Condition monitoring by means of vibration and sound measurements · 2016. 12. 13. · have been calculated from these signals. Based on these features, MIT indices have been calculated,

Condition monitoring by means of vibration and soundmeasurements

Jouni Laurila and Sulo LahdelmaMechatronics and Machine Diagnostics Laboratory, Department of Mechanical

Engineering, P.O. Box 4200, FI-90014 University of Oulu, FinlandE-mail: [email protected], [email protected]

Abstract

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

Keywords: condition monitoring, vibration analysis, real order derivatives, frac-tional derivatives, lp norms, MIT and SOL indices

1. Introduction

The use of machine condition monitoring in an effective, reliable way is even moreimportant than before in order to sustain and improve the competitiveness of com-panies. Consequently, companies also have many new needs for monitoring thecondition and operation of machines. In this field, several different measurementand analysis methods are used. However, it is important that information on thecondition of machines is as simple and reliable as possible. In addition, the aim is toimplement condition monitoring by means of economical methods and with as fewsensors as possible.

In general, vibration measurements provide a good and reliable basis for detectingof many different machine faults. In many cases displacement and velocity measure-ments are good ways of detecting e.g. unbalance or misalignment and evaluating

The Tenth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies

their severity (1,2). Bearing faults can be detected more efficiently with accelerationsignals, for example. The use of higher, real or complex order derivatives is usually amore sensitive solution to many faults. These advanced signal processing techniquescould be similarly used for both vibration and sound signals. Therefore, real orderderivatives were utilised in this study, and effective features were calculated fromthese signals. With the help of them, it is possible to find highly sensitive indicatorsfor different fault situations.

The use of sound measurements in machine condition monitoring is not very com-mon. It is known that the normal functioning of the machine always results in bothsound and vibration. For example, an axially loaded bearing will always generatevibrations (3). It is probable that when the condition of the machine changes, thevibration and sound caused by the machine also change considerably. Althoughvibration measurements are a good, reliable method for condition monitoring, itis also possible to obtain information on changes in the condition of the machineon the basis of sound. Although the topic has not been very widely studied, manystudies have been published on it, for example in (3,4). Based on sound measurement,methods have been developed for monitoring machine tool wearing (3) and internalcombustion engine fuel injection (5).

A major problem in the analysis of sound measurements is often background noise.On the other hand, the advantages with sound-based measurements are very low-priced measuring devices and non-contact measurement, which may simplify theimplementation of measurements in many situations. Based on sound measurements,it could be possible to develop methods that can be used at least in general machinecondition monitoring. If necessary, more detailed fault diagnosis could be performedseparately by means of other portable measuring systems.

In this investigation, different faults, such as unbalance, coupling misalignment,bearing cage fault, the absence of lubrication in a ball bearing and their combi-nations, are studied using a test rig. Vibration and sound measurements were per-formed using accelerometers and a sound level meter. Feature extraction was carriedout using real order derivatives and weighted lp norms. Based on these features, di-mensionless vibration indices have been calculated by combining features to MITand SOL indices.

2. Test rig

A test rig (Figure 1), which consists of an electric motor and a belt transmissionbetween two shafts, has been used here in order to obtain information on differentfaults. The test rig was originally built by PIM Bt. and was later modified in theMechatronics and Machine Diagnostics Laboratory in Oulu. It is a convertible smalldevice with a 0.18 kW AC motor. The motor and the driven shaft are coupled bymeans of a claw clutch with a four-tooth elastic element (spider). More informationon the test rig can be found in (6,7), where the same test rig has been used.

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Figure 1. Test rig

The measurements were carried out using eight accelerometers, a tachometer and asound level meter simultaneously. The accelerometer types are Wilcoxon Research726 and IMI 621B51. The first of them has a frequency range (±3 dB) up to 15 kHzand the second one up to 20 kHz. The integrating sound level meter is Brüel&KjærType 2239A with a linearly weighted AC output. The frequency range (±2 dB) ofthe microphone in the sound level meter is from 8 Hz to 16 kHz. The accelerometerswere screwed directly into the bearing housing in the radial direction, while a gluedmounting pad was used in the axial direction. Each of the four bearing housingswas measured using a horizontal sensor, and vertical and axial sensors were used onbearings 1 and 3 (Figure 1). The sound level meter was placed on the right-handside of the machine close to the belt transmission.

The measurements were performed in the LabVIEW environment by means of threeanalog input modules (NI 9233) and a four-slot USB chassis (NI cDAQ-9174), whichconfirm simultaneous measurements from all the channels. Each combination of asensor, cable and measurement channel was calibrated. The sample rate was 50 kHzand the time period for continuous data collection was 80 seconds in each case.

The tests were carried out with 16 different rotational frequencies between 4 −23.5 Hz, and the following 13 states were executed:

• initial state• rotor unbalance mass 5.5 g, 11 g and 16.5 g• coupling misalignment 0.20 mm, 0.35 mm and 0.50 mm• rotor unbalance mass 5.5 g and coupling misalignment 0.35 mm• rotor unbalance mass 11 g and coupling misalignment 0.35 mm• rotor unbalance mass 5.5 g and coupling misalignment 0.20 mm• no lubrication in bearing• no lubrication in bearing and no cage• rotor unbalance mass 11 g, coupling misalignment 0.35 mm and no lubrication

in bearing and no cage.

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In this paper, only 6 different rotational frequencies in each fault state were inves-tigated. In the initial state, the condition of the machine was quite good and theother states could be compared with the measurements of this state. Rotor unbal-ance was generated by a mass of 5.5 g, 11 g or 16.5 g in the disk close to the coupling.In these cases the unbalances (ui = mir) were 276 gmm, 552 gmm and 828 gmm,respectively. Coupling misalignment was induced by moving the motor in the hor-izontal direction, and both vertical and angular alignment was kept constant. Themeasurements were performed by means of two dial gauges. Three different caseswhere rotor unbalance and coupling misalignment occur simultaneously were alsoperformed before the grease in bearing 3 was washed away. After that three faultstates were measured, and finally all the faults occurred simultaneously. More in-formation on the testing arrangement can be found in earlier studies by Lahdelmaet al. (6).

3. Signal processing methods

This paper utilises the derivation of acceleration and sound signals and weightedlp norms, for the purposes of improving sensitivity, so that the order of derivativeand the order of norm can be a real number instead of an integer. In addition,dimensionless vibration indices are calculated for combining two or more differentfeatures into a single, powerful multi-purpose feature.

3.1 Order of derivation

Fault detection depends essentially on the order of derivative. Faults that mainlyinduce low frequency vibrations, such as unbalance or a bent shaft, can be detectedsuccessfully using signals whose order of derivative is low. Displacement or velocitysignals were usually used in these cases. Acceleration measurements are needed forthe early detection of faults, such as bearing faults, which induce vibration in thehigh frequency band. Sensitivity can often be improved considerably by means ofhigher order derivatives, especially in fault cases where impacts or friction occur.For all fault types it is probable that the best sensitivity cannot be reached onlywith a signal whose order of derivative is an integer. The use of real order derivativesenables more sensitive indicators to be found for different cases of fault detection (8,9).

The most efficient way of derivating signal x(t) is a procedure where three mainsteps are performed in the frequency domain. At first a fast Fourier transform(FFT) is used for the signal x(t) in order to obtain the complex components {Xk},k = 0, 1, 2, ..., (N − 1). The corresponding components of the derivative x(α)(t) arecalculated with the formula

Xαk = (iωk)αXk. (1)

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The signal x(α)(t), where the order of derivation is α ∈ R, can be obtained by usingthe inverse Fourier transform FFT -1 for the sequence {Xαk}, k = 0, 1, 2, ..., (N −1).

For the sinusoidal signal x = X sinωt the real order derivative is

dαx

dtα= ωαX sin(ωt+ α

π

2) = Xα sin(ωt+ φα), (2)

where α ∈ R is the order of derivation, the amplitude Xα = ωαX and the change ofthe phase angle φα = απ

2. (8,9)

3.2 Weighted lp norms

Let X be a vector space and a ∈ R. The norm satisfies the following axioms (10):

(N1) ∥x∥ ≥ 0 ∀x ∈ X, ∥x∥ = 0 if and only if x = θ,

(N2) ∥x+ y∥ ≤ ∥x∥+ ∥y∥ ∀x, y ∈ X (triangle inequality),

(N3) ∥ax∥ =| a | ∥x∥ ∀a ∈ R and ∀x ∈ X.

The norm is clearly an abstraction of our usual concept of length (10).

Let p ∈ R and 1 ≤ p < ∞. The space lp consists of all the sequences of scalars{x1, x2, ...} = x for which

∞∑i=1

|xi |p< ∞. (3)

The norm in lp is defined by

∥x∥p = (∞∑i=1

|xi |p)1p (4)

and is also called the classical lp norm. Next, we examine the generalisation of theclassical lp norm in the form

∥x∥p,w = (∞∑i=1

wi|xi|p)1p , (5)

where wi (i = 1, 2, ...) are weight factors (11,12). If wi = 1 ∀i, then the question is ofa classical lp norm.

If all the weight factors are equal to 1N

, we obtain from (5) the norm

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∥x∥p, 1N= (

1

N

N∑i=1

|xi|p)1p = (

1

N)1p∥x∥p. (6)

We suppose that the integer N ∈ [1,∞). The space l̄p consist of all the sequences ofscalars {ξ1 = x1

p√N, ξ2 =

x2p√N, ..., ξN = xN

p√N} = x̄ for which the sum

N∑i=1

|ξi|p =N∑i=1

| xip√N|p = 1

N

N∑i=1

|xi|p < ∞. (7)

Analogous to (4) we can define the l̄p norm by

∥x̄∥p = (N∑i=1

|ξi|p)1p = (

1

N

N∑i=1

|xi|p)1p = ∥x∥p, 1

N. (8)

We can call the norm ∥x̄∥p = ∥x∥p, 1N

as 1N

weighted lp norm.

3.3 Dimensionless vibration indices

In reference (13), Lahdelma introduced the measurement index MIT for rating thecondition of machinery. Dimensionless vibration indices can be combined in a mea-surement index

τMIT p1,p1,...,pnα1,α2,...,αn

=1

n

n∑i=1

bαi

∥x(αi)∥pi(∥x(αi)∥pi)0

, (9)

where the norms ∥x(αi)∥pi are obtained from the signals x(αi), i = 1, ..., n. Theindex zero denotes the reference value when the machine is in good condition andbαi

represents a weight factor. This factor allows the rating of individual faults.The sum

∑ni=1 bαi

= n. Further investigations can be found in (8,14), where a moregeneralised form of (9) has been introduced. The inverse of the MIT index is calledthe SOL health index. It provides a clear indication of the condition of the machine:high values indicate a good condition and a small values poor condition (2,9). Othermeasurement parameters, such as temperature, can also be used in the MIT andSOL indices in order to obtain more information on the condition of the machine (9).

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4. Analysis of vibration signals

Vibration signals from all the eight accelerometers in the test rig and six differentrotational frequencies in each fault state were investigated in this paper. Some ofthese signals have been studied earlier by authors et al. (6) in which the signals andspectra under different fault states have been presented more accurately. Here, thesignals were examined mostly based on advanced feature calculation. The time signalwith a sample length of 4 s was used in the calculation of features. Signal processing,such as derivation and filtering, was performed in the frequency domain and an idealfilter was used. To avoid unwanted distortion caused by signal processing in theanalysed signals, 18 % of the samples were removed from both the ends of the signalbefore analysis. The frequency range in all the cases was from 3 Hz to 10 kHz.

In a complex fault situation, where more than one fault occurs simultaneously inthe machine, various features are usually needed. The location of the measurementpoint and its direction often play an important role in the early detection of a specificfault. To find the best measurement points and sensitivity for the detection of eachfault type in different states, the signals and spectra were analysed comprehensivelyand the number of time domain features was calculated. The values of peak, root-mean-square (rms), crest factor, kurtosis and l̄p norms, when p = 0.2, 0.4, 0.6, ..., 8and α = 0.0, 0.2, 0.4, ..., 10.0 were calculated from all the signals analysed. Thevarious fault states were compared using relative features, which were calculatedby dividing the features by the corresponding value, which was measured from themachine when it was in good condition. This method provided a lot of informationon changes in vibration when the condition of the machine changes.

The detection of unbalance in different unbalance rates depends on the rotatingfrequency of the machine, the location of the measurement point, and direction.In this machine, a critical speed is 11.6 Hz, which is the rotating frequency whereunbalance can also be detected most easily. Figure 2 shows relative l̄p norms fromthe horizontal accelerometer of bearing 1 (ACC1) when the unbalance mass was5.5 g and 11 g, and the rotational frequency was 11.6 Hz. In the case of Figure 2 a),the unbalance mass is only 5.5 g, but the value of the best feature in this case is 10.7times higher than the corresponding value in the initial state. When the amountof unbalance mass was doubled to 11 g (Figure 2 b), the most sensitive feature isalmost doubled, too. In this case and also with other rotational frequencies and therates of unbalance, the best sensitivity can be obtained when α and p are low, i.e.α = 0...0.8 and p = 0.2.

Using the l̄0.2 norms we can obtain slightly better sensitivity as compared withconventional features. Figure 2 b) shows, that the relative change of feature ∥x(0)∥0.2is 19.0, when the corresponding relative peak value of the displacement signal is 10.8and the relative rms value is 16.0. The finding shows that l̄p norms also with p < 1are useful in some fault cases. In the test rig, unbalance can be detected reliablyusing these features when the rotating frequency is between 8 and 16 Hz. When therotational frequency is lower or higher, the detection of unbalance becomes more

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difficult. The best measurement point is on bearing 1 (Figure 1) in the horizontaldirection, though unbalance can also be detected quite well from the other horizontalmeasurement points.

(a) (b)

Figure 2. Relative change of the l̄p norms when the unbalance mass is5.5 g (a) and 11 g (b). The frequency range is 3 – 10000 Hz

Figure 3 shows relative l̄p norms from bearing 1 (ACC1) when the coupling mis-alignment was 0.35 mm and 0.50 mm and the rotational frequency was 8 Hz. Bothgraphs clearly show that the best sensitivity can be obtained when α is between3.2 and 3.8 and p is greater than 5. For all p, the relative change is very smallwhen a small order of derivatives is used. For example, in the case of Figure 3 a)the relative change of l̄5 norm of velocity signal is 1, the corresponding value foracceleration is 3 and for x(3.4) it is 20. In this case, the relative change also decreasesstrongly when α exceeds four. However, sensitivity is good even with α is 6. Thesensitivity of the l̄p norm is the best when p is from 5 to 8. The vibration causedby misalignment is clearly the strongest in the bearing housing next to the couplingand in the horizontal direction.

(a) (b)

Figure 3. Relative change of the l̄p norms when coupling misalignmentis 0.35 mm (a) and 0.50 mm (b). The frequency range is 3 – 10000 Hz

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When two faults occur simultaneously, it is good if we can extract from the signal thefeatures that indicate the types of the faults. The relative l̄p norms of two differentcases where rotor unbalance and coupling misalignment occur simultaneously atrotational frequency 8 Hz are shown in Figure 4. The measurements are from bearing1 (ACC1) from the cases where both unbalance and misalignment are in the smallest(Figure 4 a) and in the medium rates (Figure 4 b). The results of this and the othercombinations of these two faults are very logical. By studying the features that aresensitive to unbalance, we can evaluate its severity. The graphs in Figure 4 showthat the relative change of feature ∥x(0)∥0.2 is 1.6, when the unbalance mass is 5.5 gand 3.4 when the unbalance mass is 11 g. These values correspond to cases where thesame unbalance appears independently at rotational frequency 8 Hz. Respectively,the values that are linked with the rate of misalignment are almost equal in thecases where misalignment occurs independently or simultaneously with unbalance.For example, the relative change of feature ∥x(3.4)∥5 is 20 in Figure 3 a) and 23in Figure 4 b). These results show that at this test rig unbalance only has minorinfluence on misalignment or vice versa.

(a) (b)

Figure 4. Relative change of the l̄p norms in the cases ‘unbalance mass5.5 g and misalignment 0.20 mm’ (a) and ‘unbalance mass 11 g andmisalignment 0.35 mm’ (b). The frequency range is 3 – 10000 Hz

In one of the cases studied, bearing 3 was run completely without lubrication. Inthat situation the features of the bearing were up to 3000 times higher than in aninitial state. The fault could be seen very clearly in all the measuring points, and alsoin the furthest measurement point the values were about 120 times higher than inthe initial state. Also in this fault state derivation improves sensitivity significantly.In the faulty bearing, the relative change of acceleration x(2)

p is 100, the relativechange of jerk x(3)

p is 1000 and the relative change of napse x(4)p is 2300. The best

sensitivity in this bearing and the measuring point is achieved when α = 5...7 andp = 7...8. The peak value is usually the most sensitive feature for this fault type,but a very good sensitivity is also obtained with the l̄p norm, when p and α aregreater than 3.

The machine was also studied in a state in which there was no cage on bearing 3

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when the bearing had two faults: the absence of lubrication and the absence ofthe cage. In that situation, the bearing ran more smoothly as a result of increasedbearing clearance and smaller friction forces. This fault could be seen best in thefaulty bearing in the horizontal direction. The best sensitivity was achieved whenα = 4 and p = 8 or with x

(4)peak. Figure 5 shows relative l̄p norms from bearing 1 and

3 in the case of no lubrication and no cage when rotational frequency was 8 Hz. Inbearing 1, the relative change is at its best, 11.5, when α = 4...6 and p is low. Basedon the measurements, it can be concluded that bearing faults of this type can bedetected from all the measurement points in the test rig, but clearly the strongestvibrations are in the bearing in which the fault occurs. It is easy to locate andevaluate the severity of such bearing faults on the basis of vibration measurements.

(a) (b)

Figure 5. Relative change of the l̄p norms in the case ‘no lubrication inthe bearing and no cage’ from bearing 1 (a) and from bearing 3 (b).

The frequency range is 3 – 10000 Hz

Figure 6 shows the fault state where all the faults occurs simultaneously. Therelative l̄p norms are shown from the horizontal measurement of bearings 1, 3 and 4when the rotational frequency is 8 Hz. In the graph in Figure 6 a) from bearing 1,the effects of unbalance and misalignment are still clearly visible, as they occurindependently. The bearing faults increase relative changes especially at the smallvalues of p when α ≥ 2 in this measurement point. The values of ∥x(6)∥0.2, forexample, are approximately four times greater in this case, due to the fault inbearing 3, as compared with a case where all the bearings are in good condition.Also the features of bearing 3 (Figure 6 b) show a strong increase due to unbalanceand misalignment. When the values of the relative l̄p norms are compared with acase where only bearing fault occurs (Figure 5 b), the values are even tripled. Inthis measurement point, the increase of α and p improves sensitivity considerablybut on the other hand also the sensitivity of the peak value is approximately in thesame range as the sensitivity of ∥x(10)∥8.

The graph in Figure 6 c) shows that bearing faults also cause clear changes in thefeatures measured from bearing 4, when p is low. In this case, the best sensitivityfor detecting misalignment and bearing faults is obtained with the same derivation

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order, which is approximately 3.4, but the misalignment can see at best with highvalues of p and the bearing faults with low values of p. This can be seen as a ridgein Figure 6 c), when α = 3.2...3.6. In addition, the vibrations related to the bearingfault increase the values of relative change also the other values of p, when α ≥ 3.The changes caused by unbalance are the same in this measurement point as in theother cases where unbalance occurs.

(a) (b)

(c)

Figure 6. Relative change of the l̄p norms in case ‘rotor unbalance mass11 g, coupling misalignment 0.35 mm and no lubrication in bearing andno cage’ from bearing 1 (a), from bearing 3 (b) and from bearing 4 (c).

The frequency range is 3 – 10000 Hz

The examination of vibration signals shows that all the studied faults, if they appearindependently or simultaneously, could be detected on the basis of vibration mea-surements. In this machine, which is quite small, the vibrations caused by differentfaults are transferred quite well in the structure. That is why the faults can bedetected on measurement points that are further away. However, for the locating offaults, more accurate measurements are may needed. It is easier to detect rotor un-balance using small values of α and the best sensitivity is obtained with the l̄p normwhen the value of p is small. The coupling misalignment of a claw clutch is best de-tected from the measurement points that are next to the coupling, though this faultis also clearly visible from a distance, particularly at higher degrees of misalignment.

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The best sensitivity for detecting coupling misalignment is when α = 3.2...3.8 andp ≥ 5. For detecting the bearing faults studied in this paper, the best sensitivityis usually achieved with α ≥ 3.4 and the high values of p. Compared with thecommonly used velocity and acceleration measurements, these features offer muchhigher sensitivity.

5. Analysis of sound signals

Sound measurements were performed in all the same fault states simultaneously withvibration measurements, but only one sound level meter was used. It was placed onthe right-hand side of the machine (Figure 1) close to the belt transmission and thebearings 2 and 3. Sound signals (U) were recorded using the linearly weighted ACoutput of the meter, and measurement equipment and settings were the same as inthe vibration measurements. Sound signals were processed and calculated using thesame methods as in the case of acceleration signals. The frequency range was in allcases from 3 Hz to 10 kHz.

In general, based on studies on this test rig and measurement arrangement, it isbetter to use quite a low rotational frequency of the machine when sound signals areanalysed. When the rotational frequency increases, the noise caused by the normalrunning of the machine also increases, which complicates the detection of changescaused by faults in the sound signals. Figure 7 shows the relative l̄p norms of soundsignals in cases of rotor unbalance (a) and coupling misalignment (b) and in the casewhere they occur simultaneously (c), when the rotational frequency was 8 Hz. Therelative values were calculated by dividing the features by the corresponding soundsignal value, which was measured from the machine when it was in good condition.

The graphs in Figure 7 show that these faults cause clear changes in signals. Themost sensitive feature in both the cases reaches with the l̄p norm, when the derivativeof the sound signal is between 1.2 and 1.8 and p is large. Therefore, the peak value,which is l̄p norm with p = ∞, is the most sensitive feature. In the case wherethe unbalance mass is 11 g, the relative change of ∥U (1.4)∥8 is 3.3 (Figure 7 a) andthe relative change of peak value ∥U (1.6)∥∞ is 4.5. In the case in graph Figure 7 b),where misalignment is 0.35 mm, the values are 4.1 and 5.3, respectively. However, inthe case where both the faults occur simultaneously (Figure 7 c), the correspondingvalues are slightly smaller. The relative change of ∥U (1.4)∥8 is 2.8 and the relativechange of ∥U (1.8)∥∞ is 3.4. The results are almost consistent with the other faultcases, where unbalance and misalignment occur independently or simultaneously.In consequence, it can be concluded that it is not easy to state on the basis ofsound measurements in this arrangement whether the features of the sound signalare caused by unbalance or misalignment.

The bearing fault types studied in this paper also cause strong growth in the levelsof sound signals. Figure 8 shows how the sensitivity of l̄p norms changes in the caseof absence of lubrication in bearing 3 (Figure 8 a) and in the case of no lubrication

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and no cage in bearing 3 (Figure 8 b). The rotational frequency is 8 Hz also inthese cases. We can see that the changes are very considerable, especially in thecase of Figure 8 a). The derivation of the sound signal increases relative changeconsiderably and at best it is 29, when α = 8 and p = 8. For example, when therelative change of the l̄4 norm of the raw sound signal is 8, it is almost tripled tovalue 23 when the signal was derivated once.

(a) (b)

(c)

Figure 7. Relative change of the l̄p norms of sound signals in the casesof rotor unbalance mass 11 g (a), coupling misalignment 0.35 mm (b)

and their combination (c). The frequency range is 3 – 10000 Hz

In the case where the bearing cage was removed from bearing 3, the running of themachine could be more smoothly compared with the previous case despite the factthat there is no lubrication in the bearing. In the detection of this fault the bestsensitivity is obtained when the order of derivative is 0.4 (Figure 8 b). The relativechange of the raw sound signal is between 7 and 8, when l̄p norms or peak values areused. The derivation of this signal using the order of derivatives 0.2 to 0.6 improvessensitivity about 1.5 times. The most sensitive feature in this case is ∥U (0.4)∥0.2, butalso the rms value ∥U (0.4)∥2 of the same signal has good sensitivity. The relativechanges of these features are 11.5 and 11.0, respectively.

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(a) (b)

Figure 8. Relative change of the l̄p norms of sound signals in the cases‘no lubrication in bearing 3’ (a) and ‘no lubrication and no cage in

bearing 3’ (b). The frequency range is 3 – 10000 Hz

Figure 9 shows the relative l̄p norms of sound signals in the case where all the studiedfaults occur simultaneously and the rotational frequency is 8 Hz. From the graph inFigure 9 we can see the features that are mainly caused by unbalance or misalignmentand the other that come up as a result of bearing faults. As said before (Figure 7),the most sensitive feature in the cases of unbalance and misalignment can be achievedwith the l̄p norm, when the derivative of the sound signal is between 1.2 and 1.8 andp is large. The graph in Figure 9 shows a local top on the feature ∥U (1.6)∥8, in whichthe relative change is 4.7. The best relative change of the corresponding peak value∥U (1.8)∥∞ is 5.3. These values are in the same order as the values in Figure 7, wherethe relative changes of the l̄p norms for unbalance and misalignment are presented.

Figure 9. Relative change of the l̄p norms of sound signals in the case‘rotor unbalance mass 11 g, coupling misalignment 0.35 mm and no

lubrication in bearing 3 and no cage’. The frequency range is3 – 10000 Hz

The graph in Figure 9 also shows a ridge, which appears on the line where the orderof derivative is about 0.4 and p changes. This shape is very similar but the values

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are clearly smaller than in Figure 8 b). In the case of Figure 9, where all the faultsstudied occur simultaneously, the relative change value of the most sensitive feature∥U (0.4)∥0.2 is 7.3.

Studying the sound signals shows that it is possible to detect different kinds of faultson the basis of sound signals. The derivation of the signal increases sensitivitysignificantly in all the fault types studied. In these cases the best results can beachieved using a positive order of derivatives in the range 0.4 to 2. When the l̄p normsof these signals are used, different faults cause about two to thirty-fold increase inthe values as compared with the corresponding values in the good condition state.However, the accurate identification of the type of fault based on sound signals couldbe challenging in multi-fault states.

6. Dimensionless vibration indices

Dimensionless vibration indices are a simple, reliable indicator, which can be usedto determine whether the machine is in good or poor condition. The relative normsand other relative features that were discussed above could be used as the terms ofthe MIT index (Eq. (9)). Figure 10 shows the values of the MIT index of vibrationsignals, when the parameters of the index are: n = 3, τ = 4s, α1 = 0, α2 = 3.4,α3 = 4, p1 = 0.2, p2 = 8, p3 = ∞ and bα1 = bα2 = bα3 = 1. The first two terms of theindex were measured from bearing 1 and the last from bearing 3 in the horizontaldirection. These three terms were selected on the basis of their good sensitivity todifferent faults.

Figure 10. The values of MIT indices based on vibration signals atdifferent fault states

Figure 10 shows that MIT index changes very logically when the fault state varies.For example, when the unbalance mass grows from 5.5 g to 11 g and to 16.5 g, thevalues of the index are 3.3, 4.1 and 5.3, respectively. Otherwise, the index is 4.1in the case of unbalance mass 11 g, 9.1 in case of misalignment 0.35 mm, and 18.5when these faults occur simultaneously. The MIT index is high, 45.2, in the case of

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no lubrication and no cage, because this fault is quite severe. However, when all thefaults occur simultaneously, the MIT index is much higher. Based on these results,we can conclude that the MIT index based on vibration signals is a very effective,yet simple indicator, which indicates whether the machine is in good condition ornot. If the severity of the different faults is not equal, a weight of the different termsin the MIT index can be changed easily with coefficients bαi

.

The SOL health index, which is an inverse of the MIT index, shows whether thecondition of the machine has weakened. The SOL index is one when the machineis in very good condition, and if the condition becomes weaker, the SOL index alsodecreases. Figure 11 shows the calculated SOL indices for vibration and the soundsignals for the various fault cases. The SOL index for vibration signals is inverseof MIT index shown in Figure 10. The SOL index for sound signals is based onthe features ∥U (0.4)∥0.2, ∥U (0.4)∥8 and ∥U (1.8)∥∞. The SOL index based on vibrationmeasurements illustrates clearly the health of the machine. Also the SOL indexof the sound signals clearly indicates that in all the fault states, the health of themachine has deteriorated and is the weakest in the bearing fault cases and in thecase where all the faults occur simultaneously.

Figure 11. The values of SOL indices of vibration and sound signals atdifferent fault states

The MIT and SOL indices are good indicators for simple, effective condition monitoring.By using one of these, only one number is needed to decide whether the machineis in good or poor condition. If more accurate information on the type, locationor severity of the fault is needed, the specific parts of the index can be examined.As shown in this study, the MIT and SOL index can also be used in complex faultsituations and multi-fault states. The customization of the parameters of the indicescould prove a very sensitive index in different situations. However, the use of theseindices requires that the state of the machine in good condition is known, becausea reference value is needed.

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7. Conclusions

The use of vibration and sound signals in the condition monitoring of a multi-fault machine was investigated in this paper. Different faults, such as unbalance,the coupling misalignment of a claw clutch, a bearing cage fault, the absence oflubrication in a ball bearing and their combinations, were generated on a test rig,and vibration and sound measurements were performed using accelerometers and asound level meter. The signals measured were processed using real order derivation,and weighted lp norms were calculated from these signals. Based on these features,MIT and SOL indices were calculated.

The study showed that all the faults studied could be detected at an early stageon the basis of vibration measurements when the l̄p norms and suitable real orderderived signals were used. At least in the compact machine, the machine can bemonitored with only one sensor or a few sensors, which still allows one to concludethe type and severity of the faults. Rotor unbalance can be detected best whensignals with low α and l̄p norms with low p are used. The best sensitivity fordetecting the misalignment of the claw clutch can be obtained when α = 3.2...3.8and p ≥ 5. For detecting the bearing faults, which are studied in this study, the bestsensitivity can usually be achieved with α ≥ 3.4 and large values of p. Comparedwith the commonly used velocity and acceleration measurements, these features offermuch higher sensitivity.

The study showed that with the help of sound signals, it is also possible to detectdifferent kinds of faults. The derivation of the signal increases sensitivity signifi-cantly in all the fault types studied. In these cases, the best results can be achievedusing a positive order of derivatives in the range 0.4 to 2. Using the l̄p norms ofthese signals, different faults cause about two to thirty-fold increase in the valuesas compared with the corresponding values in the good condition state. However,the accurate identification of the type of fault on the basis of sound signals could bechallenging. In addition, background noise complicates the analysis of sound signals.

The condition of the machine could monitored reliably and simply by means of MITor SOL indices. These can be created on the basis of the desired number of mea-surement parameters from vibration, sound, temperature or other measurements.This study showed that the MIT or SOL index based on vibration signals is a veryeffective, yet simple indicator that indicates whether the machine is in good or poorcondition. By combining three different relative features ∥x(αi)∥pi , which were calcu-lated from the acceleration signal, an index is obtained that can be used effectivelyfor detecting all the faults studied. If more accurate information on the type orseverity of the fault is needed, the specific parts of the index can be examined.

The study also showed that MIT or SOL indices can be created on the basis of soundsignals. The indices indicate whether the health of the machine has deteriorated.According to the results obtained in this study, the use of real order derivatives canimprove the sensitivity of sound measurements considerably. The measurementsprovide a lot of information on the condition of the machine with the help of simple,

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inexpensive non-contacting sensors. Sound measurements could be a cost-effectivemethod to obtain an overview of machinery health.

References

1. S Lahdelma and V Kotila, ‘Complex derivative - a new signal processingmethod’, Kunnossapito, Vol 19, No 4, pp 39 – 46, 2005, [in Finnish].

2. S Lahdelma and E Juuso, ‘Advanced signal processing and fault diagnosis incondition monitoring’, Insight, Vol 49, No 12, pp 719 – 725, December 2007.

3. N Tandon and A Cloudhury, ‘A review of vibration and acoustic measurementmethods for the detection of defects in rolling element bearings’, TribologyInternational, Vol 32, pp 469–480, 1999.

4. M Amarnath, V Sugumaran and H Kumar, ‘Exploiting sound signals for faultdiagnosis of bearings using decision tree’, Measurement, Vol 46, pp 1250–1256,2013.

5. A Albarbar, F Gu and A Ball, ‘Diesel engine fuel injection monitoring usingacoustic measurements and independent component analysis’, Measurement,Vol 43, pp 1376–1386, 2010.

6. S Lahdelma, J Laurila, J Strackeljan and R Hein, ‘Separating different vibrationsources in complex fault detection’, In Proceedings of CM2011/MFPT 2011, TheEight International Conference on Condition Monitoring and Machine FailurePrevention Technologies, Cardiff, UK, June 2011.

7. S Lahdelma and J Laurila, ‘Detecting misalignment of a claw clutch usingvibration measurements’, In Proceedings of CM2012/MFPT 2012, The NinthInternational Conference on Condition Monitoring and Machine Failure Preven-tion Technologies, London, UK, June 2012.

8. S Lahdelma and E Juuso, ‘Signal processing and feature extraction by usingreal order derivatives and generalised norms. Part 2: Applications’, TheInternational Journal of Condition Monitoring, Vol 1, No 2, pp 54 – 66, 2011.

9. S Lahdelma and E Juuso, ‘Signal processing and feature extraction by usingreal order derivatives and generalised norms. Part 1: Methodology’, TheInternational Journal of Condition Monitoring, Vol 1, No 2, pp 46 – 53, 2011.

10. D G Luenberger, ‘Optimization by vector space methods’, Series in Decisionand Control. John Wiley & Sons, New York, USA, 1969.

11. A Kufner and L E Persson, ‘Weighted Inequalities of Hardy Type’, WorldScientific Publishing Co, Singapore, 2003.

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12. S G Samko, A A Kilbas and O I Marichev, ‘Fractional Integrals and Derivatives.Theory and Applications’, Gordon and Breach, Amsterdam, The Netherlands,1993.

13. S Lahdelma, ‘New vibration severity evaluation criteria for conditionmonitoring’, Research report no 85, University of Oulu, Oulu, Finland, 1992,[In Finnish].

14. S Lahdelma and E Juuso, ‘Signal processing in vibration analysis’, InProceedings of CM2008/MFPT 2008, The Fifth International Conference onCondition Monitoring and Machinery Failure Prevention Technologies, pp 879–889, Edinburgh, UK, July 2008.

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Documents

Condition monitoring by means of vibration and sound measurements · 2016. 12. 13. · have been calculated from these signals. Based on these features, MIT indices have been calculated,