table 1.2 Condition monitoring technique selectors. Vibration Analysis Acoustic Analysis Acoustic Emission Debris Analysis Thermal Imaging Corrosion Monitoring Bearing YES YES YES YES YES YES Boilers YES YES Compressors YES YES YES YES Coupling YES YES Elevators YES YES YES YES Escalators YES Filters YES YES Gearboxes YES YES YES YES YES YES M/c Tools YES YES Pressure Vessels YES YES YES Pumps YES YES YES YES Structures YES YES YES Transformers YES Turbines YES YES YES YES YES YES Welding YES I.C. Engine YES YES GEARBOX MONITORING 1.3.1 Needs Manufacturing industry drives the world. Every manufacturing industry is having number of machines and gearboxes, which are used for power conversion, speed reduction and torque amplification, can control many of them. It has been estimated that annually 10 million new gearboxes enter operation with a combined component value of more than 5 billion dollars. Economics of industries totally depend upon reliable operation of gear driven machinery and gearboxes. [1] Any defect induced in gear may costs high at the time of failure. For that, early prediction of breakage of gear tooth is essential to avoid stoppage of that machine thereby increase in utilization. Condition monitoring is gaining importance because it can make contributions towards reducing equipment downtime and maintenance expenditure. It can also contribute towards safety in critical application by providing an early warning of potential catastrophic failure. So the use of the various monitoring techniques is gaining prime importance to establish a unique solution to take over the monitoring problems. 1.3.2 Gearbox Diagnostic Techniques There are number of causes, which lead to the failure of the gearboxes. The various techniques are discussed in this article. 1.3.2.1 Noise and Vibration Sensing Power losses in gearboxes are a normal consequence of less than perfect operating efficiency. These power losses result in energy dissipation as vibration and heat. The analysis for the detection of faults in the gearboxes is normally related to a change in the characteristic of the gearbox vibration. This change may be in overall vibration amplitude, change in the amplitude of certain frequencies of vibration, or in the pattern of the vibration signature. Changes in these signal amplitudes can be used to indicate degradation in these components and the onset of failure. The analysis of gearbox vibration data can be broadly classified into two categories; spectral analysis and feature analysis. 1.3.2.2 Acoustic analysis technique Sound is ubiquitous. Sound is defined mechanical energy vibrations transmitted as waves through a solid, liquid, or a gas that can be detected by the human ear. The study of sound is called acoustics and covers all fields of sound production, sound propagation and sound reception, whether created and received by human beings or by machines and measuring instruments. Sound usually arises when rubbing between two material surfaces or rolling contact in bearings, gears etc., take place during its operational life. The acoustic noise measurement can also be used for condition monitoring. Listening the noise of machines, as a means of detecting malfunction in them. The analysis of noise signal is carried out much the same way as vibration signal using similar instrumentation. By monitoring the acoustic conditions of plants and machineries at critical position in a mechanical manner, and by analyzing the acoustic signal in an intelligent way, it is possible to avoid the cost and avoidable breakdowns. The use of acoustic analysis is not restricted to predictive maintenance but also this technique is useful for diagnostic applications as well. Acoustic monitoring and analysis are primary diagnostic tools for most mechanical systems that are used to manufacture products. When used properly, acoustic data provides the means of maintaining optimum operating conditions and efficiency of critical plant system. The philosophy behind acoustic monitoring is to provide useful information to designer and maintenance manager to enhance the operational reliability, minimize early failures, and provide improved protection to operating personnel, extend the systems life cycle and remain highly competitive in the global market. As is well known, of the many parameters that can be monitored, acoustic monitoring has been widely accepted as one of most powerful parameter, which can be employed to diagnostic of fault and prevent machinery failures. In acoustical analysis technique either sound pressure measurement or sound intensity measurements are carried out. But sound intensity measurement is having distinct advantages. As it is vector quantity it gives sound pressure as well as direction of sound so it gives idea about the location of fault. 1.3.2.3 Oil Debris Detection While vibration analysis may allow one to infer gear faults, monitoring of the lubricating oil flow for metallic debris is a more direct method for the detection of wear and surface failure type faults in gearboxes. Two different approaches are commonly used. One involves the analysis of the oil samples and/or debris in an off line laboratory. The second involves detecting particles on line and in real time. Oil debris detection can provide a good backup to vibration monitoring, especially in complex gearboxes or where vibration levels are high enough to render conventional vibration analysis ineffective. 1.3.2.4 Thermal Diagnostic Techniques Perhaps the most economical monitor of gearbox condition is temperature. A rise in oil temperature increases the power loss in the gearbox. This is almost near to the failure. Parameters such as rate of temperature increase and the increase of this rate (temperature “acceleration”) are useful in the detection in the final stages. The use of temperature is recommended as a monitor of the lubricating system operation, as the failure of this function may lead to the gearbox damage. SUMMARY Condition monitoring emerged from being critical need into mainstream and widespread use as a critical element in the management strategy of companies operating rotating machines all over world. However, it is historically been bogged down in a focus on the technology involved in making the measurements, and not on achieving financial benefits. There are still improvements are made, and although many will come from the advent of the computers and associated technologies. SCOPE OF WORK In this dissertation work, the technique of condition monitoring is applied to selected gearbox to assess the condition of gear teeth. It is well established fact that any change in condition of gear such as wear, a crack, lack of oil or one tooth missing cause a corresponding change in the motion and hence in the vibration acoustic pattern. These signals for known defect are collected by vibration accelerometer and sound pressure level probe ( microphone ) during working of gearbox. The gear box is considered as a linear mechanical system and an individual meshed gear vibrate and produces sound which propagates from individual meshing gears to measuring points which is in gear box casing. By introducing gears of known faults, the vibration and acoustic spectrum are collected by using Fast Fourier Transformer (FFT) and the corresponding change in pattern is compared with the signals obtained from gear without fault. These changes in signals are correlated to the faults of gear tooth. ORGANISATION OF REPORT Chapter 1 deals with the importance of condition monitoring and various methods of condition monitoring. Chapter 2 deals with the historical and present status of the technique of condition monitoring and diagnosis technique of gearbox. The fundamental, the detection procedure of the vibration and acoustic data measurement and its instruments are discussed in Chapter 3. Chapter 4 contains common problems of gear and various analysis methods of vibration and acoustic analysis. Chapter 5 discusses the experimental setup and the arrangement done to acquire the vibration and acoustic signals from gearbox for condition monitoring of and fault diagnosis of gear tooth. Results of the readings are discussed in Chapter 6. Chapter 7 draws the conclusion and suggests the future work to be carried out in this field. 2. LITERATURE SURVEY 2.1 INTRODUCTION The literature review of this dissertation work is broadly divided in to two parts. The first part gives the history of vibration monitoring and its use to diagnose the machinery faults. It covers the development in signature analysis technique due to the digital frequency analyzer. The measuring and analyzing techniques of gearbox vibration, which are offered by different researchers, are discussed in second part. Scope of this chapter is to get familiar with work done by various investigators in the field of condition monitoring and gearbox fault diagnostics. 2.2 DEVELOPMENT OF DIAGNOSTIC TECHNIQUE THROUGH ACOUSTICS The architecture of condition monitoring system today has largely been dictated by the technical focus but prior to World War II the practical solution of incipient failure through acoustics was more of an art rather than a science and was dependent on experience and expertise of the user. It requires a certain skill, which often is very high on the part of the `listener’ and the result is not getting perfect information about malfunction. This was primarily due to the absence of experimental tools to determine nature of noise causing problem. There was virtually nothing, which the engineer could measure other than noise level and frequency except on relatively, low speed machines. Theoretical analysis was also limited by the lack of computational aids; mechanical calculators were the exception rather than the rule. The art of diagnosis was, therefore to be able to isolate the problem by examination of failure. There was little scope for characteristic acoustic analysis leading to predictions of ultimate machine life. Balancing or similar techniques were used only when acoustic was seen or felt excessive. The rapidness in condition monitoring was take place when development of digital frequency analyzer was the invention of the Fast Fourier Transform (FFT) algorithm by Cooley et al [12] in 1965. However the rapid development of low cost high performance frequency analyzer since the late 1970s was due to the rapid performance microprocessors and analog to digital (A/D) voltage converters. By mid forties a series of electrical transducers and recorders were developed to measure and store data in electrical form. The advancement in data storage provides means of conditioning data continuously for all forms of analysis, line spectrum, power spectral density, and correlation etc. without transport of the analyses equipment in to factory. Wavelet Analysis :- There are many analysis techniques, which have been fully developed and established over the years for processing vibration signals to obtain diagnostic information about progressing gear faults. Earlier research on gear failure detection focused on the use of time-averaged vibration signal, spectrum, cepstrum and amplitude and phase modulation techniques to detect different types of gear failures. Most of these conventional approaches work well to detect abnormality and indicate faults without providing much information about them, such as location and severity of the faults. Application of these methods to detect gear faults can be found. During the last decade, some time–frequency methods have received growing attention and gained reliable acceptance in the field of condition monitoring. Generally, the dynamic signals in the field of engineering problems such as vibration, sound so on, have been analyzed using the fast Fourier transform (FFT) The FFT has been the most common method to analyze frequency properties of the signals. In the FFT analysis, the signal as the function of time is converted to the power spectra in a frequency domain. However, except for a special case, the frequency components of the most signals encountered in the engineering problem change with time. Based on the FFT alone, it is hard to investigate whether the frequency components of the signals vary with time or not, even though the phase of the Fourier transform relates to time shifting. The FFT analysis is no more adequate for those applications. Therefore, it is significant and important to adopt the time frequency analysis for those signals varying with time. It is possible by using the time-frequency analysis to investigate how the frequency components of the signal vary with time. The time frequency components of the signals vary with time. The time-frequency analysis can provide more beneficial information about the frequency compared with the FFT. During last two decades, a new mathematical technique for the time – frequency analysis, which has been called the wavelet transform, has been extensively developed. Wavelet transform provide a constant frequency to bandwidth ratio analysis. In consequence, Wavelet transform possess fine time resolution in the high frequency ranges and excellent frequency resolution in the high frequency ranges and excellent frequency resolution in low frequency region. This feature of wavelet transform uniquely fits the requirement in failure diagnosis. 2.3 GEARBOX FAULT DIAGNOSTIC EVOLUTION Gearbox is used in various engineering applications such as in machine tools, automobiles, helicopters, etc. for torque and speed conversions or to achieve definite torque and speed requirement. In gearbox as the number of stages increase, fault diagnosis becomes more difficult. Some important inventions in gearbox fault diagnostics are as follows. N. Baydar & A. Ball have presented [1] “Detection of gear failures via vibration and acoustic signals using wavelet transform”. In their work they have used vibration and acoustic signals for detection failure of gear. Two commonly encountered local faults, tooth breakage and tooth crack, were simulated. The results of acoustic signals were compared with vibration signals. Naim Baydar and Andrew Ball have presented [2] “A comparative study of acoustic and vibration signals in detection of gear failures using winger-ville distribution”. This paper examines whether acoustic signals can be used to detect faults in gearbox using smoothed pseudo-winger-ville distribution. Three types of progressing local faults, broken tooth, gear crack and localized wear, were simulated. Yuji Ohue & Akira Yoshida have presented [3] “New evolution method on dynamics using continuous and discrete wavelet transforms”. This paper deals with the new method of gear dynamics using the continuous and discrete wavelet transform. In order to evaluate the difference in the gear dynamics due to the gear materials, which are sintered & steel ones, the dynamic characteristics of gears were measured using a power circulating gear testing machine. The gear dynamics were analyzed in a time frequency domain by the continuous & discrete wavelet transforms. The new evaluation method using the wavelet transform proposed in this paper was more useful compared with the conventional one to investigate the damping characteristics & the dynamic of the gear equipment. Wen-xian Yang & Peter W. Tse have presented [4] “An advanced strategy for detecting impulses in mechanical signals”. The appearance of overlapping in the results derived by continuous wavelet transform (CWT) smears the spectral features and makes the results difficult to interpret. This will significantly affect the accuracy of analysis of anomalous signals. Aiming at minimizing the undesired effect of overlapping a new soft-thresholding method in terms of exponential functions is proposed. Using the proposed soft-threshold & combining with Donoho’s approach for reducing the structures induced by noise, a strategy for purifying the results derived by the CWT are further purified & thereby the spectral features of the inspected signal become more explicit & much more easily identified. Peter W. Tse, Y. H. Peng, Richard Yam have presented [5] “Wavelet analysis and envelope detection for rolling element bearing fault diagnosis- Their effectiveness and flexibilities”. This paper commences with technique of wavelet analysis and envelope detection for fault diagnosis. The components which often fail in a rolling element bearing are the outer race, the inner race, and the cage. Such failure generates a series of impact vibrations in short time intervals, which occur at bearing characteristics frequencies (BCF). Since BCF contain very little energy, and are usually overwhelmed by noise and higher levels of micro structural vibrations, they are difficult to find in their frequency spectra when using the common technique of Fast Fourier Transform. Therefore, Envelope Detection (ED) is always used with FFT to identify faults occurring at the BCF. However computation of ED is complicated, and requires expensive equipment and experienced operators to process. This, coupled with the incapacity of FFT to detect nonstationary signals, makes wavelet analysis a popular alternative for machine fault diagnosis. Wavelet analysis provides multi- resolution in time-frequency distribution for easier detection of abnormal vibrational signals. From the results of extensive experiments performed in a series of motor – pump driven systems, the methods of wavelet analysis and FFT with ED are proven to be efficient in detecting some types of bearing faults. D.F. Shi, W. J. Wang and L. S. Qu have presented [6] “Defect detection for bearing using envelope spectra of wavelet transform”. This paper considers wavelet transform for defect detection of bearing. In order to overcome the shortcoming in the traditional envelope analysis in which manually specifying a resonant frequency band is required, a new approach based on the fusion of the wavelet transform and envelope spectrum is proposed for detecting and localized defects in rolling element bearing. This approach is capable of completely extracting the characteristics frequencies related to the defect from the resonant frequency band. Based on the Shannon entropy of wavelet- based envelope spectra, a criterion to select optimal scale to monitor the condition of bearings is also presented. Experiment results show that proposed approach is sensitive and reliable in detecting defects on the outer race, inner race, and rollers of bearing. Jing Lin, Ming J. Zuo, Ken R. Fyfe have presented [7] “Mechanical fault detection based on the wavelet de-noising technique”. This paper commences with technique of wavelet de-noising for mechanical fault detection. For gears and roller bearings, periodic impulses indicate that there are faults in the components. However, it is difficult to detect the impulses at the early stage of fault because they are rather weak and often immersed in heavy noise. Existing wavelets, which do not match the impulse very well and do not utilize prior information on the impulses. A new method for wavelet threshold de-noising is proposed in this paper; it not only employs the Morlet wavelet as the basic wavelet for matching the impulses, but also uses the maximum likelihood estimation for thresholding by utilizing prior information on the probability density of the impulse. This method has performed excellently when used to de-noise mechanical vibration signals with a low signal-to-noise ratio. Jing Lin, Ming J Zuo have presented [8] “Extraction of periodic components for gearbox diagnosis Combining wavelet filtering and cyclostationary analysis”. This paper commences with wavelet filtering is combined with cyclostationary analysis for detection of gear tooth faults in a gearbox. The parameters of the wavelet filter are optimized by using the proposed entropy minimization rule. This method is shown to be effective in detecting gear faults when cyclostationary analysis by itself fails. W. X Yang and X.M. Ren have presented [9] “Detecting impulses in mechanical signals by wavelets”. This paper commences development of an effective impulses detection technique is necessary and significant for revaluating the working condition of these machines ,diagnosing their malfunctions, and keeping them running normally over prolong periods. With the aid of wavelet transforms, a wavelet –based envelope analysis method is proposed. In order to suppress any undesired information and highlight the features of interest, an improved soft threshold method has been designed so that inspected signal is analyzed in a more exact way. Furthermore ,an impulse detection technique is developed based on the aforementioned methods The effectiveness of the proposed technique on the extraction of impulsive features of mechanical signals has been proved by both simulated and practical experimental Martin J. Dowling has presented [10] “Application of nonstationary analysis to machinery monitoring”. The paper discusses how non-stationary signal processes such as the wavelet transform and wigner-ville distribution can be applied to machinery monitoring and diagnostic in industry. Wesley G Zanardelli, Elias G. Stragas, and Selin Aviyente [11] “Failure prognosis for permanent magnet AC drives based on wavelet analysis”. This paper commences with prognosis for failure of an electric machine through the detection of non-catastrophic faults. In this work, two types of stator faults are studied. The methods developed are based on analysis of the undecimated discrete wavelet transform of the field of the oriented machine currents. -J.Lin and M. J. Zuohave presented [12] “Gearbox fault diagnosis using adaptive wavelet filter”. In this paper an adaptive wavelet filter based on Morlet wavelet is introduced. The parameters in the Morlet wavelet function are optimized based on the kurtosis maximization principle. The adaptive wavelet filter is found to be very effective. -H.Zheng , Z. Li and X. Chen presented [13] “Gear fault diagnosis based on continuous wavelet transform”. In this paper a new approach of gear fault diagnosis based on continuous wavelet transform is presented. Continuous wavelet transform can provide a finer scale resolution than orthogonal wavelet transform. It is more suitable for extracting mechanical fault information. In this paper, the concept of time-averaged wavelet spectrum (TAWS) based on Morlet continuous wavelet transform is proposed. Two fault diagnosis methods named spectrum comparison method (SCM) and feature energy method (FEM) based on TAWS are established. The results of the application to gearbox gear fault diagnosis show that TAWS can effectively extract gear fault information. The feature energy of the TAWS features the gear fault advancement very well and is conically proportional to the gear fault advancement. - Wilson Q. Wang, Fathy Ismail and M. Farid Golnaraghi have presented [14] “Assessment of gear damage monitoring technique using vibration measurement”. This paper experimentally investigates the sensitivity and robustness of the currently well-accepted techniques: phase and amplitude demodulation, beta kurtosis and wavelet transform. Four gear test cases were used: healthy gears, cracked, filed and chipped gears. The vibration signal was measured on the gearbox housing and processed, online, under three "filtering conditions: general signal average, overall residual and dominant meshing frequency residual. Test results show that beta kurtosis is a very reliable time-domain diagnostic technique. Phase modulation is very sensitive to gear imperfections, but other information should be used to confirm its diagnostic results. Continuous wavelet transform provides a good visual inspection especially when residual signals are used. The diagnosis based only on dominant meshing frequency residual, however, should not be used independently for gear health condition monitoring, it may give false alarms. -Ulo Lepik has presented [15] “ Application of wavelet transform technique to vibration studies’. In this paper wavelet transform techniques are applied to analysis of linear vibrations. It is shown that in some simple cases wavelet transform can be accomplished analytically. Damped and forced vibrations of single and two degrees of freedom are considered. The achieved results can be used for interpreting more complicated cases. -G. Dalpiaz , A. Rivola and R. Rubini have presented [16]“ Effectiveness and Sensitivity of vibration processing techniques for local fault detection in gears”. This paper deals with gear condition monitoring based on vibration analysis techniques. The detection and diagnostic capability of some of the most effective techniques are discussed and compared on the basis of experimental results, concerning a gear pair affected by a fatigue crack. In particular, the results of new approaches based on time-frequency and cyclostationarity analysis are compared against those obtained by means of the well accepted cepstrum analysis and time-synchronous average analysis. Moreover, the sensitivity to fault severity is assessed by considering two different depths of the crack. The effect of transducer location and processing options are also shown. In the case of the experimental results considered in this paper, the power cepstrum is practically insensitive to the crack evolution. Conversely, the spectral correlation density function is able to monitor the fault development and does not seem to be significantly influenced by the transducer position. Analysis techniques of the time-synchronous average, such as the &residual' signal and the demodulation technique, are able to localise the damaged tooth; however, the sensitivity of the demodulation technique is strongly dependent on the proper choice of the filtering band and affected by the transducer location. The wavelet transform seems to be a good tool for crack detection; it is particularly effective if the residual part of the time-synchronous averaged signal is processed. -S. A. Adewusi and B. O. Al.- Bedoor have presented [17]“ Wavelet analysis of vibration signals of an overhang rotor with a propagating transverse crack’. This paper presents an experimental study of the dynamic response of an overhang rotor with a propagating transverse crack using the discrete wavelet transform (DWT)-a joint time frequency analysis technique. Start-up and steady state vibration signatures are analyzed using Daubechies (Db6) mother wavelet and the results are presented in the form of scalograms and space-scale energy distribution graphs. The start-up results showed that crack reduces the critical speed of the rotor system. The steady state results showed that propagating crack produces changes in vibration amplitudes of frequency scale levels corresponding to 1X, 2X and 4X harmonics. The vibration amplitude of frequency scale level corresponding to 1X may increase or decrease depending on the location of the crack and side load. However, the amplitude of frequency scale level corresponding to 2X increases continuously as the crack propagates. -W. J . Staszewski and G. R. Tomlinson have presented [18] “ Application of wavelet transform to fault detection in spur gear”. This paper present an application of wavelet transform in machinery diagnostic . The theoretical background and some basic properties of wavelet transform are given. The method is implemented and validated by a series of simulated numerical examples. Finally the method is applied to detection of damaged tooth in spur gear. A fault detection algorithm is presented , based on a similarity analysis of pattern obtained the modulus of the wavelet transform. -S. Prabhakar , A. S. Shekhar and A.R. Mohanty have presented [19] “ Detection and monitoring of cracks in a rotor – system bearing using wavelet transform”. The dynamics and diagnostics of cracked rotors have been gaining importance in recent years. Vibration monitoring during start-up or shut-down is as important as during steady-state operation to detect cracks especially for machines such as aircraft engines which start and stop quite frequently and run at high speeds The vibration signals during machine start-up or shut-down are non-stationary in nature. Wavelets provide a time-scale information of a signal, enabling the extraction of features that vary in time and thus can be used for damage detection . However, to the best of the authors' knowledge, there is no work reported on the application of the wavelet transforms to detect cracks in a rotor-bearing system. In the present study, the continuous wavelet transform (CWT) has been used as a tool to detect and monitor cracks in a rotor-bearing system from the time domain signals. -Darley Fiacrio de Arruda Santiago have presented [20] “Application of wavelet transform to detect faults in rotating machinery”. The field of fault diagnostic in rotating machinery is vast, including the diagnosis of items such as rotating shafts, rolling element bearings, couplings, gears and so on. The different types of faults that are observed in these areas and the methods of their diagnosis are accordingly great, including vibration analysis, model-based techniques, statistical analysis and artificial intelligence techniques. However, they have difficulties with certain applications whose behavior is non-stationary and transient nature. In the present study, a rotor system model capable of describing the theoretical dynamic behavior resulting from shaft misaligned and unbalanced rotor is developed during run-up motion. A comparison between experimental and numerical results clearly indicates that validity of the theoretical model was successfully verified for fault misalignment. The results show that the fault mechanical looseness and the effect of the evolution of fault misalignment can be monitored and detected during the machine run-up without passing by critical speed. Extensive numerical and experimental results show that ability and feasibility of the application of wavelet analysis in the diagnostic of faults inserted in the experimental set-up is very suitable to non-stationary signal analysis. Results show that the sensitivity and efficiency in the fault diagnostic using transient response during start-up is higher than steady state response of rotating machinery. -A Belsak and J Flasker have presented [21] “ Method for detecting fatigue cracks in gears”. The most undesirable damage that can occur in gear units is crack in the tooth root as it often makes gear unit operation impossible. Monitoring vibrations can be used to detect defects. Time signals are acquired experimentally and afterwards. Different methods can be used to analyse them. The changes in tooth sti.ness caused by a fatigue crack in the tooth root are of significance. The dynamic response of a gear unit with a damaged tooth differs from the one of an undamaged tooth. Amplitudes of time signal are, by time–frequency analysis, presented as a function of frequencies in spectrum. -E . B. Halim , S .L . Shah , M . J . Zuo and M . A. Shaukat Choudhary have presented [22] “ Fault detection of gearbox from vibrational signals using time – frequency domain averaging”. In this paper early fault detection is done by analyzing vibration signal using different signal processing technique. Time domain averaging technique is used. - W. J. Staszewski , K Worden and G. R. Tomlison have presented [23] “Time – Frequency analysis in gearbox fault detection using winger -ville distribution and pattern recognisition”. In this paper the study of the Wigner-Ville distribution in gearbox condition monitoring is presented. In contrast to other applications of the Wigner-Ville distribution this paper reports the application of two pattern recognition procedures to detect tooth faults reliably. These procedures are based on statistical and neural pattern recognition. The methods are applied to the detection of a broken tooth in a spur gear. - F. K. Choy, D. H Mugler and J Zhou have presented [24] “ Damage identification of gear transmission using vibration signature”. This paper demonstrates the use of vibration signature analysis procedures for health monitoring and diagnostics of a gear transmission system. The procedures used in this paper include (i) the numerical simulation of the dynamics of a gear transmission system with single and multiple tooth damage, (ii) the application of the Wigner-Ville Distribution (WVD) and the Wavelet transform in damage identification and quantification of damaged tooth based on the numerically generated vibration signal, and iii) the application of both WVD and the Wavelet transform on experimental data at various stage of gear failure obtained from an accelerated gear damage test rig. This paper demonstrates that the developed signature analysis procedure can successfully detect faulty gears in both numerically simulated and experimental tested transmission system. General conclusions on identification and quantification of gear tooth damage are drawn based on the results of this study. 3. VIBRATION AND SOUND MEASUREMENT 3.1 INTRODUCTION: The measurement of vibration sound and its characteristics plays an important role in development of a systematic approach to vibration and acoustic analysis. In particular, the measurement of overall vibration and sound levels can be used to determine compliance with regulations or pertinent criteria. These measurements can also be used to assess the effectiveness of various condition monitoring technique and to establish realistic goals. Although measuring vibration and sound level is an essential aspect of characterizing vibration and acoustic analysis. Today, Vibration and sound measurement instrumentation embodies a wide range of complexity and sophistication explained. So this chapter of dissertation discusses the various instruments Basic vibration measurement system Basic sound measurement system 3.2 CAUSES OF MACHINE VIBRATION AND SOUND To generate noise from machine the primary cause must be a force variation which generates a vibration (in components), which is then transmitted to the surrounding structure. It is only when the vibration excites external panels that the airborne noise is produced. 3.2.1 Overall Path of Vibration Noise Gear Errors, Deflections, Distortions, etc. Transmission Error Gear Body Vibrations Bearing Housing Forces Panel Vibrations Noise Fig. 3.2 Path of Vibration and Noise in Gearbox 3.3 FUNDAMENTALS OF VIBRATION AND ACOUSTICS Vibration Monitoring Vibrations are always resent in any rotating/ moving machine. These can’t be eliminated but can be controlled. It is important to keep the vibrations in a machine within acceptable limits for its good health. Vibration as a parameter, therefore, can be used as an indicator of the health of a machine is considered good. However, when these levels become unacceptable, some malfunction in the machine is indicated Basically, vibration is oscillating motion of a particle or body about a fixed reference point. Such motion may be simple harmonic (sinusoidal) or complex (non-sinusoidal). It can also occur in various modes - such as bending or translational modes - and, since the vibration can occur in more than one mode simultaneously, its analysis can be difficult. Units of vibration The units of vibration depend on the vibrational parameter, as follows: a) Acceleration, measured in g or [m/s2] ; b) Velocity, measured in [m/s] ; c) Displacement, measured in [m]. The displacement is the simplest vibration signature.It can be represented mathematically by a sine function and therefore is called simple harmonic motion. Time to complete one cycle is as called time period, T. Frequency, representing the number of vibration cycles completed in unit time is equal to 1/T. When unit of time is second, the unit of frequency, f, is Hertz (Hz). The maximum displacement of the body from its mean position is termed as amplitude of vibration, and if it is X then the displacement can be expressed as X = X sin ωt ω = 2πf Where w is the angular velocity in radian / second. The mass vibrating about its mean position is also subjected to velocity and acceleration. When the body is at its extreme positions. It is at rest, i.e. its velocity as these positions is zero, but it is subjected to maximum acceleration. Their nature of variation is similar to that of displacement. Only difference is that velocity plot is advanced by π/2 and acceleration plot is advanced by π with respect to the displacement as shown below. X = X sin ω t The velocity of motion is : x = dx / dt x = ω X cos ωt = ωX sin (ωt + π/2) x = d / dt (dx / dt) x = -ω2X sin ωt = ω2 sin (ωt + π) The following relations relate amplitudes of velocity and acceleration to displacement amplitude: V = ωX and A = ω2X Velocity is a good parameter for mid frequency range. The division by ω to obtain displacement attenuates low frequency signals. The multiplication by ω to obtain acceleration emphasizes high frequency signals. Accelerometers : Accelerometers are seismic type transducers, which have to be attached to the vibrating object. Inside the accelerometer is a mass mounted on a spring and damper. These devices are used for the measurement of absolute vibration in those cases where a fixed reference for relative motion is not available as in the case of a moving vehicle. In many other situations measurement of absolute motion is easier and more desirable. The transducer is attached to the object whose motion is to be measured. Inside the transducer, is a mass m supported on a spring of stiffness k and a viscous damper, with damping coefficient c. The motion of the mass relative to the frame or case gives an indication of the motion of the object and is the output of the instrument. These device may be used to measure acceleration at frequencies ω < 0.3 < ωn. ωn is the natural frequency of the spring mass system of the accelerometer. In case the value of frequency ω of the object is high, ωn of the device should be high or a stiff spring should be used. Constructional Features of Accelerometer (Charge Output) Basically a seismic transducer consists of a mass supported on a spring with damper, with a relative motion transducer as shown in the figure. They crystal is fairly stiff and held in compression by a spring. Quartz is a natural piezoelectric material used in accelerometers. Lead zirconate titinate (PZT) ceramic is another common material used, after it has been polarized. These devices are very sensitive, light weight, small sized and can be used over a wide frequency range. Acoustic (Noise) monitoring The sound travels in the form of a longitudinal pressure waves . noise is defined as unwanted sound . It is sensed as unpleased sound . The speed of sound waves , c in air 20 0 C is 343 m/s. The wavelength, λ of sound waves is Λ = c T = c / f Where T is the time period and f is the frequency of sound wave The audible frequency range of sound is from 20 Hz to 20 kHz. 3.3.1 Sound Pressure The total instantaneous atmospheric pressure at a point, minus the static (average) pressure at that point. p is the symbol used for sound pressure. If the sound pressure is given in logarithmic or relative units, it is called sound pressure level. 3.3.1.1 Sound Pressure Measurement Sound pressure measurement in decibels is defined as: Lp = 10 Log (P / Po) 2 dB Where P is sound pressure measured and Po is the reference sound pressure measured of 20 micropascals. Pascal is N/m2. Reference value of 20 µPa is chosen as it is the quantity that represents the threshold of hearing of an average person. There should of pain occur at 100 Pa. The logarithmic scale of noise measurements is used to accommodate this large ratio. The sound pressure is a scalar quantity. In a free field condition (i.e. where there are no reflecting surfaces present) inverse square law applies according to which the sound pressure level decreases by 6 dB for each doubling of distance (i. e. if the SPL at 1 meter distance is 90 dB then at 2 meters it will be 84 dB) 1.2 Instrumentation and Measurements. The transducer for noise measurements is called a microphone. Two types of microphones are commonly used for noise measurements – condenser and electret type. Condenser microphones are of high performance and expensive. In the condenser microphone , its diaphragm is set in motion by sound pressure. The movement of the diaphragm changes the capacitance between the diaphragm and a flat electrode plate. The change in capacitance is used to develop and electrical signal when a polarization voltage is applied to the capacitor. A constant charge is maintained on the capacitance, so that the voltage varies with capacitance. Electrets microphones are self polarizing condenser microphones. They have two plastic films, one for the diaphragm and one for supplying a bonded charge. The plastic film containing electric charge is called an electret and is bonded to a metallic back plate. Electret microphones do not need a bias voltage. A sound level meter basically comprises a microphones, an amplifier with adjustable amplification, a rectifier and a meter to display the measured level. The noise signal can also be recorded on an instruments tape/ cassette recorder using a microphones and its preamplifier for analysis. The background noise level should ideally be at lest 10 dB lower than the noise level of the source to be measured. Measurements should be made at points where there are minimum reflections present and minimum interference from other sources. 4. GEARBOX VIBRATION AND NOISE: CAUSES AND ANALYSIS METHOD 4.1 INTRODUCTION As discussed in previous chapter the vibration and noise of machinery can be measured by selecting proper transducer, check points and mounting method. The time and frequency domain data is used to monitor the condition of machine and hence to diagnosis the faults of machinery. In case of gear box, vibration and noise is generated at meshing of the gear and transmits through the shaft and bearing to other parts of the gear box. This vibration and noise in a gear box may result into sever failure of machines. Therefore, it is necessary to be aware of causes of this vibration and noise. Vibration and noise signals from gear box are measured and the information from these signals is extracted by signal analysis. In gear box vibrational and acoustical diagnosis, it is extensively for assessing the condition and hence the causes of this vibration and noise. Signal analysis can be done in time domain or frequency domain. This chapter deals with various causes of gear box vibration and noise such as, defect in gear, shaft and bearing, type of housing etc. but more emphasis on defects related with gear and discusses various signal analysis techniques used for diagnostic of gear box. 4.2 CAUSES OF GEARBOX VIBRATION AND NOISE To generate vibration and noise from gears the primary cause must be a force variation (in the components), which is then transmitted to the surrounding structure. It is only when vibration excites external panels that airborne noise is produced. 4.2.1 Transmission Error Transmission error is the error between teeth. Transmission error (TE) is defined as the deviation of the relative angular position of two gear shafts from the position determined by the gear rotation and perfect conjugate mesh action. TE is a consequence of a torsional vibration of the gear system and it is a function of tooth profile errors, tooth meshing errors, tooth spacing errors, undercut, backlash, tooth surface roughness, misalignment of gear tooth and an elastic deformation of gear tooth. TE, also denoted as static error, is very much related to vibration and noise of gears. Common gear problems are usually easy to identify because the noise and vibration usually occurs at a frequency equal to gear meshing frequency, i.e. the no of gear teeth times the rpm of faulty gear, but in complex gear drives several meshing frequencies are possible. Common gear problems which results in noise and vibration at gear meshing frequency includes excessive gear wear, improper adjustment of backlash or excessive gear clearance, gear tooth inaccuracy, faulty lubrication, fatigue crack on gear tooth or broken tooth of gear. 4.2.1.1 Uniform Wear There is sliding action between the contacting teeth on either side of pitch circle, but no sliding takes place at the pitch circle itself. Therefore the uniform wear tends to distort the harmonic nature of tooth mesh cycle and results into higher amplitudes of tooth mesh frequency and its harmonics. This effect does not become apparent until it becomes larger than the effect due to tooth deflection. When monitoring the teeth wear using the comparison of frequency spectrum of gear noise signals, it is essential to introduce at least three harmonics of highest tooth mesh frequency in order to detect wear at earliest possible stage. 4.2.1.2 Backlash Excessive gear clearance or improper adjustment of backlash may result into frequency modulation and will give rise to excessive noise at gear mesh frequency. So far it has been assumed that the rotational speed of gear is constant, and tooth spacing perfectly uniform, but if either of the condition is violated, frequency modulation of the tooth meshing frequency may occur. If the gear clearances are within tolerances and gears are properly lubricated, the transfer of load from one tooth to next will be in the form of tooth impact and result will be increasing noise. If gear tooth clearances increases more, the initial tooth may cause the gear tooth to bounce in the clearances available, resulting in sound or vibrating frequency at harmonics of gear mesh frequency. This is 1x, 3x …or perhaps even higher multiples of gear mesh frequency. 4.2.1.3 Eccentricity Eccentricity occurs when shaft centerline does not coincide with the gear geometric centerline. It is common source of unbalance, resulting in more weight on the gear geometric centerline. It is common source of unbalance, resulting in more weight on one side of rotating centerline than on the other side. Eccentric gear can produce reaction forces because of cam like action against the meshing gear. Eccentricity of one gear or misalignment may give rise to amplitude modulation by frequency corresponding to its rotational frequency. Since the gear noise results from excessive misalignment, the gear frequency noise or vibration is actually modulated by the noise and vibration at rotation speed frequency, producing side band frequencies at gear mesh frequency plus or minus gear rpm. The predominant noise due to misalignment is 2x shaft rpm, additional side band frequency plus or minus 2 x rpm may also be present. 4.2.1.4 Cracked Tooth As the gear rotates, the space left by the chipped tooth increases the mechanical clearance between the pinion and bull gear. The result is low amplitude sideband to the left of actual gear mesh frequency. When the next (i.e. undamaged) teeth mesh, the additional clearance results in higher amplitude as a result; the paired sidebands have nonsymmetrical amplitude, which is due to the disproportional clearance and impact. 4.2.1.5 Broken Tooth Broken tooth results mechanical clearance between the teeth. While shifting load from one tooth to another, impact is going to occur, this results in increase the noise of gear box. 4.2.1.6 Improper Lubrication Proper lubrication is essential for gear box because majority of the problems arise due to lack of lubrication. Due to lubrication problem of spalling is developed on the tooth flank, leading to rough gear mesh and rapid deterioration occurs in spectrum near meshing frequency. There will be increase in the amplitude of fundamental frequency and its harmonics due to improper lubrication. 4.2.2 Gearbox Internal Responses When the internal responses of gearbox are considered, the input is relative vibration between gear teeth and the outputs (as far as noise is concerned) are the vibration forces transmitted the bearings to gear case. In general the output force through the bearing should have six components: three forces and three moments and it is usually neglected. But it gives axial forces which result in end panel vibration of gearbox and causes the noise. Internal responses such as 1. Gear Defects 2. Bent shaft 3. Misalignment 4. Effect of bearing characteristics 5. Type of housing As stated above, in addition to actual gear problems, acoustic characteristics of gear box may also be affected as a result of other disturbing forces in the machine, such as misalignment or bent shaft. Misalignment of a gear case with a driver or driven equipment, initial misalignment of gear box bearings can also cause gear noise and vibration. Type of housing or gear case also affects the acoustical characteristics of gears. Response of gear case including gears, shaft, bearing etc. coincides with their operating frequency. Still, the problems related with these gears are more dominating among the causes of gearbox noise, so it discussed in detail in later section. Noise problems in gearing are concerned less with the strength of gear than their smoothness of drive, since it is a speed variation and consequent forced vibration that generates trouble as well as noise. The corresponding research and development shows that the main source of gear noise and vibration is transmission error 4.2.3 Gearbox External Responses The external responses are gear case or structure. In certain situation vibration transmits through gear case or main structure and that becomes predominant source of noise. 4.3 TRANSMISSION PATH OF NOISE The vibration transmission path starts from the combination of manufacturing errors, design errors, tooth and gear deflection to generate T.E. The T.E. is then source of the vibration and it drives the internal dynamics of the gear to give vibration forces through the bearing support. In turn, this bearing force drives the external gear case vibration or via isolation mounts, drives the external structure which causes airborne noise. Thermal Distortion Pinion Distortion Wheel Distortion Gear case deflection Gear case accuracy Pinion Movement Wheel movement Pinion Tooth Deflection Wheel Tooth deflection Pinion Profile accuracy Wheel Profile Accuracy Pinion Pitch Accuracy Wheel Pitch Accuracy Pinion Helix Accuracy Wheel Helix Accuracy TRANSMISSION ERROR Gear Masses Support Stiffness Combined Damping Internal Dynamic Response BEARING FORCES Casing Masses Casing Stiffness Casing Damping GEAR CASE FOOT VIBRATIONS Anti Vibration Mounts TRANSMITTED STRUCTURE VIBRATION Sound Radiating Panel AIRBORNE NOISE Fig. 4.1 Vibration Excitation and Transmission Path 4.4 ANALYSIS METHODS In this chapter, is review is made of some current vibration and acoustic analysis techniques used for condition monitoring in geared transmission systems. The perceived advantages, disadvantages, and the role each of these techniques may play in the diagnosis of safety critical failure modes is discussed. A summary of the findings is then made to establish which techniques to pursue further, and to identify any deficiencies which need to be addressed. 4.4.A Time Domain Analysis. 4. 4. A .1 Waveform analysis. Prior the commercial availability of spectral analyzers, almost all vibration and acoustic analysis was performed in the time domain. By studying the time domain waveform using equipment such as oscilloscopes, oscillographs, or ‘vibrographs’, is was often possible to detect changes in the vibration or acoustic signature caused by faults. However, diagnosis of faults was a difficult task; relating a particular component required the manual calculation of the repetition frequency based on the time difference observed between facture points. 4. 4. A .2 Time domain signal metrics. Although detailed study of the time domain waveform is not generally used today, a number of simple signal metrics based on the time domain waveform still have widespread application in mechanical fault detection; the simplest of these being the peak and RMS value of the signal which are used for overall vibration level measurements. 4. 4. A . 2. a) Peak. The peak level of the signal is defined simply as half the difference between the maximum and minimum vibration or acoustic levels. 4. 4. A . 2. b) RMS. The RMS (Root Mean Square) value of the signal is the normalized second statistical moment of the signal (standard deviation) Where T is the length of the time record used for the RMS calculation and is the mean value of the signal. For discrete (sampled) signals, the RMS of the signal is defined as; The RMS of the signal is commonly used to describe the ‘steady-state ‘or ‘continuous’ amplitude of a time varying signal. 4. 4. A . 2. c) Crest Factor. The crest factor is defined as the ratio of the peak value to the RMS of the signal. The crest factor is often used as a measure of the ‘spikiness’ or impulsive nature of a signal. It will increase in the presence of discrete impulses which are larger in amplitude than the background signal but which do not occur frequently enough to significantly increase the RMS level of the signal. 4. 4. A . 2. d) Kurtosis. Kurtosis is the normalized fourth statistical moment of the signal. For continuous time signals this is defined as. For discrete signal The kurtosis level of a signal is used in a similar fashion to the crest factor that is to provide a measure of the impulsive nature of the signal. Raising the signal to the fourth power effectively amplifies isolated packs in the signal. 4. 4. A .2. e) Overall vibration or noise level. The most basic vibration or noise monitoring technique is to measure the overall vibration or noise level over a broad band of frequencies. The measured vibration or noise level is trended against time as in indicator of deteriorating machine condition and / or compared against published vibration or noise criteria for exceedences.The measurements are typically peak or RMS velocity recordings which can be easily made using a velocity transducer (or integrating) and an RMS meter. Because the peak level is not a statistical value, it is often not a reliable indicator of damage; spurious data caused by statistically insignificant noise may have a significant effect on the peak level. Because of this, the RMS level is generally preferred to the peak level in machine condition monitoring applications. Trending of overall vibration or noise level may indicate deteriorating condition in a simple machine; however it provides no diagnostic information and will not detect faults until they cause a significant increase in the overall in the overall vibration or noise level. Localized faults in complex machinery may go undetected until significant secondary damage or catastrophic failure occurs. 4. 4.A .3. Waveshape metrics. The overall vibration or noise level provides no information on the wave form of the vibration or noise signal. With a member of fault, types, the shape of the signal is a better indicator of damage then the overall vibration or noise level. For example, faults which produce short term impulses such as bearing faults and localized tooth faults may no significantly alter the overall vibration or noise level but may cause a statistically significant change in the shape of the signal. Crest factor or kurtosis is often used as non – dimensional measures of the shape of the signal waveform. Both signal metrics increase in value as the ‘spikiness’ of the signal increases ( i. e., as the signal changes from a regular continuous pattern to one containing isolated peaks.) Kurtosis, being a purely statistical parameter, is usually preferable to crest factor in machines condition monitoring application for the same reasons that RMS is preferable to peak. However, crest factor is in more widespread use because meters which record crest factor are more common (and more affordable) than kurtosis meters. Because of the non – directional nature of the crest and kurtosis values, some assessment of the nature of a signal can be made without trend information. Both waveshape metrics will give a value of 0.0 for a DC signal and 1.0 for a square wave. For a pure sine wave, the crest factor will be and the kurtosis will be 1.5 for normally distributed random noise, the kurtosis will be 3.0 and the crest factor will be approximately 3 (note that because the crest factor is not a statistical measure, its value in the presence noise will vary). Trending of the waveshape metrics can also used to help identify decorating condition. However, the trend of the these values way be misleading in some cases, faults which produce a small number of isolated peaks (such as the initial stages of bearing damage) may cause a increase in the crest factor and kurtosis but, as the damage becomes more widely spread, a large number or impulses may occur causing both the crest factor and kurtosis to decrease again. Both the kurtosis and crest factor will decrease if the number of pulses increases (increasing the RMS value of the signal) without an increase in the individual pulse height. As with the overall vibration or noise level, the waveshape metrics will not detect faults unless the amplitude of the vibration or noise from the faulty component is large enough to cause a significant change in the total vibration or noise signal. This limits their use to components whose vibration or noise signature forms a significant portion of the measured overall vibration or noise. 4. 4. A .4. Frequency band analyses. Often, the fault detection capability using overall vibration or noise level and / or waveshape metrics can be significantly improve by dividing the vibration or noise signal into a number of frequency bands prior to analysis. This can be done with a simple analogue band – pass filter between the vibration sensor or noise sensor and the measurement device. The rationale behind the use of band – pass filtering is that, even through a fault may not cause a significant change in overall vibration signal (due to masking by higher energy, non – fault related vibrations), it may produce a significant change in change in a band of frequencies in which the non – fault related vibrations are sufficiently small. For a simple gearbox, with judicious selection of frequency bands are frequency band may be dominated by shaft vibrations, another by gear tooth – meshing vibrations and another by excited structural resonances, providing relatively good coverage of all gearbox components. 4. 4. A .5. Advantages. Meters for recording overall vibration or noise levels, crest factor and / or kurtosis are readily available, relatively cheap and simple to use. Because of this, they can be a very cost effective method of monitoring simple machine components which are relatively cheap and easily replaceable but perform a critical role (for example small pumps and generators.) The time domain signal metrics may detect the imminent failure of these components allowing replacement prior to total failure, although the damaged component may be beyond repair by this time, the component replacement cost is generally insignificant compared to the potential cost of catastrophic failure (secondary damage, loss of utility, etc.) 4. 4. A .6. Disadvantages. For more complex or costly machines, it is generally preferable to detect damage at an early stage to allow the machine to be repaired rather than replaced. This requires techniques which are more sensitive to changes in the vibrations of individual components and which can provide at least some diagnostic capabilities. 4. 4. A .7. Applicability to safety critical failure modes. Simple time domain signal metrics, even with the use of band pass filtering, do not provide any diagnostic information and, therefore, cannot be used to distinguish any of the safety critical failure modes from other failure modes. For very simple safety critical systems, overall vibration or noise level and / or kurtosis level (in combination with oil debris and / or temperature monitoring) may be useful as part of a cost effective failure detection system. 4. 4. B Spectral analysis Spectral (or frequency) analysis is a term used to describe the analysis of the frequency domain representation of a signal. Spectral analysis is the most commonly used vibration or noise analysis technique for condition monitoring in graced transmission systems and has proved a valuable tool for detection and basic diagnosis of faults in simple rotating machinery. Whereas the overall vibration or noise level is a measure of the vibration or noise product over a broad band of frequencies, the spectrum is measure of the vibrations or noise over a large number of discrete contiguous narrow frequency bands. The fundamental process common to all spectral analysis techniques is the conversion of a time domain representation of the vibration or noise signal into a frequency domain representation. This can be achieved by the use of narrow band filters, or more commonly in recent times, using the discrete fourier transform (DFT) of digitized data. The vibration level at each ‘frequency’ represents the vibration over a narrow frequency band centered at the designated ‘frequency’ with a bandwidth determined by the conversion process employed. For the machines operating at a known constant speed, the frequencies of the vibrations produced by the various machine components can be estimated. Therefore, a change in vibration level within a particular frequency band can usually be associated with a particular machine component. Analysis of the relative vibration levels at different frequency bands can often give an indication of the nature of a fault, providing some diagnostic capabilities. 4. 4. B . 1. Conversion to the frequency domain. The frequency domain representation of a signal can be described by the Fourier transform (67) of its time domain representation. The inverse process (Inverse Fourier Transform (67) can be used to convert from a frequency domain representation to the time domain. There are a number of limitations inherent in the process of converting vibration data from the time domain to the frequency domain. 4. 4. B . 2 Bandwidth – time limitation. All frequency analysis is subject to a bandwidth – time (often called the uncertainty principle due to the analogous concepts in quantum mechanics, enunciated by Werner Hirschberg in 1927) Frequency analysis made with bandwidth of B hertz for each measurement and duration in time of T seconds has bandwidth – time limitation of If an event lasts for T seconds, the best measurement bandwidth (The minimum resolvable frequency) which can be achieved is I/T hertz. If an analyzing filter with a bandwidth of B hertz is used, at least 1/B seconds will be required for a measurement. The measurement uncertainty due to the bandwidth – time limitation imposes a resolution restriction on the frequency conversion. To resolve frequencies separated by B hertz at cast 1/B seconds of data must be taken. 4. 4. B . 3 FFT Analyzers. Most modern spectrum analyzers use the Fast Fourier Transform (FFT) , which is an efficient algorithm for performing a Discrete Fourier Transform (DFT) of discrete sampled data. The Discrete Fourier Transform is defined as and the Inverse discrete Fourier Transform is The sampling process used to convert the continuous time signal into a discrete signal can cause some undesirable effects. 4. 4. B. 4. a ) Aliasing. Frequencies which are greater than half the sampling rate will be aliased to lower frequencies due to the stroboscope effect. To avoid aliasing, analogue low – pass ‘ant aliasing’ filter is used prior to sampling to ensure that there are no frequencies above half the sampling rate. 4. 4. B . 4. b) Leakage. When applying the FFT, it is assured that the sampled data is periodic with the time record. If this is not case, spurious results can arise from discontinuities between the start and end points of the time record. This ‘leakage’ is normally compensated for by applying a smooth window function which has zero values at the start and end of the tie record. This entails a resolution trade – off since it effectively reduces the time duration of the signal. For a simple machine, the time record can be synchronized with the rotation of the machine, ensuring that the major vibration components are periodic within the time record; this is difficult to achieve with complex machines due to the large number of non – harmonically frequencies. 4. 4. B . 4. c) Picket Fence Effect. The picket fence effect is a result of the discrete frequency nature of the FFT, Where a frequency does not lie on one of the discrete frequency lines, the amplitude will be reduced. If the frequency is well separated from other frequency components, a correction can be made by curve fitting to samples around the peak. Windowing reduces the effect due to the increase in bandwidth caused by the windowing process. 4. 4. B . 5 Speed variations. The ability to resolve frequency components is not only related to the bandwidth- time limitation but also to the stability of the vibration signal over the analysis period. For FFT analyzers, the resolution imposed by the bandwidth – time limitation is constant for all frequencies, however, the frequency of vibration signals due to the mechanically linked rotational speed of the machine, imposing a resolution limitation which is a constant percentage of the frequency. Even with ‘constant’ speed machines, some drift in operating speed over time likely to occur and, in some cases, may cause frequency variations (and uncertainty) which are greater than those due to the bandwidth – time limitations. For example, performing and FFT on one second of data would give a spectrum with a resolution of one hertz, however, a one percent speed variation over the analysis period would cause a 5 hertz uncertainty at a frequency of 500 hertz. 4. 4. B . 5. a) Synchronous sampling. The effects of speed variations can be overcome to a certain extent by the use of ‘synchronous sampling’ in which the sampling rate of the analyzer is linked to the speed of the machine. However, this adds further complication to the monitoring process as it requires a speed attached to the machine being monitored, a frequency multiplier to convert the speed signal into a ‘clock pulse’ signal suitable for driving the signal analyzer, and often needs on external anti – aliasing filter to avoid aliasing problems (although almost all modern FFT analyzers have in – built anti – aliasing filters, when they are driven from an ‘external clock ’ these are often bypassed or have inappropriate frequencies due to the unknown external clock frequency) 4. 4. B . 6 Fault Detection. 4. 4 . B . 6 a) Spectral comparison. The most common spectral analysis technique employed for machine condition monitoring is spectral comparison, where a baseline power (magnitude squared) spectrum is taken under well defined normal operating conditions with the machine in known good condition (preferably soon after commissioning) This ‘baseline’ spectrum is used as reference for subsequent power spectra taken at regular intervals throughout the machine life under similar operating conditions. The comparison is usually done on a logarithmic amplitude scale, with increase of 6-8 dB considered to be significant and changes greater than 20 dB from the baseline considered serious. 4. 4. B . 6 b) Spectral trending. In addition to spectral comparisons, various forms of spectral trending can be used to give some indication of the rate of fault progression. In its simplest form, spectral trending involves the trending of the changes in amplitude of all (or a number of selected) spectral lines over time. For complex, machines, this can often involve a large amount of data, resulting in information overload due to the large number of significant spectral lines. In an attempt to simplify the detection process, a number of parameters based on spectrum have been proposed with provide statistical measurements of spectral differences. 4. 4. B . 6 c) Spectral masks. Spectral masks are a method of spectral comparison sometimes employed to identify and evaluate changes in the signature spectrum, with allowances made for variation in operating condition. A spectral mask is derived from the baseline spectrum by adding an allowable tolerance limit to the logarithmic amplitude. To allow for variations in speed, the constant bandwidth spectrum is sometimes converted to a constant percentage bandwidth spectrum, with the percentage bandwidth being determined by the estimated speed differences which can occur between recordings Once a spectral mask is defined, comparison of individual recordings is made with reference to the mask to identify exceed ness. 4. 4. B . 7 Fault diagnosis. Even for relatively simple machines, the vibration spectrum can be quite complex due to the multiple harmonic structures of the vibration from various components in combination with the transmission path effects. This makes detailed diagnostic analysis of an individual spectrum very difficult. The diagnostic process is simplified when performed in conjunction with spectral comparison and/ or trending; typically, only the frequencies identified as having significant changes are analyzed in detail for diagnostic purposes. Distributed faults with cause significant change in the mean amplitude of the vibration at discrete frequencies, such as heavy wear and unbalance, should be relatively simple to diagnose using spectral analysis, as they would translate to changes in a few associated frequency lines in the spectrum. Faults which cause low frequency sinusoidal modulations, such as an eccentric or misaligned gear, may also be diagnosed as they will translate to increases in the sidebands surrounding the tooth meshing frequency and harmonies. Very localized faults, such as tooth cracking or spelling, are not easily diagnosed (and may not even be detected) as the short term impulsive vibrations produced translate to a large number of low amplitude lines in the spectrum 4. 4. B . 8 Advantages. A number of companies manufacture and / or supply high quality FFT analyzers at a reasonable price. In addition to marketing analysis, several of these companies also provide comprehensive after sales support in the form of literature and training in diagnostic methods using their equipment. Because of the fairly widespread use of spectral analysis over a number of years, there is a fairly comprehensive collection of literature on its use for machine fault diagnosis 4. 4. B .9 Disadvantages. The major disadvantage with spectral analysis lies in its complexity. Even with the amount of literature available, specialist skills are still required to exploit the diagnostic faults such as gear tooth faults, even expert analysis find diagnosis difficult. 4. 4. B .10 Applicability to safety critical failure modes. For relatively simple machines, and those where the first few harmonies of the shaft vibration frequencies can be identified (i. e. can be well separated from other vibration frequencies within the limits of bandwidth and / or speed variations), diagnosis of shaft related faults (fracture, unbalance, misalignment and bent shaft) should be quiets simple with spectral analysis, by trending of the amplitudes of the shaft related vibrations or use of spectral masks. 4.4. C. Wavelet Analysis Fourier Analysis Signal analysts already have at their disposal an impressive arsenal of tools. Perhaps the most well known of these is Fourier analysis, which breaks down a signal into constituent sinusoids of different frequencies. Another way to think of Fourier analysis is as a mathematical technique for transforming our view of the signal from time-based to frequency-based. For many signals, Fourier analysis is extremely useful because the signal’s frequency content is of great importance. So why do we need other techniques, like wavelet analysis? Fourier analysis has a serious drawback. In transforming to the frequency domain, time information is lost. When looking at a Fourier transform of a signal, it is impossible to tell when a particular event took place. If the signal properties do not change much over time — that is, if it is what is called a stationary signal — this drawback isn’t very important. However, most interesting signals contain numerous nonstationary or transitory characteristics: drift, trends, abrupt changes, and beginnings and ends of events. These characteristics are often the most important part of the signal, and Fourier analysis is not suited to detecting them. Short-Time Fourier Analysis: In an effort to correct this deficiency, Dennis Gabor (1946) adapted the Fourier transform to analyze only a small section of the signal at a time — a technique called windowing the signal. Gabor’s adaptation, called the Short-Time FourierTransform (STFT), maps a signal into a two-dimensional function of time and frequency. The STFT represents a sort of compromise between the time- and frequency-based views of a signal. It provides some information about both when and at what frequencies a signal event occurs. However, you can only obtain this information with limited precision, and that precision is determined by the size of the window. While the STFT compromise between time and frequency information can be useful, the drawback is that once you choose a particular size for the time window, that window is the same for all frequencies. Many signals require a more flexible approach — one where we can vary the window size to determine more accurately either time or frequency. 4.4. C.1 Fourier Transforms:- The Fourier transforms utility lies in its ability to analyze a signal in the time domain for its frequency content. The transform works by first translating a function in the time domain into a function in the frequency domain. The signal can then be .analyzed for its frequency content because the Fourier coefficients of the transformed function represent the contribution of each sine and cosine function at each frequency. An inverse Fourier transform does just what you'd expect; transform data from the frequency domain into the time domain. (5.1) a) Discrete Fourier Transform:- The discrete Fourier transform (DFT) estimates the Fourier transform of a function from a finite number of its sampled points. The sampled point’s arc supposed to be typical of what the signal looks like at all other times. The DFT has symmetry properties almost exactly the same as the continuous Fourier transform. In addition, the formula for the inverse discrete Fourier transform is easily calculated using the one for the discrete Fourier transform because the two formulas are almost identical. b) Windowed Fourier Transform:- If (t) is a non periodic signal, the summation of the periodic functions, sine and cosine, does not accurately represent the signal. You could artificially extend the signal to make it periodic but it would require additional continuity at the endpoints. The windowed Fourier transform (WFT) is one solution to the problem of better representing the non periodic signal. The WFT can be used to give information about signals simultaneously in the time domain and in the frequency domain. With the WFT, the input signal f (t) is chopped up into sections, and each section is analyzed for its frequency content separately. If the signal has sharp transitions, we window the input data so that the sections converge to zero at the endpoints. This windowing is accomplished via a weight function that places less emphasis near the interval's endpoints than in the middle. The effect of the window is to localize the signal in time. c) Fast Fourier Transform:- To approximate a function by samples, and to approximate the Fourier integral by the discrete Fourier transform, requires applying a matrix whose order is the number sample points n. Since multiplying an n X n matrix by a vector costs on the order of 2" arithmetic operations, the problem gets quickly worse as the number of sample points increases. However, if the samples are uniformly spaced, then the Fourier matrix can be factored into a product of just a few sparse matrices, and the resulting factors can be applied to a vector in a total of order nlogn arithmetic operations. This is the so-called fast Fourier transform or FFT. 4.4.C .2 Wavelet Analysis:- Wavelet analysis represents the next logical step: a windowing technique with variable-sized regions. Wavelet analysis allows the use of long time intervals where we want more precise low-frequency information, and shorter regions where we want high-frequency information. Here's what this looks like in contrast with the time-based, frequency-based, and STFT views of a signal: 4.4.C .2.a) Wavelet Definition:- A wavelet is a waveform of effectively limited duration that has an average value of zero. Figure (a) Morlet wavelet of arbitrary width and amplitude, with time along the X-axis. (b) Construction of the Morlet wavelet (blue dashed) as a Sine curve (green) modulated by a Gaussian (red), 4.4.C .2 b) Wavelet Properties:- 1 .The definition domain is compact support, which ensures that the function is fast decaying, and so time localization can be obtained. 2. The admissibility condition (5.2) Where This condition means that the waveform of the mother wavelet function must be oscillating i.e. the average value of the wavelet in the time domain must be zero. 4.4.C .2. c) Wavelet Transform:- The driving force behind wavelet transforms (WTs) is to overcome the disadvantages embedded in short time Fourier transform (STFT), which provides constant resolution for all frequencies since it uses the same window for the analysis of the inspected signal x (t). On the contrary, WTs use multi-resolution, that is, they use different window functions to analyze different frequency bands of the signal x (t). Different window functions y(s,b,t);which are also called son wavelets, can be generated by dilation or compression of a mother wavelet y(t) , at different time frame. A scale is the inverse of its corresponding frequency. WTs can be categorized as discrete WTs or continuous WTs. I ) Continuous Wavelet Transform:- In the continuous wavelet transform, a given signal of finite energy is projected on a continuous family of frequency bands.      (5.3) Where * denotes complex conjugation. This equation shows how a function f (t) is decomposed into a set of basis functions, called the wavelets. The variables s and, scale and translation, are the new dimensions after the wavelet transform. For completeness sake( 5.4)gives the inverse wavelets transform.      (5.4) The wavelets are generated from a single basic wavelet (t), the so-called mother wavelet, by scaling and translation:      (5.5) In (5.5) is the scale factor is the translation factor and the factor s-1/2 is for energy normalization across the different scales. II ) Discrete Wavelets:- Now that we know what the wavelet transform is, we would like to make it practical. However, the wavelet transform as described so far still has three properties that make it difficult to use directly in the form of. The first is the redundancy of the CWT. In the wavelet transform is calculated by continuously shifting a continuously scalable function over a signal and calculating the correlation between the two. It will be clear that these scaled functions will be nowhere near an orthogonal basis and the obtained wavelet coefficients will therefore be highly redundant. For most practical applications we would like to remove this redundancy. Even without the redundancy of the CWT we still have an infinite number of wavelets in the wavelet transform and we would like to see this number reduced to a more manageable count. This is the second problem we have. The third problem is that for most functions the wavelet transforms have no analytical solutions and they can be calculated only numerically or by an optical analog computer. Fast algorithms are needed to be able to exploit the power of the wavelet transform and it is in fact the existence of these fast algorithms that have put wavelet transforms where they are today. Let us start with the removal of redundancy. As mentioned before the CWT maps a one-dimensional signal to a two-dimensional time-scale joint representation that is highly redundant. The time-bandwidth product of the CWT is the square of that of the signal and for most applications, which seek a signal description with as few components as possible, this is not efficient. To overcome this problem discrete wavelets have been introduced. Discrete wavelets are not continuously scalable and translatable but can only be scaled and translated in discrete steps. This is achieved by modifying the wavelet representation (3.5) to crate.      (5.6) Although it is called a discrete wavelet, it normally is a (piecewise) continuous function. In (5.6) j and k are integers and s0 > 1 is a fixed dilation step. The translation factor 0 depends on the dilation step. The effect of discretizing the wavelet is that the time-scale space is now sampled at discrete intervals. We usually choose s0 = 2 so that the sampling of the frequency axis corresponds to dyadic sampling. This is a very natural choice for computers, the human ear and music for instance. For the translation factor we usually choose 0 = 1 so that we also have dyadic sampling of the time axis. 4.4.C .3. Wavelet Analysis : Now that we know some situations when wavelet analysis is useful, it is worthwhile asking “What is wavelet analysis?” and even more fundamentally, “What is a wavelet?” A wavelet is a waveform of effectively limited duration that has an average value of zero. Compare wavelets with sine waves, which are the basis of Fourier analysis. Sinusoids do not have limited duration — they extend from minus to plus infinity. And where sinusoids are smooth and predictable, wavelets tend to be irregular and asymmetric. Fourier analysis consists of breaking up a signal into sine waves of various frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (or mother) wavelet. Just looking at pictures of wavelets and sine waves, you can see intuitively that signals with sharp changes might be better analyzed with an irregular wavelet than with a smooth sinusoid, just as some foods are better handled with a fork than a spoon. It also makes sense that local features can be described better with wavelets that have local extent. A) Number of Dimensions Thus far, we’ve discussed only one-dimensional data, which encompasses most ordinary signals. However, wavelet analysis can be applied to two-dimensional data (images) and, in principle, to higher dimensional data. This toolbox uses only one- and two-dimensional analysis techniques. B) The Continuous Wavelet Transform Mathematically, the process of Fourier analysis is represented by the Fourier transform: which is the sum over all time of the signal f(t) multiplied by a complex exponential. (Recall that a complex exponential can be broken down into real and imaginary sinusoidal components.) The results of the transform are the Fourier coefficients , which when multiplied by a sinusoid of frequency yield the constituent sinusoidal components of the original signal. Graphically, the process looks like Similarly, the continuous wavelet transform (CWT) is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function : The results of the CWT are many wavelet coefficients C, which are a function of scale and position. Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the constituent wavelets of the original signal: C) Scaling We’ve already alluded to the fact that wavelet analysis produces a time-scale view of a signal, and now we’re talking about scaling and shifting wavelets. What exactly do we mean by scale in this context? Scaling a wavelet simply means stretching (or compressing) it. To go beyond colloquial descriptions such as “stretching,” we introduce the scale factor, often denoted by the letter If we’re talking about sinusoids, for example, the effect of the scale factor is very easy to see: The scale factor works exactly the same with wavelets. The smaller the scale factor, the more “compressed” the wavelet. It is clear from the diagrams that, for a sinusoid , the scale factor is related (inversely) to the radian frequency . Similarly, with wavelet analysis, the scale is related to the frequency of the signal. We’ll return to this topic later. ùt ( ) sin a ù D) Shifting Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically, delaying a function by k is represented by: f t ( ) f t k – ( ) E) Scale and Frequency Notice that the scales in the coefficients plot (shown as y-axis labels) run from 1 to 31. Recall that the higher scales correspond to the most “stretched” wavelets. The more stretched the wavelet, the longer the portion of the signal with which it is being compared, and thus the coarser the signal features being measured by the wavelet coefficients. Thus, there is a correspondence between wavelet scales and frequency as revealed by wavelet analysis: • Low scale a . Compressed wavelet . Rapidly changing details . High frequency • High scale a . Stretched wavelet . Slowly changing, coarse features . Low frequency F) The Scale of Nature It’s important to understand that the fact that wavelet analysis does not produce a time-frequency view of a signal is not a weakness, but strength of the technique. Not only is time-scale a different way to view data, it is a very natural way to view data deriving from a great number of natural phenomena. G) Frequency – Scale relation As explained above scale is inversely related the frequency. Though there is no exact mathematical relation for this , With approximation it can be stated as Fa = ∆ x Fc / S Fa = pseudo frequency ( For the scale value S ) ∆ = Sampling Frequency S = Scale Fc = Central frequency of mother wavelet in Hz. Central frequency of the mother wavelet used in this project is 0.8125 Hz. 4. 4. C . 4 Applications :- Generally, the DWT is used for source coding whereas the CWT is used for signal analysis. Consequently, the DWT is commonly used in engineering and computer science and the CWT is most often used in scientific research. Wavelet transforms are now being adopted for a vast number of different applications, often replacing the conventional Fourier transform. Many areas of physics have seen this paradigm shift, including molecular dynamics, ab initio calculations, astrophysics, density-matrix localisation, seismic geophysics, optics, turbulence and quantum mechanics. Other areas seeing this change have been image processing, blood-pressure, heart-rate and ECG analyses, DNA analysis, protein analysis, climatology, general signal processing, speech recognition, computer graphics and multifractal analysis. In computer vision and image processing, the notion of scale-space representation and Gaussian derivative operators is regarded as a canonical multi-scale representation. 4.4. D COMARISION BETWEEN FT AND WT a) Similarities between Fourier and Wavelet Transforms:- The fast Fourier transform (FFT) and the discrete wavelet transform (DWT) are both linear operations that generate a data structure that contains Iog2 n segments of various lengths, usually filling and transforming it into a different data vector of length 2 n. The mathematical properties of the matrices involved in the transforms are similar as well. The inverse transform matrix for both the FFT and the DWT is the transpose of the original. As a result, both transforms can be viewed as a rotation in function space to different domain. For the FFT, this new domain contains basis functions that are sines and cosines. For the wavelet transform, this new domain contains more complicated basis functions called wavelets, mother wavelets, or analyzing wavelets. Both transforms have another similarity. The basis functions are localized in frequency, making mathematical tools such as power spectra (how much power is contained in a frequency interval) and scalograms useful at picking out frequencies and calculating power distributions. b) Dissimilarities between Fourier and Wavelet Transforms:- The most interesting dissimilarity between these two kinds of transforms is that individual wavelet functions are localized in space. Fourier sine and cosine functions are not. This localization feature, along with wavelets' localization of frequency, makes many functions and operators using wavelets "sparse" when transformed into the wavelet domain. One way to see the time-frequency resolution differences between the Fourier transform and the wavelet transform is to look at the basis function coverage of the time-frequency plane. Figure 6.1 shows a windowed Fourier transform, where the window is simply a square wave. The square wave window truncates the sine or cosine function to fit a window of a particular width. Because a single window is used for all frequencies in the WFT, the resolution of the analysis is the same at all locations in the time-frequency plane. Figure (6.1): Fourier basis functions, time-frequency tiles, and coverage of the time-frequency plane. An advantage of wavelet transforms is that the windows vary. In order to isolate signal discontinuities, one would like to have some very short basis functions. At the same time, a in order to obtain detailed frequency analysis, one would like to have some very long basis functions. A way to achieve this is to have short high-frequency basis functions and long low-frequency ones. This happy medium is exactly what one gets with wavelet transforms. Figure 4.2 shows the coverage in the time-frequency plane with one wavelet function, the Daubechies wavelet. Figure (6.2): Daubechies wavelet basis functions, time-frequency tiles, and coverage of the time-frequency plane. One thing to remember is that wavelet transforms do not have a single set of basis functions like the Fourier transform, which utilizes just the sine and cosine functions. Instead, wavelet transforms have an infinite set of possible basis functions. Thus wavelet analysis provides immediate access to information that can be obscured by other time-frequency methods such as Fourier analysis. 5. TEST CRITERIA AND SPECIFICATION 5.1 INTRODUCTION In previous chapter different measurement and analysis techniques has been discussed. As per the objective of dissertation work to measure the vibration and sound pressure of a gearbox for condition monitoring the following experimental setup will be prepared as shown in fig. no. 5.1 and Plate No.1. Extensive experimentation will be done in laboratory for measurement of vibration and sound pressure level. Keeping in view the financial constraints a commercially available geared motor is chosen for experimentation eliminating the need of a separate costlier gearbox. For giving the rated load on geared motor, a rope-brake dynamometer is used, where by varying load the power can also be varied and it is easy to achieve the same condition for taking readings for different gears. It is decided to make deliberate faults, such as wear, crack on one tooth of gear, and one tooth broken or missed on spur gear and lack or no lubrication of the gearbox. The analysis of vibration and acoustic signals of each fault is carried out separately. For that purpose, gears of same specifications is procured. And on each gear separate faults are made. The vibration and acoustic signals of each faulty gear and gear without any fault is obtained. Thus the signals obtained is analyzed which are valuable for fault diagnosis. 5.2 EXPERIMENTAL SETUP The schematic diagram of vibration and acoustic measurement for fault diagnosis of gearbox shown in Fig. 5.1. The geared motor is rigidly mounted on concrete foundation to isolate vibration and acoustics from foundation. Accelerometer and Microphone Fig. 5.1 Schematic Set Up For vibration and Sound pressure Measurement Plate No.1: Schematic Setup for Vibration and Sound pressure Measurement 5.3. SPECFICATIONS OF THE INSRUMENTS The equipments, which are used for carrying out the experimental procedure with their specifications, are explained below; 5.3.1 Geared Motor: Gearbox is the main part used for the experimentation. Here the geared motor of following specification is selected. The specification of the motor: Make: Shri Shakti Make No: SGO/63/4/B3 Motor type Squirrel cage induction motor Phase 3 Phase Power 0.18 kW/ 0.25 Hp. Operating Voltage 400/440 volts No. of cycles 50 Supply AC supply Insulation B class Type of mounting Horizontal foot mounted 2) The specifications of gearbox: Power 0.25 Hp Input rpm 1420 rpm Input frequency 1420/60 = 23.67 Hz Output rpm 200 rpm Output frequency 200/60 = 3.33 Hz No. of stapes 2 stage Types of gears: First pinion Type Spur No. of teeth 12 Pitch circle diameter 18 mm Module 1.5 Speed 1420 rpm Rotational frequency Hz (rpm/60) Hz Tooth meshing frequency= 284 Hz (rpm x no. of teethes/60) Hz First gear: Type Spur No. of teeth 48 Pitch circle diameter 72 mm Module 1.5 Speed 355 rpm Rotational frequency Hz Tooth meshing frequency = 284 Hz (rpm x no. of teeth /60) Second pinion: Type Helical No. of teeth 19 Pitch circle diameter 32.37 mm Module 1.7 Speed 355 rpm Rotational frequency 355/60 = 5.19 Hz Tooth meshing frequency = 112.42 Hz ( rpm x no. of teeth/60) Second gear: Type Helical No. of teeth 34 Pitch circle diameter 57.8 mm Module 1.7 Speed 200 rpm Rotational frequency 200/60 = 3.33 Hz 5.3.2. Digital Frequency Analyzer (FFT) For the experimental work the digital analyzer will used (Make- Larson-Davis, model is 2900B) . Facility of selecting various parameters such as scale ( linear or logarithmic ), windows ,base band ,filters and zoom analysis is available with this model .The specifications of FFT as bellows, Make and model Larson - Davis 2900B Physical Characteristics- Size -28 cm (width) x 19.7 cm (height) x 6.1 cm (thick) Weight- 3.4 Kg Input Characteristics- Measuring range-10-200 dB Impedance-10 G Polarization Voltage-0, 28, 200 VDC Gain-30 to 90 dB in 10 dB steps Analog Input filters -High pass 1 Hz, 20Hz -Low pass 10 kHz, 20 kHz. Digital Characterization- Digitization-16-bit A: D per channel Dynamic Range->80 dB Amplitude stability-  0.1 dB Fast Fourier Transform- Lines – 100,200.400,800 line FFT analyser Limit-Upper frequency limit: 20 kHz Power- Battery-Ni-Cd (Nickel- Metal Hydride) DC Power-1.5 A @ 11 V and 0.5 a 216 V Display Characterstics- Internal LCD – Backlighting : Electroluminesent -Resolution : 128 x 489 , with full Graphics External Display- 1,2 or 4 Display Environmental- Operating Temperature- -10C to 50 C 5.3.3. Acoustic Pickup (Sound Pressure Probe) Condensor microphone is used for measuring sound pressure. 5.3.4 Vibration Pickup As the acceleration signals gives good results for wide frequency range, the piezoelectric accelerometer was chosen for this work. The specification is given as follows. Make- Dytron Sensitivity- 10mV/g 5.4 CREATION OF FAULTS ON GEAR TOOTH For creation of artificial faults on gear tooth, four different gears are procured. For that, the spur gear having 48 teeth and module of 1.5 is selected. The common faults of gear tooth are as follows. 1. Wear on one tooth 2. Crack on one tooth 3. One tooth broken or missed 4. Lack of lubrication 1. Wear: - Wear on one tooth of gear is made by filing one tooth and removing material from tooth in direction of rotation. The wear is made near the pitch circle. 2. Crack on one Tooth: - A crack is produced on tooth of gear. This is made by cutting the tooth with hacksaw blade at root of tooth in the direction of rotation. 3. Broken Tooth: - For making this fault, one tooth of gear is removed by hacksaw blade and original non-defective gear is replaced with this gear. 4. Inadequate Lubrication or No Lubrication: - Many times unsatisfactory operation of gearbox may be caused by failure of lubrication. To enable one to identify this condition an experiment is carried out by completely darning lubrication oil from the gearbox. The gearbox will run for 15 minutes so that exact condition of no lubrication will achieved. 5.5 EXPERIMENTAL PROCEDURE In experimental procedure the gearbox is run at its rated power and speeds by applying different load condition of 0 kg, 2.5 kg, 5 kg, 7.5 kg on rope break dynamometer having diameter of pulley 71.38 mm Plate No.2: Actual Measurement The positioning of sound pressure level probe was done properly on the top of the gear under consideration for measuring sound pressure For vibration measurement accelerometer is kept on the top of gearbox. By making all above arrangements, readings are taken for non-defective gear and good lubrication condition. This data will be stored in FFT for further analysis. Vibration and noise spectrums are taken for gears having various faults and the data is stored in the memory of notebook PC for further analysis. For different condition of faults and different load conditions data was collected. 6. RESULT ANALYSIS AND CONCLUSION 6.1 INTRODUCTION As discussed in previous chapter, the various faults were created deliberately on spur gear of gearbox and acoustic pressure and vibration signatures were obtained. In this present chapter these signatures are compared with good gear signatures and an attempt is made to correlate them with their faults. The aim was to check the features of acoustic spectrum and vibration spectrum for different faults of gear tooth to condition monitoring and hence fault diagnose of gearbox. 6.2 VIBRATION SPECTRAL ANALYSIS Various vibration spectrums are taken for healthy and various defective gears and are discussed below. 6.2.1 Spectrum of Healthy Gear Fig. 6.1 shows the vibration spectrum of healthy (non-defective) gear. It shows that there is remarkable vibration level at gear mesh frequency, which is may be due to the inherent unbalance in gear and manufacturing defects. It is, therefore obvious that, there will be some vibration level at gear mesh frequency due to created faults. Fig. 6.1 Fig. 6.2, 6.3 , 6.4, 6.5 respectively shows comparison of cracked tooth and healthy gear spectrums, Broken tooth and healthy gear ,wear of teeth and healthy gear , Improper lubrication and healthy respectively. As the crack was produced on the gear, it reflects the change in vibration spectrum. From above results following characteristics can be associated to fault. The amplitude level increases considerably at gear mesh frequency. The amplitude level increases by considerable margin at side bands. 6.2.2 Crack on One Tooth Fig. 6.2 6.2.3 Gear with Broken Tooth Fig. 6.3 6.2.4 Wear of Teeth Fig.6.4 6.2.5 Improper Lubrication Condition Fig. 6.5 Fig 6.6 Fig. 6.6 shows comparison of vibration signatures of all faults, stated above with each other. From this figure, it is also seen that the amplitude change of mesh frequency occurs during tooth wear. In terms of crack on tooth the amplitude at gear mesh frequency increases considerably. While improper lubrication results in only spikes at meshing frequency and its harmonics. For worn-out teeth the amplitude level increases significantly. 6.3 ACOUSTIC SPECTRAL ANALYSIS Various acoustic spectrums are taken for healthy and various defective gears and are discussed below 6.3.1 Spectrum of Healthy Gear Fig. 6.7 shows the acoustic spectrum of healthy (non-defective) gear. It shows that there is remarkable sound pressure level at gear mesh frequency, which is may be due to the inherent unbalance in gear and manufacturing defects. It is, therefore obvious that, there will be some sound pressure level at gear mesh frequency due to created faults. Fig. 6.7 Fig. 6.8, 6.9, 6.10, 6.11 Shows comparison of cracked tooth and healthy gear spectrums, Broken tooth and healthy gear ,wear of teeth and healthy gear , Improper lubrication and healthy respectively. As the fault was produced on the gear, it reflects the change in acoustic spectrum. It is observed from figure the amplitude of gear mesh frequency has increased considerably. From above results following characteristics can be associated to fault. The amplitude level increases considerably at gear mesh frequency. The amplitude level increases by small margin at side bands. 6.3.2 Gear with crack on tooth Fig. 6.8 6.3.3 Gear with Broken Tooth Fig 6.9 6.3.4 Wear of Teeth Fig 6.10 6.3.5 Improper Lubrication Condition Fig. 6.11 Fig. 6.12 Fig. 6.12 shows comparison of acoustic signatures of all faults, stated above with each other. From this figure, it is also seen that the amplitude change of mesh frequency occurs during tooth wear. In terms of crack on tooth the amplitude at gear mesh frequency increases considerably. While improper lubrication results in only spikes at meshing frequency and its harmonics. For worn-out teeth the amplitude level increases significantly. While diagnosing gearbox, gear mesh faults prove the importance of spectrum comparison. By monitoring changes over the time that the seriousness of developing problem can be estimated. To analyze either gearbox the essential factor is not the either acoustic or vibration level, but the changes between surveys and the changed frequencies. By analyzing the acoustic or vibration spectrum, a developing fault can be detected even through the overall acoustic or vibration level may not change significantly. A reference spectrum was taken when the gearbox is known to be in good condition and all subsequent spectrums were compared with this spectrum 6.4 EFFECT OF LOAD ON CRACK ON ONE TOOTH Various vibration and acoustic spectrums are taken for healthy gear at various loads and are discussed below. Fig. 6.13, 6.14, 6.15, 6.16 respectively shows comparison of cracked tooth at no load and at 2.5 kg load, at 5 kg load and at 7.5 kg load. As the load was given on the gear, it reflects the change in vibration spectrum. From above results following characteristics can be associated to varying load. The amplitude level increases considerably at gear mesh frequency. The amplitude level increases by considerable margin at side bands Vibration Spectrum of crack on teeth at various loads Fig. 6.13 Fig. 6.14 Fig 6.15 Fig 6.16 Fig 6.17 Acoustic Spectrum of crack on teeth at various loads Fig 6.18 Fig 6.19 Fig. 6.20 Fig 6.21 Fig 6.22 6.5 EFFECT OF LOAD ON BROKEN TOOTH Various vibration and acoustic spectrums are taken for healthy gear at various load and are discussed below. Fig. 6.8, 6.9, 6.10, 6.11 respectively shows comparison of broken tooth at no load and at 2.5 kg load, at 5 kg load and at 7.5 kg load. As the load was given on the gear, it reflects the change in vibration and acoustic spectrum. From above results following characteristics can be associated to varying load. The amplitude level increases considerably at gear mesh frequency. The amplitude level increases by considerable margin at side bands Vibration Spectrum of crack on teeth at various loads Fig. 6.23 Fig. 6.24 Fig. 6.25 Fig. 6.26 Fig. 6.27 Acoustic Spectrum of crack on teeth at various loads Fig. 6.28 Fig. 6.29 Fig. 6.30 Fig. 6.31 Fig. 6.32 6.6 TIME DOMAIN ANLYSIS OF VIBRATION SIGNAL 6.7 TIME DOMAIN ANALYSIS OF ACOUSTIC ( NOISE) SIGNAL 6.8 EFFECT OF LOAD ON CRACKED TOOTH VIBRATION SIGNAL ACOUSTIC SIGNAL 6.9 EFFECT OF LOAD ON BROKEN TOOTH VIBRATION SIGNAL ACOUSTIC SIGNAL 6.10 OBESERVATION TABLE :- RMS VALUES HEALTHY CRACK ON TOOTH BROKEN TOOTH WEAR OF TEETH IMPROPER LUBRICATION VIBRATION 0.9331 1.0233 1.3712 1.5736 1.7933 ACOUSTIC 13404.7 14624.2 15277.4 15401.5 16886.6 EFFECT OF LOAD ON CRACK ON TOOTH O KG 2.5 KG 5 KG 7.5 KG VIBRATION 1.0283 1.142 1.2204 1.4029 ACOUSTIC 14624.2 20681.7 24764.5 27457.3 EFFECT OF LOAD ON BROKEN TOOTH O KG 2.5 KG 5 KG 7.5 KG VIBRATION 1.3712 1.5919 1.7083 1.9892 ACOUSTIC 15277.4 23510.3 23983.2 25826.2 It is observed from observation table that RMS value was increased as fault was produced in the gear. It is also observed that as load increases, RMS value also increases 6.11 WAVELET TRANSFORM OF VIBRATION SIGNAL It is observed that increases in the fault conditions do not only cause low-frequency components in the wavelet representation, but also the meshing frequency changes and gradually becomes discontinuous CONCLUSION The condition monitoring of gears can significantly reduce the costs of maintenance. Firstly it can allow the early detection of major faults, which could be extremely expensive to repair. Secondly it allows the implementation of condition based maintenance rather than periodic or failure based maintenance. In these cases delaying scheduled maintenance can make significant savings until convenient or necessary. In this research, vibration and acoustic signals were used in a two-stage gearbox. It was shown that various types of gear failures can be detected successfully by both acoustic and vibration signals analysis. The acoustic analysis method has gained wide industrial acceptance for gearbox condition monitoring. Condition monitoring using acoustics tool is presented in this dissertation, shows the considerable freedom in positioning of the microphones - distance and plane with respect to the source, and being able to detect the characteristic frequency spectrum of the gearbox and consequently fault detection and diagnosis using advanced signal processing. In this dissertation work, experimentation is carried out to detect gear tooth defects through acoustic and vibration analysis and feasibility of practical application is investigated. The acoustic and vibration spectrums obtained for different tooth defects are presented in previous chapter based on which following conclusions can be drawn. Using Frequency Domain Acoustic Spectrums and Vibration Spectrums With comparison of faulty crack on tooth and healthy gear spectrums, Broken tooth and healthy gear ,wear of teeth and healthy gear , Improper lubrication and healthy respectively it is shown that as the fault was produced on the gear, it reflects the change in acoustic and vibration spectrum. It is observed from the amplitude of gear mesh frequency has increased considerably. From above results following characteristics can be associated to fault. 1. The amplitude level increases considerably at gear mesh frequency. The amplitude level increases by small margin at side bands. It is also observed that as load is increased on the crack on tooth or broken tooth, there is change in acoustic and vibration spectrum. The amplitude level also increases at gear meshing frequency as load increases. Using Time Domain Acoustic Spectrums and Vibration Spectrums With comparison of time domain acoustic and vibration spectrum, it is observed that an RMS value was increased as fault was produced in the gear. It is also observed that as load increases, RMS value also increases. III Using Wavelet Transform of Vibration Signals It is observed that wavelet transform can be used for condition monitoring of gear. Wavelet transform possess fine time resolution in the high frequency ranges and excellent frequency resolution in low frequency region. This feature of wavelet transform uniquely fits the requirement in failure diagnosis Due to the varying size of window, the wavelet is computationally more efficient and less time consuming. This is because it carries out analysis with varying window sizes automatically, instead of repeating computation with different window sizes as happens in ordinary time–frequency techniques. Because of its good resolution capability and the varying window size feature, the wavelet had an ability to detect the tooth breakage and crack earlier than any other analysis method Further increases in the fault conditions do not only cause low-frequency components in the wavelet representation, but also the meshing frequency changes and gradually becomes discontinuous. Application of Condition monitoring & Wavelet analysis technique for detection of gear failures PAGE 1