[mechanisms and machine science] vibration engineering and technology of machinery volume 23 ||...

Coherent Composite HOS Analysisof Rotating Machines with DifferentSupport Flexibilities

Akilu Yunusa-Kaltungo and Jyoti K. Sinha

Abstract Earlier studies have shown the possibilities of detecting different faultson a rigidly supported rotating machine through coherent composite spectrum(CCS) and coherent composite bispectrum (CCB) data fusion techniques. Thecurrent paper is also related to the use of CS, CB and a newly introduced coherentcomposite trispectrum (CCT) for faults identification in flexibly supported rotatingmachines. Six experimentally simulated cases have been considered on two sets offlexibly supported (FS1 and FS2) rotating machines, at 1,200 RPM (20 Hz) speed.Vibration data were then collected from both FS1 and FS2, using only fouraccelerometers (one per bearing pedestal in the diagonal direction), for the com-putation of CCS, CCB and CCT. Some combinations of CCB and CCT compo-nents were then used to further test the robustness of the techniques in rotatingmachines’ faults differentiation. The observations and results of the experiments arehereby discussed here.

Keywords Rotating machines � Flexible supports � Condition monitoring � Faultdiagnosis � Data fusion � Coherent composite spectrum � Coherent compositebispectra � Coherent composite trispectra

1 Introduction

Rotating machines are often subjected to a wide variety of operational conditions,which in turn leads to the emergence of different faults (e.g. shaft misalignment,bent shaft, looseness, cracked shaft, shaft rub, etc.). The presence of such faults

A. Yunusa-Kaltungo (&) � J.K. SinhaSchool of Mechanical, Aerospace and Civil Engineering, The University of Manchester,Oxford Road, Manchester M13 9PL, UKe-mail: [email protected]

J.K. Sinhae-mail: [email protected]

© Springer International Publishing Switzerland 2015J.K. Sinha (ed.), Vibration Engineering and Technology of Machinery,Mechanisms and Machine Science 23, DOI 10.1007/978-3-319-09918-7_12

145

(irrespective of their severities) usually alters the dynamic characteristics of thisclass of valuable and versatile machines, which emphasizes the significance ofdetection at incipient stages. Over the years, the application of several sensors(accelerometers, proximity probes, tachometers, etc.) at individual bearing pedestalsfor the collection and diagnosis of vibration data related to rotating machines hasbeen the norm [1]. However, when dealing with large and complex rotatingmachines, such as multi-staged drive assemblies and turbo-generator sets (which areoften characterized by the existence of numerous bearings), there is bound to be acorrespondingly large number of vibration measurement sensors (usually 2 or 3accelerometers per bearing pedestal, 2 eddy current probes per bearing pedestal anda tachometer for shaft speed reference measurement) for collecting data that will beused to accurately detect and differentiate changes in machine characteristics due toemerging fault(s).

Sinha [2] comprehensively studied various health monitoring techniques forrotating machines. Studies by Jardine et al. [3] and Mehrjou et al. [4] respectivelyprovided extensive reviews of the widely applied condition monitoring techniquesfor rotating machines and squirrel-cage induction machines. Similarly, a host ofother studies [5–13] have also given details of different vibration-based conditionmonitoring techniques for faults detection in rotating machines, ranging from fullspectrum analysis [5]; wavelet analysis [6]; intelligent order tracking [7]; vibrationsymptoms trend analysis [8]; higher order spectra (HOS) analysis [9–11]; etc.,through the application of measured vibration data.

Relatively recent efforts aimed at simplifying rotating machines conditionmonitoring as well as reducing the number of sensors needed were exploredthrough the development of the coherent composite spectrum (CCS) and coherentcomposite bispectrum (CCB) data fusion (in the frequency domain) techniques [12,13]. Both CCS and CCB techniques showed meaningful diagnosis and fault dif-ferentiation potentials on a relatively rigid rotating machine with several simulatedcases (healthy, misalignment, crack and rub). The current study is also related to thediagnosis of faults in flexibly mounted rotating machines, through the inclusion ofthe new coherent composite trispectrum (CCT) technique (in addition to the earlierCCS and CCB techniques), with the sole aim of minimizing the number of vibrationsensors needed for diagnosis.

In this study, different operational conditions (healthy with residual misalign-ment, shaft misalignment, cracked shaft, bearing looseness, bent shaft and shaftrub) were simulated on two experimental rigs with varying support mountingflexibilities (i.e. flexible support 1 and flexible support 2) at 1,200 RPM (20 Hz)rotational speed, so as to observe the consistency and versatility of the proposedtechnique. Furthermore, vibration data from both flexible supports (FS1 and FS2)were collected using a single sensor (accelerometer) at each bearing pedestal in thediagonal direction. The measured vibration data were then used for computing theCCS, CCB and CCT for the individual machines through data fusion in the fre-quency domain, which aims to eliminate the need for computations at individualmachine bearings. Hence, the results and observations of the CCS, CCB and CCTfor FS1 and FS2 are discussed in the paper.

146 A. Yunusa-Kaltungo and J.K. Sinha

2 CCS, CCB and CCT Computations

The potentials of CCS and CCB data fusion techniques for the diagnosis of faultsrelated to rotating machines were initially presented in earlier studies by Elbhbahet al. [12] and Sinha et al. [13]. In the current study however, the use of CCT isproposed for the diagnosis of different simulated cases on two flexibly supportedexperimental rigs (FS1 and FS2), with the aim of further simplifying faults diagnosis.Hence, the computational approaches of CCS, CCB and CCT are discussed here.

Assuming that vibration measurements were collected at “b” number of bearinglocations on a rotating machine, and the measured data were divided into “ns”number of equal segments, then the CCS for the entire machine was computed as[12, 13];

SCCS fkð Þ ¼Pns

r¼1 XrCCS fkð ÞXr�

CCS fkð Þns

ð1Þ

where XrCCS fkð Þ and Xr�

CCS fkð Þ are respectively the coherent composite FourierTransformation (FT) and its complex conjugate for the rth segment of the measuredvibration data collected from “b” number of bearings at frequency, fk . Xr

CCS fkð Þ isthus computed as [12, 13];

XrCCS fkð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Srx1c212x2fkð ÞSrx2c223x3 fkð ÞSrx b�1ð Þc2b�1ð Þbxb

fkð Þ� � 1

b�1ð Þs

ð2Þ

In Eq. 2, c212; c223 and c2b�1ð Þb respectively represent the coherence between

bearings 1–2, 2–3, …, (b−1)−b. Also, Srx1c212x2fkð Þ Srx2c223x3 fkð Þ Srx b�1ð Þc2b�1ð Þbxb

fkð Þrespectively denote the coherent cross-power spectrum between bearings 1–2, 2–3,…, (b−1)−b, which was computed as [12, 13];

Srx1c212x2fkð Þ ¼ Xr

1 fkð Þc212Xr�2 fkð Þ� � ð3Þ

HOS [9, 10], mainly bispectrum and trispectrum provide information about therelationship between frequency components in a time domain signal xðtÞ. Thebispectrum represents a combination of two frequencies (each having amplitude andphase), fl and fm with a third frequency fl þ fm which is equal to the sum of the priortwo. Similarly, the trispectrum represents a combination of three frequencies (eachhaving amplitude and phase), fl, fm and fn with a fourth frequency fl þ fm þ fn whichis equal to the sum of the prior three. Hence, the CCB and CCT for the measuredvibration data were computed as [11, 13];

B fl; fmð Þ ¼Pns

r¼1 XrCCS flð ÞXr

CCS fmð ÞXrCCS

� ðfl þ fmÞ� �

nsð4Þ

Coherent Composite HOS Analysis of Rotating Machines… 147

T fl; fm; fnð Þ ¼Pns

r¼1 XrCCS flð ÞXr

CCS fmð ÞXrCCS fnð ÞXr

CCS� ðfl þ fm þ fnÞ

� �

nsð5Þ

3 Experimental Rigs

Two sets of flexibly supported experimental rigs (Figs. 1, 2) have been used tosimulate different cases of typical rotating machines. Although both experimentalrigs are made up of similarly dimensioned components, however, their dynamicproperties differ significantly, due to the varying stiffness of their supports. In bothset-ups, two mild steel shafts (1,000 and 500 mm lengths respectively) of 20 mmdiameters are rigidly coupled together. The 1,000 mm shaft is then coupled to a0.75 kW electric motor, while the entire rotor assemblies are supported by 4 anti-friction bearings, using 10 and 6 mm diameter threaded bars respectively. Also,there are three mild steel balance discs of dimensions 125 mm (outside diameter) ×15 mm (thickness), with two of the discs fitted on the long shaft (first disc is300 mm from the drive motor and the second is 190 mm from the second bearing)and the third on the shorter shaft (210 mm from both bearings 3 and 4). In Fig. 2,a–m respectively represent accelerometer, rigid coupling, shaft, balance disc,bearing flange, threaded bar, anti-friction ball bearing, flexible coupling, tachom-eter, electric motor, motor base, lathe bed and neoprene rubber pad.

4 Experimental Simulation of Faults

The experiments were conducted on two different set-ups (FS1 and FS2) at a rota-tional speed of 1,200 RPM (20 Hz) for a total of six cases, namely; healthy withresidual misalignment (HRM), shaft misalignment (SM), cracked shaft (CS), bearinglooseness (BL), bent shaft (BS) and shaft rub (SR). According to the authors’experience with long slender shafts, it is usually very difficult to achieve a perfectalignment; owing to the fact that such shafts are sometimes slightly bowed, whichcould cause alignment problems. Therefore, the HRM case represents the baselinecase. A 0.4 mm shim was used to introduce misalignment in the vertical directionnear bearing 1 (SM case). A 4 mm (depth) × 0.25 mm (width) breathing crack wasinduced on the 1,000 mm shaft at a distance of 160 mm from bearing 1 (CS case).The BL case was studied by loosening the threaded bar nuts on bearing 3. A centreline run-out of 3.4 mm was created on the 1,000 mm shaft for the BS case. The SRcase was simulated using 2 Perspex blades placed at 275 mm from bearing 1.Vibration responses were then collected from both set-ups, using 4 accelerometersper set-up (i.e. one accelerometer per bearing in the diagonal direction, so as toacquire vibration data representing both vertical and horizontal directions), and thenrecorded on to a PC for eventual analysis using a MATLAB code.


Fig. 1 Typical flexible bearing pedestals with anti-friction ball bearings: a FS1 (10 mm threadedbars) and b FS2 (6 mm threaded bars)

Fig. 2 Schematic representation of experimental rig (all dimensions in mm)


5 Data Analysis and Results

Figures 3, 4 and 5 show typical CCS, CCB and CCT plots of the measuredvibration data for two (HRM and BL) of the six experimentally simulated cases, onboth set-ups at 20 Hz speed, which were computed as per Eqs. (1)–(5). Themeasured vibration data were analysed using a 95 % overlap, frequency resolution(df ) = 1.2207 Hz, sampling frequency (fs) = 10,000 Hz and number of data points(N) = 8,192.

The CCS plots (Fig. 3), clearly show a distinction between the two cases (HRMand BL) on both FS1 (Fig. 3a, c) and FS2 (Fig. 3b, d). On both set-ups, BL casewas characterized by several higher harmonics of the machine speed with corre-spondingly higher amplitudes when compared to the HRM case. The compositeHOS (CCB and CCT) plots in Figs. 4 and 5 show the relation between differentfrequency components (each having amplitude and phase) in the measured vibra-tion data. For instance, B11 CCB component (Fig. 4) denotes the relation between1× (twice) and 2× frequency components, while B12 denotes the relation between1×, 2× and 3× frequency component, and so on. Similarly, T111 CCT component(Fig. 5) denotes the relation between 1× (thrice) and 3× frequency components inthe measured vibration data and so on. It can be seen that CCS, CCB and CCT plotsprovides a distinction between the different experimentally simulated cases.Additionally, a set of 20 measurements have been collected for each of theexperimentally simulated cases at 20 Hz speed, for which the CCB and CCT foreach set of data was computed as per Eqs. (1)–(5). Figure 6 shows plots of the

Fig. 3 Typical coherent composite spectra (CCS): a HRM (FS1), b HRM (FS2), c BL (FS1), andd BL (FS2)


Fig. 4 Typical coherent composite bispectra (CCB): a HRM (FS1), b HRM (FS2), c BL (FS1),and d BL (FS2)

Fig. 5 Typical coherent composite trispectra (CCT): a HRM (FS1), b HRM (FS2), c BL (FS1),and d BL (FS2)


magnitudes of T111 CCT component against the magnitudes of B11 CCB compo-nent for all cases, so as to ascertain the capabilities of CCB and CCT in faultsdiagnosis, which has been observed to show encouraging classification potentialsfor the different cases.

6 Conclusion

The current research has explored the possibilities of using CCS, CCB and thenewly introduced CCT data fusion techniques for the diagnosis of differentexperimentally simulated cases on flexibly supported rotating machines, using areduced number of vibration sensors. The experimental results have also shownencouraging possibilities of rotating machines’ faults identification and differenti-ation, through the application of a combination of very few CCB and CCT com-ponents amplitudes. However, further experiments are planned at differentmachines’ speeds, so as to further boost the certainty of the techniques.

References

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2. Sinha JK (2002) Health monitoring techniques for rotating machinery. Ph.D. thesis, Universityof Wales (Swansea University), Swansea, UK

3. Jardine AKS, Lin D, Banjevic D (2006) A review on machinery diagnostics and prognosticsimplementing condition-based maintenance. Mech Syst Signal Process 20(2006):1483–1510

10-4

10-3

10-2

10-1

100

10-4

10-3

10-2

10-1

T111

Magnitude

B11

Mag

nit

ud

e

(a)

10-4

10-2

100

102

10-3

10-2

10-1

100

101

T111

Magnitude

B11

Mag

nit

ud

e

(b)

Fig. 6 Typical plots of T111 CCT versus B11 CCB components amplitudes: a FS1 and b FS2


4. Mehrjou MR, Mariun N, Marhaban MH, Misron N (2011) Rotor fault condition monitoringtechniques for squirrel-cage induction machine—a review. Mech Syst Signal Process 25(2011):2827–2848

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11. Yunusa-Kaltungo A, Sinha JK, Elbhbah K (2013) HOS analysis of measured vibration data onrotating machines with different simulated faults. Advances in condition monitoring ofmachinery in non-stationary operations, Chap. 6 (Proceedings of the International Conferenceon Condition Monitoring of Machinery in Non-Stationary Operations 2013). SpringerPublishing, Series: 11236. ISBN: 978-3-642-39347-1

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[mechanisms and machine science] vibration engineering and technology of machinery volume 23 ||...

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