Content uploaded by Sulo Lahdelma

Author content

All content in this area was uploaded by Sulo Lahdelma on Nov 24, 2015

Content may be subject to copyright.

A preview of the PDF is not available

Any attempt to detect different types of machine faults reliably at an early stage requires advanced signal processing methods. It is well known that vibration measurements provide a good basis for condition monitoring and fault detection. The complexity of signal processing techniques depends on the type of fault. In many cases root mean square and peak values are useful features for fault detection. Unbalance, misalignment, bent shaft, mechanical looseness and some electrical faults, for example, can be detected using features of displacement and velocity. Advanced filter settings and higher order derivatives provide additional possibilities if faults cause high frequency vibrations or impacts. This paper presents results from investigations about various faults, e.g. unbalance, misalignment, resonance, cage fault, absence of lubrication in a ball bearing and their combinations. To detect the faults, also higher order derivatives, lp norms and dimensionless measurement index MIT are utilised.

Figures - uploaded by Sulo Lahdelma

Author content

All figure content in this area was uploaded by Sulo Lahdelma

Content may be subject to copyright.

Content uploaded by Sulo Lahdelma

Author content

All content in this area was uploaded by Sulo Lahdelma on Nov 24, 2015

Content may be subject to copyright.

A preview of the PDF is not available

... The motor and the driven shaft are coupled by means of a claw clutch with a four-tooth elastic element (spider). More information on the test rig can be found in (7,8) , where the same test rig has been used. ...

... After that three fault states were measured, and finally all the faults occurred simultaneously. More information on the testing arrangement can be found in earlier studies by Lahdelma et al. (7) 3. Signal processing This paper mainly discusses the signal processing of acceleration signals by means of derivation, so that the order of derivative can be a complex number. The order of derivative of the vibration signal is very important in fault detection. ...

... Measurements were carried out widely on the test rig ( Figure 1) but signals from only one horizontal accelerometer of bearing 1 and only one rotational frequency (8 Hz) were investigated. Some of these signals have been studied earlier by authors et al. (4,7) . Signal processing, such as derivation and filtering, was performed in the frequency domain and an ideal filter was used for band pass filtering the signals to a frequency range from 5 Hz to 10 kHz. ...

There is a wide range of signal processing methods in the field of machine condition monitoring, which are used in feature extraction and fault diagnosis. Derivation and integration are very common and important operations in vibration signal processing. Often a signal that has been measured using an accelerometer is integrated to obtain velocity or displacement signal. These commonly used three signals and an infinite number of other signals can be obtained by means of fractional order derivation. Especially in challenging fault and process cases, signals whose order of derivation is a real or complex number could be clearly more sensitive to fault detection than the commonly used signals. This paper discusses the application of complex order derivation to acceleration signals in order to detect various faults at an early stage.

... The motor and the driven shaft are coupled by means of a claw clutch with a four-tooth elastic element (spider). More information on the test rig can be found in (Lahdelma et al., 2011;Lahdelma and Laurila, 2012), where the same test rig has been used. ...

... After that three fault states were measured, and finally all the faults occurred simultaneously. More information on the testing arrangement can be found in earlier studies by Lahdelma et al. (2011) 3. SIGNAL PROCESSING This paper mainly discusses the signal processing of acceleration and sound signals by means of differentiation or derivation, so that the order of derivative can be a complex number. The order of derivative of the vibration signal is very important in fault detection. ...

... Measurements were carried out widely on the test rig (Figure 1) but signals from only one horizontal accelerometer of bearing 1 and sound level meter with only one rotational frequency (8 Hz) were investigated. Some of these signals have been studied earlier by authors et al. (Lahdelma et al., 2011;Lahdelma, 2013, 2014a). Signal processing, such as differentiation and filtering, was performed in the frequency domain and an ideal filter was used for band pass filtering the signals to a frequency range from 5 Hz to 10 kHz. ...

The reliable condition monitoring of machines and the early detection of faults play an important role in condition-based maintenance. Information on the condition of machines is needed in different forms but finally it has to be in as simple form as possible so that it can be utilised in the decision-making by the maintenance and management personnel. In the field of machine condition monitoring, there is a wide range of signal processing methods, which are used in feature extraction and fault diagnosis. Differentiation and integration are very common and important operations in vibration signal processing. The order of derivative is typically an integer number but it can also be any fractional number. Especially in the challenging fault and process cases, signals whose order of derivative is a real or complex number could be clearly more sensitive in fault detection than the commonly used signals: displacement, velocity and acceleration. In this paper, the application of complex order differentiation of acceleration and sound signals was discussed. With the help of them, it is possible to find good and sensitive new types of methods and indicators for different fault detection situations.

... Excessive misalignment of a claw clutch does not cause any major increase in low-frequency vibrations, which can be detected reliably using displacement and velocity measurements. In this case it is better to use signals and features, which are sensitive to impact-like faults and high frequency vibrations (5) . Therefore, the acceleration signal and higher order derivatives were utilised in this study. ...

... The type of the coupling is ROTEX GS 14, manufactured by KTR. More information about the test rig can be found in (5) , where the same test rig has been used. ...

... Horizontal displacement was performed by means of two dial gauges. More information about the testing arrangement can be found in earlier studies by Lahdelma et al. (5) . ...

Coupling misalignment is a fairly common fault in rotating machines and causes excessive loads to bearings and other machine components. In general, misalignment and its severity can be detected reliably using vibration measurements. Misalignment is typically detected on the basis of the velocity spectrum. An increase in amplitude at rotational frequency and its harmonics are an indication of misalignment or a bent shaft. However, the behaviour of a claw clutch (jaw coupling) is very different as compared with a conventional elastic coupling. This paper presents the results of research where the detection of claw clutch misalignment is investigated based on acceleration signals. Real order derivatives and lp norms are calculated from the signals. In a test rig, which is used in this study, different degrees of misalignment are generated by moving a motor in the horizontal direction with steps of 0.1 mm. The tests were carried out at five rotational frequencies. Studies show that after a certain level of misalignment, the claw clutch gives rise to impacts that induce high frequency vibrations.

... The motor and the driven shaft are coupled by means of a claw clutch with a four-tooth elastic element (spider). More information on the test rig can be found in (6,7) , where the same test rig has been used. ...

... After that three fault states were measured, and finally all the faults occurred simultaneously. More information on the testing arrangement can be found in earlier studies by Lahdelma et al. (6) . ...

... Vibration signals from all the eight accelerometers in the test rig and six different rotational frequencies in each fault state were investigated in this paper. Some of these signals have been studied earlier by authors et al. (6) in which the signals and spectra under different fault states have been presented more accurately. Here, the signals were examined mostly based on advanced feature calculation. ...

Reliable machine condition monitoring and the early detection of faults play an important role in asset management. Information on the condition of machines in a clear, simple form is very valuable for the maintenance and management personnel of the company. This kind of information can be obtained by combining features of vibration signals and the desired number of features from other physical measurements into a dimensionless MIT index. The resulting value gives us information on the condition of the machine. The inverse of MIT index is called the SOL health index. This paper presents the results of investigations concerning the detection of many simultaneous faults using vibration and sound measurements. The signals measured have been processed using real order derivation, and effective features have been calculated from these signals. Based on these features, MIT indices have been calculated, which reliably shows if there are problems with the condition of the machine.

... Unstable running of an electric motor [26,62,67] Bearing faults [26,[66][67][68][69]72,[84][85][86][87][88][89][90]93,94,98] Bent shaft [88] Misalignment [88,91,92] Cavitation [95][96][97] Poor lubrication [91] A laboratory experiment is examined in which automatic diagnostics were used with acceleration and jerk signals. The outer race of a rolling bearing contained the faults shown in Table 6 [69,87,94] . ...

... Unstable running of an electric motor [26,62,67] Bearing faults [26,[66][67][68][69]72,[84][85][86][87][88][89][90]93,94,98] Bent shaft [88] Misalignment [88,91,92] Cavitation [95][96][97] Poor lubrication [91] A laboratory experiment is examined in which automatic diagnostics were used with acceleration and jerk signals. The outer race of a rolling bearing contained the faults shown in Table 6 [69,87,94] . ...

The time derivatives of acceleration offer a great advantage in detecting impact-causing faults at an early stage in condition monitoring applications. Defective rolling bearings and gears are common faults that cause impacts. This article is based on extensive real-world measurements, through which large-scale machines have been studied. Numerous laboratory experiments provide additional insight into the matter. A practical solution for detecting faults with as few features as possible is to measure the root mean square (RMS) velocity according to the standards in the frequency range from 10 Hz to 1000 Hz and the peak value of the second time derivative of acceleration, ie snap. Measuring snap produces good results even when the upper cut-off frequency is as low as 2 kHz or slightly higher. This is valuable information when planning the mounting of accelerometers.

... It is a simple operation, where the DFT is performed first and frequency components in the stop band of the filter are replaced with zeros, and the inverse DFT is applied after. The techniques presented above have been applied before for example in (14,15,16) . ...

Periodically repeating shocks are a quite common indication of certain defect in machinery. Detecting these shocks in early stage, before the defect is severe enough to cause failure, can provide a huge advantage in maintenance planning. The earliest possible warning of a defect may be highly important, especially in targets where failure can lead to a vast loss of production or a safety risk. Shock-like vibrations are, however, usually rather faint when the defect is a minor one. This simply means that the shocks may often be too low in magnitude to be easily detected. In this paper, we use different techniques based on real order derivative to detect gear defects. Higher real order derivative, discrete Fourier transform, and Hilbert transform are discussed.

... The motor and the driven shaft are coupled by means of a claw clutch with a four-tooth elastic element. More information on the test rig and the original measurements can be found in (31) . We have studied the detection of the offset misalignment of a claw clutch in (32) . ...

The processing of measured signals plays a very important role when information is needed on a physical phenomenon or machine faults. The differentiation of a signal is one of the basic methods used in many signal processing applications. The order of derivative is typically an integer though it can also be any real or complex number. This paper discusses the application of real and complex order fractional differentiation. The aim is to bring out different applications of these derivatives, especially in the field of condition monitoring.

... Detecting faults is a very common topic, and instructions on this are provided in handbooks (8) . When there are multiple faults, however, the situation is more complicated in this respect, but separating different sources of vibration has proved to be possible (9) . ...

Cavitation is a somewhat common and well-known phenomenon and can cause erosion in machines, such as water turbines and pumps. The detection of cavitation in different machines has been quite widely investigated. However, when cavitation occurs simultaneously with different types of mechanical faults, the task is slightly more complicated. This paper discusses the application of real order derivatives, weighted lp norms and S surfaces in order to detect cavitation, mechanical looseness, the lack of lubrication and certain combinations of these. It is shown that these methods can produce easily interpretable information on a complex situation of this kind.

The calculation of fractional or integer order derivatives and integrals has been demonstrated to be simple and fast in the frequency domain. It is also the most sensible method if one wishes to calculate derivatives or integrals of periodic signals. In this paper, error analysis is carried out for the numerical algorithm for Weyl fractional derivatives. To derive an upper bound for the numerical error, some knowledge of the smoothness of the signal must be known in advance or it must be estimated. The derived error analysis is tested with sampled functions with known regularity and with real vibration measurements from rotating machines. Compared to previous publications which deal with error analysis of integer order numerical derivatives in the frequency domain using L^2 errors, the result of this paper is in terms of maximum absolute error and it is based on a novel result on the signal's regularity. The general conclusion using either error estimates is the same: the error of numerical Weyl derivatives is bounded by some constant times the sequence length raised to a negative power. The exponent depends on the smoothness of the signal. This contrasts with using difference quotients in numerical differentiation, in which case the error is bounded by a constant times the sequence length raised to a some fixed negative power and the order of the method defines that exponent.

Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. Any attempt to detect different types of machine faults reliably at an early stage requires the development of improved signal processing methods. Vibration measurements provide a good basis for condition monitoring. In some cases the simple calculation of root-mean-square and peak values obtained from vibration signals are useful features for detecting various faults. Unbalance, misalignment, bent shaft, mechanical looseness and some electrical faults, for example, can be detected using features of displacement and velocity. Higher order derivatives provide additional possibilities for detecting faults that introduce high-frequency vibrations or impacts. New generalised moments and norms related to lp space have been used for diagnosing faults in a roller contact on a rough surface. This paper extends the field of possible applications from roller bearing fault detection to more complex faults situations where different kinds of fault occur simultaneously. In consequence, feature calculation and signal processing have to be adopted and optimized for each fault type on the basis of one measured signal. The features of x(4) indicate well the intact case and the outer race fault. Velocity x(1) is needed for detecting unbalance. This approach also works for the combined case, outer race fault and unbalance. Derivation reduced the effect of noise by amplifying higher frequency components from bearing faults more than the added noise components.

Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. Root-mean-square and peak values obtained from vibration signals are useful features for detecting various faults. Unbalance, misalignment, bent shaft, mechanical looseness and some electrical faults, for example, can be detected using features of displacement and velocity. Higher order derivatives provide additional possibilities for detecting faults that introduce high-frequency vibrations or impacts. Real order derivatives increase the number of signal alternatives. New generalised moments and norms related to lp space have been used for diagnosing faults in a roller contact on a rough surface. Kurtosis provides a strong indication if the order of derivation, α, is at least 4. For peak values, the change is smaller but already starts at α = 3. The generalised moment and norm can be defined by the order of derivation, the order of the moment, p, and sample time, τ. Reliable results can be obtained by relative norms if α and p are in the range between 4 and 6. For the impact of a small scratch, sensitivity is further improved with short sample times, but several sequential samples are required to guarantee the detection of impacts. Then the order p can also be reduced.

Machine condition monitoring enables reliable and economical way of action for maintenance operations in modern industrial plants. Increasing number of measurement points and more demanding problems require automatic fault detection. Advanced signal processing methods exposed failures earlier and then it's possible to plan more operating time and less shutdowns. Intelligent methods have been increasingly used in model based fault diagnosis and intelligent analysers. Intelligent methods provide various techniques for combining a large number of features. A test rig was used to simulate different fault types and changes in operating conditions. Linguistic equation (LE) models were developed for the normal operation and nine fault cases including rotor unbalance, bent shaft, misalignment and bearing faults. Classification is based on the degrees of membership developed for each case from the fuzziness of the LE models. The classification results of the experimental cases are very good and logical. As even very small faults are detected by a slight increase of membership, the results are very promising for early detection of faults. Together with the compact implementation and the operability of the normal model, this makes the extension to real world problems feasible.

The investigation provides new criteria for use in the evaluation of the results obtained from vibration measurements performed as part of condition monitoring. The author sets out from practical long-term tests which involved paper machines and woodpulp manufacturing machines in a number of mills, pointing out reasons for which displacement time derivates of a higher order than acceleration x(2) should be employed for technical diagnostic purposes. Practical results are presented for the measurement parameters x(2), x(3) and x(4).

Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. The signals x(3) and x(4) are very suitable for the condition monitoring of slowly rotating bearings since rapid changes in acceleration become emphasised upon the differentiation of the signal x(2). Real order derivatives x(α) provide additional possibilities, e.g. in a bearing fault case the sensitivities of some features have been found to reach a maximum when α = 4.75. In earlier cavitation indicators, the rms values were combined with either kurtosis or peak values. Generalised moments τMαp can be defined by the order of derivation (α), the order of the moment (p) and sample time (τ). The moment normalised by standard deviation can be used as kurtosis in the model-based analysis.
This paper introduces a new norm ‖τMαp‖p = (τMαp)1/p = [1/NΣi=1N|xi(α)|p]1/p, where the orders α and p are real numbers. The number of signal values s N =τ N where Ns is the number of samples per second. The new norm has the same dimensions as the corresponding signals x(α ) . The cavitation of a Kaplan water turbine was analysed in the power range 1.5…59.4 MW based on measurements collected with sampling frequency 12800 Hz. The order p was compared in the range from 0.25 to 8 with a step 0.25, and a total of 11 sample times were used: τ = 1, 2,…, 6, 8, 10, 20, 30, and 40 seconds. An optimum order p was detected for each sample time τ. The relative max(‖3^M_4^2.75‖) compared to a cavitation-free case is alone a good indicator for cavitation: strong cavitation and cavitation-free cases are clearly detected, and the power ranges for shortterm cavitation are only slightly wider than in the previously developed knowledge-based cavitation index. Short sample times and relatively small requirements for the frequency ranges make this approach feasible for on-line analysis and power control. The weighted sums of features on a different order of derivation form fault-specific measurement indices MIT, and several indices MIT define the health index SOL. The sensitivity increases with the order of derivation to some limit of α. For faults causing impacts, high MIT values for lower orders of derivation indicate an increase in the severity of the fault.

A combined signal processing and feature extraction approach can be based on generalised moments and norms, which are defined by the order of derivation (α), the order of the moment (p) and sample time (τ), where α and p are real numbers. The analysis can be further improved by taking into account nonlinear effects by monotonously increasing scaling functions. Several features can be combined in condition indices and, in some cases, only one feature is needed if the orders p and α are chosen properly. The aim of the application analysis is to test new features and whether their sensitivity is sufficient to detect faults from the absolute values of the dynamic part of the signals x(α) at an early stage when the faults are still very small. For faults causing impacts, the sensitivity of the features is clearly improved by higher and real order derivation, and low order norms can be used if the order of derivation is sufficient. Correspondingly, subharmonic vibrations can be amplified by integration. A limit of sensitivity is reached on a certain order α, and on each order α an optimal sensitivity is chosen by the order p. Both the orders can be chosen fairly flexibly from the optimal area. Sample time, which connects the features to the control application, is process-specific. The analysis methods allow the use of lower frequency ranges, and a multisensor approach can also be used. The approach is well suited for rotating process equipment with speeds ranging from very slow to very fast. In this article, the types of slow rotating equipment are a lime kiln, a washer and the scraper of a digester, all from pulp mills. A centrifuge and a turbo compressor are examples of very fast rotating machines. Features can also be combined in stress indices, which react to harmful process conditions. For example, strong cavitation, cavitation-free cases and even short-term cavitation are clearly detected in a Kaplan water turbine. Several features, also from different frequency ranges, can be combined in condition and stress indices.

Cavitation is harmful to water turbines and may cause operation delays of several weeks. The real-time detection of cavitation risk is increasingly important, and even narrow cavitation-free power ranges can be utilised in load optimisation. Higher derivative signals x(3) and x(4) calculated from acceleration signals are very suitable for detecting impacts. This paper introduces a generalised moment τσMpα which is defined by three parameters: the sensitivity of the moment improves when the order p of the moment increases, especially when short sample time τ is used. In this study, sufficently good results were obtained with moments where the order of derivation α =4, p ≈ 4, and τ =3s. These moments detect the normal operating conditions, which are free of cavitation, and also provide a clear indication for cavitation risk at an early stage. Sufficiently long signals are required for producing reliable maximum moments and data for analysing short-term cavitation. On-line cavitation monitoring is feasible with this approach since the analysis does not need high frequency ranges and the sample times are very short. The moment can be analysed first, and it is then possible to obtain the cavitation index if the moment value exceeds the threshold. Data compression is very efficient as the detailed analysis only requires the feature values of the appropriate samples.

Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring even when long periods of continuous operation are required. The parameters x(3) and x(4) are very suitable for the condition monitoring of slowly rotating bearings, as although the acceleration pulses are weak and occur at long intervals, the changes in acceleration are rapid and become emphasised upon differentiation of the signal x(2). Grounds for the need of x(-n) signals, ie integration of displacement n times with respect to time, have been indicated. In addition, derivatives where the order is a real number or a complex number + i have been developed. These signals can be utilised in process or machine operation by combining the features obtained from the derivatives. The importance of each derivative is defined by weight factors.
Dimensionless indices are obtained by comparing each feature value with the corresponding value in normal operation. These indices provide useful information on different faults, and even more sensitive solutions can be obtained by selecting suitable features. Widely used root-mean-square values are important in many applications, but the importance of the peak values increases in slowly rotating machines. Further details can be introduced by analysing the distributions of the signals. The features are generated directly from the higher order derivatives of the acceleration signals, and the model can be based on data or expertise. The intelligent models extend the idea of dimensionless indices to nonlinear systems. Variation with time can be handled as uncertainty by presenting the indices as time-varying fuzzy numbers. The classification limits can also be considered fuzzy. The reasoning system will produce degrees of membership for different cases. Practical long-term tests have been performed e.g. for fault diagnosis in bearings, cogwheels, gear boxes, electric motors and supporting rolls, and for cavitation in turbines and pumps.

Some experimetnal observations and results are given comparing acceleration shock pulse transducer, acoustic emission and jerk measurements from slightly damaged bearings at medium to low speeds. Additional results showing defects at very low speeds with an acoustic emission transducer are not easily explained