Vibration-based Condition Monitoring E-Book

Robert Bond Randall

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 817

Veröffentlichungsjahr: 2021

Beschreibung

Vibration-based Condition Monitoring

Stay up to date on the newest developments in machine condition monitoring with this brand-new resource from an industry leader

The newly revised Second Edition of Vibration-based Condition Monitoring: Industrial, Automotive and Aerospace Applications delivers a thorough update to the most complete discussion of the field of machine condition monitoring. The distinguished author offers readers new sections on diagnostics of variable speed machines, including wind turbines, as well as new material on the application of cepstrum analysis to the separation of forcing functions, structural model properties, and the simulation of machines and faults.

The book provides improved methods of order tracking based on phase demodulation of reference signals and new methods of determining instantaneous machine speed from the vibration response signal. Readers will also benefit from an insightful discussion of new methods of calculating the Teager Kaiser Energy Operator (TKEO) using Hilbert transform methods in the frequency domain.

With a renewed emphasis on the newly realized possibility of making virtual instruments, readers of Vibration-based Condition Monitoring will benefit from the wide variety of new and updated topics, like:

• A comprehensive introduction to machine condition monitoring, including maintenance strategies, condition monitoring methods, and an explanation of the basic problem of condition monitoring
• An exploration of vibration signals from rotating and reciprocating machines, including signal classification and torsional vibrations
• An examination of basic and newly developed signal processing techniques, including statistical measures, Fourier analysis, Hilbert transform and demodulation, and digital filtering, pointing out the considerable advantages of non-causal processing, since causal processing gives no benefit for condition monitoring
• A discussion of fault detection, diagnosis and prognosis in rotating and reciprocating machines, in particular new methods using fault simulation, since “big data” cannot provide sufficient data for late-stage fault development

Perfect for machine manufacturers who want to include a machine monitoring service with their product, Vibration-based Condition Monitoring: Industrial, Automotive and Aerospace Applications will also earn a place in university and research institute libraries where there is an interest in machine condition monitoring and diagnostics.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Dedication

Foreword

About the Author

Preface to The Second Edition

About the Companion Website

1 Introduction and Background

1.1 Introduction

1.2 Maintenance Strategies

1.3 Condition Monitoring Methods

1.4 Types and Benefits of Vibration Analysis

1.5 Vibration Transducers

1.6 Torsional Vibration Transducers

1.7 Condition Monitoring – The Basic Problem

References

2 Vibration Signals from Rotating and Reciprocating Machines

2.1 Signal Classification

2.2 Signals Generated by Rotating Machines

2.3 Signals Generated by Reciprocating Machines

References

3 Basic Signal Processing Techniques

3.1 Statistical Measures

3.2 Fourier Analysis

3.3 Hilbert Transform and Demodulation

3.4 Digital Filtering

3.5 Time/Frequency Analysis

3.6 Cyclostationary Analysis and Spectral Correlation

References

4 Fault Detection

4.1 Introduction

4.2 Rotating Machines

4.3 Reciprocating Machines

References

5 Some Special Signal Processing Techniques

5.1 Order Tracking

5.2 Determination of Instantaneous Machine Speed

5.3 Deterministic/Random Signal Separation

5.4 Minimum Entropy Deconvolution

5.5 Spectral Kurtosis and the Kurtogram

References

6 Cepstrum Analysis Applied to Machine Diagnostics

6.1 Cepstrum Terminology and Definitions

6.2 Typical Applications of the Real Cepstrum

6.3 Modifying Time Signals Using the Real Cepstrum

References

7 Diagnostic Techniques for Particular Applications

7.1 Harmonic and Sideband Cursors

7.2 Gear Diagnostics

7.3 Rolling Element Bearing Diagnostics

7.4 Reciprocating Machine and IC Engine Diagnostics

References

8 Fault Simulation

8.1 Background and Justification

8.2 Simulation of Faults in Gears

8.3 Simulation of Faults in Bearings

8.4 Simulation of Faults in Engines

References

9 Fault Trending and Prognostics

9.1 Introduction

9.2 Trend Analysis

9.3 Advanced Prognostics

9.4 Future Developments

References

Appendix: Exercises and Tutorial Questions

Introduction

A.1. Introduction and Background

A.2. Vibration Signals from Machines

A.3. Basic Signal Processing

A.4. Fault Detection

A.5. Cepstrum Analysis Applied to Machine Diagnostics

A.6. Diagnostic Techniques for Particular Applications

A.7. Prognostics

Index

End User License Agreement

List of Tables

Chapter 2

Table 2.1 Vibration reduction by realignment.

Chapter 3

Table 3.1 Properties of various windows.

Chapter 7

Table 7.1 Planet bearing frequencies.

Chapter 8

Table 8.1 Full reduced FE model – summary of DOFs.

Chapter 9

Table 9.1 Distribution of data with networks from simulation and experiment.

List of Illustrations

Chapter 1

Figure 1.1 Illustration of absolute vs relative vibration.

Figure 1.2 Proximity probes installed in a turbine bearing cap.

Figure 1.3 Comparison of spectra measured on a centrifugal compressor (a) Proximity probe (b) Accelerometer signal (integrated to displacement).

Figure 1.4 Schematic diagram of one realisation of a velocity pickup.

Figure 1.5 Frequency response of a seismically suspended vibrometer [25]. (a) Amplitude characteristicy (b) Phase characteristic. ζ = critical damping ratio.

Figure 1.6 Typical accelerometer designs (a) Compression type (b) Shear type.

Figure 1.7 Typical frequency and dynamic ranges for the three main transducer types with superimposed ranges for an accelerometer and integrator.

Figure 1.8 Illustration of a number of measured responses of a system due to a number of excitation sources.

Figure 1.9 Combination of forcing function and transfer path to give response vibration for one source.

Figure 1.10 Comparison of the spectra of discrete frequency components at 400, 800, and 1200 Hz with that of a narrow band resonance at 1000 Hz.

Chapter 2

Figure 2.1 Signal types.

Figure 2.2 Ensemble averaging.

Figure 2.3 Typical signals in the time and frequency domains.

Figure 2.4 Operation of a gear coupling.

Figure 2.5 Example of the improvement given by realignment.

Figure 2.6 Effect of unbalance location on cracked rotor response (Ref. [13]).

Figure 2.7 Increasing response at critical speed caused by growth of a crack (Ref. [14]).

Figure 2.8 Generation of exact half order components (and harmonics) due to loose assembly of a journal bearing in a centrifugal compressor.

Figure 2.9 Basic dimensions of a pair of spur gears.

Figure 2.10 Illustration of Mark's division of TE into elemental functions in terms of Legendre polynomials, both axially, and along the tooth profile.

Figure 2.11 Typical individual error components for tooth spacing error [25] (a) Error spectrum (b) Corresponding mesh transfer function Reprinted by permission of the Acoustical Society of America.

Figure 2.12 Typical double‐scalloped wear pattern from sliding on either side of the pitch circles.

Figure 2.13 Comparison of the effects of local and distributed faults in gears in the time and frequency domains.

Figure 2.14 Illustration of the generation of ghost components.

Figure 2.15 Effect of load on ghost and toothmesh components.

Figure 2.16 Effects of wear on toothmesh and ghost components.

Figure 2.17 Typical signals and envelope signals from local faults in rolling element bearings.

Figure 2.18 Bearing fault pulses with and without random fluctuations (a, d) Time signals (b, e) Raw spectra (c, f) Envelope spectra.

Figure 2.19 Typical modulating signal from the effect of an extended inner race fault on a gear signal.

Figure 2.20 Load variation to distinguish the cause of an observed effect.

Figure 2.21 Use of FFT zoom to separate the harmonics of shaft speed from those of mains (line) frequency in an induction motor vibration spectrum. (a) Baseband spectrum with zoom band around 100 Hz highlighted (b) Zoom spectrum showing that twice mains frequency dominates over twice shaft speed.

Figure 2.22 Illustration of the various frequencies associated with a fault on the stator or rotor of an induction motor.

Figure 2.23 Example of a rotor fault on an induction motor, showing modulation sidebands around the shaft speed component of 29.75 Hz (spacing 1 Hz).

Figure 2.24 Cross‐section through a gas engine/compressor.

Figure 2.25 Time‐frequency analysis procedure.

Figure 2.26 Time‐frequency diagrams for the compressor of Figure 2.24 in single‐ and double‐acting modes. BDC = Bottom dead centre; TDC = top dead centre.

Figure 2.27 Averaged spectra for the two signals of Figure 2.26.

Figure 2.28 Time‐frequency diagrams for different measurement positions on an engine.

Figure 2.29 Angular velocity fluctuations for a misfire in one cylinder.

Chapter 3

Figure 3.1 Random signal.

Figure 3.2 Probability distribution for a random signal with maximum value

x

max

and minimum value

x

min

.

Figure 3.3 Probability density function for the Gaussian distribution.

Figure 3.4 Representation of a sinusoid as a sum of two rotating vectors.

Figure 3.5 Equivalence of the vector sum of positive and negative frequency components, and projection on the real axis of a positive frequency component.

Figure 3.6 Various forms of the Fourier transform (a) Fourier integral transform (b) Fourier series (c) Sampled functions (d) Discrete Fourier transform.

Figure 3.7 Matrix representation of the DFT (note the rotated real and imaginary axes).

Figure 3.8 Modified matrix B, with rows shifted to bit‐reversed address.

Figure 3.9 Matrix B factorised into three factor matrices X, Y, Z.

Figure 3.10 Running average as a convolution.

Figure 3.11 Convolution with delta functions.

Figure 3.12 Spectrum of a squared cosine by convolution.

Figure 3.13 Spectrum of a half cosine pulse by convolution.

Figure 3.14 FRF of a SDOF system by convolution.

Figure 3.15 Representations of the FRF of a SDOF system.

Figure 3.16 Fourier series of a half‐wave rectified cosine from the Fourier transform of a half‐cosine pulse.

Figure 3.17 Autocorrelation vs autospectrum for three signals. Note that spectrum of (c) is the convolution of (a) and (b).

Figure 3.18 Schematic diagram of FFT zoom process.

Figure 3.19 Three steps in passing from the FT to the DFT (a–c) Time sampling (d, e) Truncation (f, g) Frequency sampling.

Figure 3.20 (a) Time signal correctly lowpass filtered (b) Spectrum of (a) (c) Time signal without lowpass filtration (d) Spectrum of (c) (note aliasing).

Figure 3.21 How frequency sampling affects the apparent filter characteristic of a window. (a) Extra half period in record; (b) Integer number of periods in record (Courtesy Brüel & Kjær)

Figure 3.22 Data windows for continuous signals ([9]). (a) Rectangular (b) Hanning (c) Kaiser‐Bessel (d) Flat top.

Figure 3.23 Compensation for the picket fence effect with a Hanning window ([4]). ΔdB = difference between two highest spectrum samples. ΔL = picket fence error. Δf = frequency error (a), (b), (c) Minimum, maximum, and intermediate error cases (d) Error nomogram.

Figure 3.24 Decomposition of a causal signal into even and odd components, and relationships in the time and frequency domains.

Figure 3.25 Manipulation of the positive frequency spectrum to obtain a real time signal.

Figure 3.26 Analytic signal for an amplitude modulated cosine [4].

Figure 3.27 Analytic signal for a phase/frequency modulated cosine [4].

Figure 3.28 Phase relationships of the sidebands for amplitude modulation [4].

Figure 3.29 Phase relationships of the sidebands for phase modulation [4].

Figure 3.30 Procedure for demodulation by shifting the carrier frequency and reducing the transform size.

Figure 3.31 Effect of repeatedly halving the sampling frequency.

Figure 3.32 Conversion from FFT spectra to a CPB spectrum.

Figure 3.33 Comparison of time‐frequency distributions for a diesel engine vibration signal (a) STFT (b) Wigner‐Ville distribution (c) Smoothed pseudo Wigner‐Ville.

Figure 3.34 Example of advanced wavelet denoising (a) Raw vibration signal; denoised signal using NeighCoeff shrink based on (b) DTCWT, (c)

DWT

(

discrete wavelet transform

) and (d)

SGWT

(

second‐generation wavelet transform

).

Figure 3.35 Filter characteristics of the octave band Morlet wavelet filters.

Figure 3.36 Comparison of two wavelet types for the analysis of a small crack in a gear (a) Real Morlet wavelets (b) Impulse wavelets.

Figure 3.37 Extraction of IMFs of a tone plus chirp.

Figure 3.38 Example of amplitude modulated white noise (from Antoni [32]) (a) time signal over four periods of cyclic frequency (b) Two‐dimensional autocorrelation function vs time (sample)

n

and time lag

τ

.

Figure 3.39 Spectral correlation for the case of Figure 3.38. Source: From Antoni [32]. (a) First transformation from

τ

to

f

(b) Result of two transforms.

Figure 3.40 Spectral correlation for a mixture of first and second order cyclostationarity illustrated using modulation by gear and bearing signals (a) gearmesh modulation by a gear signal (b) gearmesh modulation by an extended inner race bearing fault (c) spectral correlation for case (b).

Figure 3.41 Spectral correlation and spectrum of the squared envelope for a local bearing fault.

Figure 3.42 Impulse response of a nonlinear SDOF system excited by a burst random signal, expressed as a Wigner‐Ville spectrum (WVS) and compared with the Wigner‐Ville distribution (WVD) with interference components [37].

Figure 3.43 Bearing fault responses for varying machine speed [39]. (a) In time domain (b) In angle domain.

Figure 3.44 Development of order‐frequency spectral correlation [40].

Chapter 4

Figure 4.1 General machinery criterion chart [3].

Figure 4.2 Table C.1 from ISO Standard 20816‐1 [6] giving the recommended ranges of boundary values for different vibration severity zones, in terms of RMS velocity measured on non‐rotating parts of rotating machines in different classes. By permission of Standards Australia on behalf of ISO under Licence CL2020rbr.

Figure 4.3 Overall impedance envelope measured on 14 machines in an ethylene plant [8].

Figure 4.4 Direct digital comparison of two spectra with no change in machine condition.

Figure 4.5 Generation of a mask spectrum from an original measured spectrum.

Figure 4.6 FFT spectrum comparison with a small speed change.

Figure 4.7 Spectrum comparison using CPB spectra.

Figure 4.8 (Upper) Comparison of new spectrum with mask, velocity dB re 1 × 10

−6

 m s

−1

. (Lower) dB difference spectrum.

Figure 4.9 Spectrum comparisons for a ball mill in a copper mine.

Figure 4.10 FFT spectra for the ball mill drive in original and deteriorated condition.

Figure 4.11 Table A.1 from ISO Standard 10 816‐6 [12] giving recommended vibration limits for reciprocating machines. By permission of Standards Australia on behalf of ISO under Licence CL2020rbr.

Figure 4.12 Time‐frequency diagrams for the compressor of Figure 2.24 in single‐ and double‐acting modes. The comparison diagram at bottom left shows maximum decreases of the order of 20 dB. (

BDC

 = 

Bottom dead centre

; TDC = top dead centre).

Figure 4.13 Effect of a misfire in a gas engine.

Figure 4.14 Effect of increased piston clearance in a diesel engine.

Figure 4.15 Comparison of sound signals for the same case as Figure 4.14.

Figure 4.16 Proximity probe (indicated) used to detect the passage of ring gear teeth.

Figure 4.17 Spectrum of ring gear signal for a spark ignition engine with a complete misfire in one cylinder.

Figure 4.18 Demodulation of the first harmonic of the encoder signal in Figure 4.17 (a) Phase demodulation. (b) Frequency demodulation (angular velocity).

Figure 4.19 Spectrum of typical phase modulation signal.

Figure 4.20 Partial misfire caused by a loose spark plug in Cyl. 6.

Figure 4.21 Effects of different full and partial misfires in cyl. 1 on the torsional vibration for a 6‐cylinder spark ignition engine (a) spark plug disconnected (b) leak in inlet manifold (c) simulated ‘burnt valve’.

Chapter 5

Figure 5.1 Resample times for equal angle increments.

Figure 5.2 Linear interpolation by convolution of samples with a triangle.

Figure 5.3 Digital resampling with four times higher sampling frequency. (a) Signal sampled at f

s1

and its spectrum (b) Addition of zeros which changes sampling frequency to f

s2

(c) Lowpass filtration and rescaling.

Figure 5.4 Comparison of frequency characteristics for interpolation at different orders. Source: from [1].

Figure 5.5 Envelope of permissible combinations of frequency deviation and modulation frequency. Source: from [4].

Figure 5.6 (a) Phase modulation sidebands for a tacho signal with two harmonics of the fundamental frequency (b) PDF for a sinusoid. Source: from [4].

Figure 5.7 Signals with ±10% speed variation: (a, b) tacho, (c, d) acceleration, (a, c) time signals, (b, d) spectra. Source: from [4].

Figure 5.8 (a), (b) Spectra of order tracked tacho signal using third harmonic of (a) tacho signal (b) acceleration signal; (c) Envelope spectrum of order tracked acceleration signal showing two harmonics of BPFI (ballpass frequency, inner race). Source: from [4].

Figure 5.9 Comparing spectra of order‐tracked tacho from all four stages for ±10% case.

Figure 5.10 Scheme of the algorithm of the method of Ref. [7].

Figure 5.11 Windowing functions for two adjacent segments.

Figure 5.12 Spectrograms (a) Force signal (b) Response acceleration.

Figure 5.13 (a) Low frequency part of Figure 5.5 (b) Equivalent modulation frequency.

Figure 5.14 Spectra of segment tacho signals (a) Segment 1 (b) Segment 5.

Figure 5.15 Typical order spectra of response signal after order tracking (a) Segment 1 (b) Segment 5.

Figure 5.16 Overlaid order tracked signals for the five segments (a) Tacho (b) Response.

Figure 5.17 Order spectra of the re‐combined signals (a) Tacho (b) Response.

Figure 5.18 Spectrograms for the order tracked signals (a) Tacho (b) Response signal.

Figure 5.19 Effect of differentiation for a signal with pure AM, and carrier frequency 500 Hz.

Figure 5.20 Effect of transfer function on errors in IAS based on response signal. (a, b) Signal spectrum and FRF; (c, d) % Errors, (oscillating): TKEO, (smooth): Exact; (a, c) Signal spectrum on spring line; (b, d) Signal spectrum on mass line

Figure 5.21 (a) Comparison of speed estimates from acceleration (solid) and tacho (dotted) adjusted for ratio (b) Zoom on end effects for acceleration signal wraparound error (light), smoothed result (solid).

Figure 5.22 Speed estimates using TKEO (Eq. (5.13a)) on a bandpass filtered signal encompassing the first harmonic of the acceleration signal. (a) Raw speed estimate and smoothed version (b) Spectrum of bandpass filtered signal.

Figure 5.23 Use of an exponential lifter to extract the modal part (solid line) of the response acceleration signal.

Figure 5.24 (a) Spectrogram with pre‐whitened noise base (b) PDF of the IAS at each time step, considering fundamental meshing orders (c) PDF of the IAS at each time step, including 10 first harmonics of each fundamental order (d) Final estimate obtained by smoothing (c).

Figure 5.25 Filter (amplitude) characteristic corresponding to 8 synchronous averages. Source: from [20].

Figure 5.26 Use of tracking to avoid smearing of shaft speed related components.

Figure 5.27 Application of synchronous averaging to data of Figure 5.26. (a) Spectrum synchronous with low speed gear (b) Spectrum synchronous with high speed gear (c) Spectrum dominated by bearing fault after effects of two gears removed.

Figure 5.28 Envelope spectra of short time recording (1.29 revolutions) just spanning the first two sections where the inner race fault passes the loading zone [25]. (a) Envelope signal after bandpass filtration in frequency range 2.7 ∼ 3.3 kHz, (b) Envelope spectrum without interpolation, (c) Envelope spectrum with interpolation, (d) Maximum entropy envelope spectrum

Figure 5.29 Schematic diagram of Adaptive Noise Cancellation.

Figure 5.30 Schematic diagram of Self‐Adaptive Noise Cancellation used for removing periodic interference (Widrow and Stearns [27]).

Figure 5.31 Minimum filter order vs number of discrete spectrum components.

Figure 5.32 Application of DRS to a helicopter gearbox vibration signal (a) Original spectrum (zoomed) (b) Amplitude characteristic of filter (c) Spectrum of deterministic part (d) Spectrum of random part.

Figure 5.33 Inverse filtering (deconvolution) process for MED.

Figure 5.34 The effect of processing gear signals for the case of a spall on one tooth (Upper) – time signals (Lower) – Autospectra

Figure 5.35 Example of applying both AR and MED filtering to bearing signals with an inner race fault in a high speed bearing (a) Original time signal (b) After application of AR filtering (c) After additional MED filtering.

Figure 5.36 Calculation of SK from the STFT for a simulated bearing fault signal (a) simulated time signal (b) STFT (c) SK as a function of frequency.

Figure 5.37 Comparison of SK with dB spectrum difference for an inner race bearing fault. Frequency scale normalised to sampling frequency 48 kHz. (a) dB spectrum comparison over frequency range 0‐24 kHz with and without the fault (b) dB spectrum difference (c) Spectral kurtosis.

Figure 5.38 Use of SK as a filter on a signal from a gear test rig with a weak outer race bearing fault. (a) Total signal (b) Output from Wiener filter (c) Output from matched filter. Source: from [42].

Figure 5.39 Kurtogram for signal of Figure 5.38. Source: from [42]. N

W

is window length defining spectral resolution. SK is spectral kurtosis. Maxima are projected onto each plane.

Figure 5.40 (a) Optimal bandpass filter compared with SK (b) Outer race fault signal obtained using the filter of (a). Source: from [42].

Figure 5.41 Combinations of centre frequency and bandwidth for the 1/3‐binary tree kurtogram estimator [43].

Figure 5.42 Comparison of (a) the fast kurtogram with (b) the full kurtogram for an impulsive signal from loose parts monitoring [43].

Chapter 6

Figure 6.1 Showing that an echo gives a periodic component in the signal spectrum.

Figure 6.2 Echo removal using the complex cepstrum [3].

Figure 6.3 Comparison of the complex cepstrum with the impulse response function for a SDOF system.

Figure 6.4 Artefacts affecting the cepstrum. (a) Effect of noise (b) Effect of filter characteristic (c) Effect of vibration parameter.

Figure 6.5 Advantage of the analytic cepstrum for zoom spectra.

Figure 6.6 Comparison of cepstrum and autocorrelation function for the case of a bearing fault.

Figure 6.7 Use of the cepstrum to detect missing blades in a steam turbine [11].

Figure 6.8 Comparison of spectra for low frequency range and of the corresponding cepstra. (a, b) Faulty (c, d) Healthy (a, c) Spectra (b, d) Cepstra.

Figure 6.9 Comparison of spectra for intermediate frequency range and of the corresponding cepstra. (a, b) Faulty (c, d) Healthy (a, c) Spectra (b, d) Cepstra.

Figure 6.10 Comparison of spectra for high frequency range and of the corresponding cepstra. (a, b) Faulty (c, d) Healthy (a, c) Spectra (b, d) Cepstra.

Figure 6.11 Extraction of the complex cepstrum of a transfer function from the response of a beam (a) driving point response autospectrum (b) measured and regenerated cepstra [14].

Figure 6.12 Use of an exponential lowpass lifter to enhance modal information (a) Full cepstrum (of (d)) (b) Exponential lifter (c) Liftered cepstrum (d) Original spectrum (e) Liftered spectrum.

Figure 6.13 Use of liftering in the cepstrum to remove the forcing function component from the cepstra for a gear with and without cracked teeth, leaving the part dominated by the structural transfer functions [15].

Figure 6.14 Schematic diagram of the cepstral method for editing time signals using the real cepstrum and the original phase spectrum.

Figure 6.15 Time domain signals for gearbox test rig Source: From [16]. (a) Raw signal (b) Residual signal after removing the synchronous average. (c) Residual signal after editing the cepstrum to remove the shaft rahmonics.

Figure 6.16 Squared envelope spectra (1–20 kHz) Source: From [16]. (a) raw signal (b) Residual signal (after removing the synchronous average) (c) Residual signal after editing the cepstrum to remove the shaft rahmonics.

Figure 6.17 Log spectra from a wind turbine (a) before and (b) after removal of sidebands.

Figure 6.18 Cepstra corresponding to Figure 6.17. (a) original cepstrum (b) Cepstrum after liftering with a comb notch lifter of notch width ±15%.

Figure 6.19 Spectra of IS TSA average (a) Original including four rotations of the HSS. Harmonics at 88 (HS mesh), sidebands at 4 (HS shaft) (b) Residual after removal of the HSS average. Harmonics at 23 (IS pinion mesh).

Figure 6.20 Cepstra of the IS shaft signal before (a) and after (b) the application of a notch lifter Type 2 to remove HSS rahmonics.

Figure 6.21 Log spectra corresponding to the cepstra of Figure 6.20 (a) Original signal. Harmonics at HS gearmesh. Sidebands at HS shaft speed. (b) Liftered signal. Harmonics at IS pinion mesh frequency.

Figure 6.22 Spectra of the original (a) and ‘liftered’ (b) signal. The thicker line in (a), representing the modal response, which was subtracted in the cepstrum, was produced using an exponential lifter in the cepstrum [20].

Figure 6.23 Effect of liftering on order tracked spectra (a, b) Signal varying around 22 Hz (c, d) Signal varying around 15 Hz (a, c) Original (b, d) Liftered [20].

Figure 6.24 (a) Raw signal (b) DRS‐LP (c) Signal processed by cepstrum pre‐whitening. Source: From [21].

Figure 6.25 Envelope spectra for different processed signals and frequency ranges. (a)–(b) DRS‐LP‐SK (c)–(d) Cepstral whitening. Source: From [21].

Chapter 7

Figure 7.1 Harmonic cursor used to find the number of teeth in a gear pair.

Figure 7.2 Spectrograms in two frequency ranges for wind turbine gearbox. (a) Including 1st harmonic of HS gearmesh. (b) Including 1st harmonic of IS gear mesh.

Figure 7.3 FFT spectra of the raw and order tracked signals: (a) Raw signal (0–3500 Hz). (b) Order tracked raw signal (corresponding 0–3500 Hz in orders of the HSS). (c) Raw (0–500 Hz). (d) Order tracked (corresponding 0–500 Hz in orders of the HSS).

Figure 7.4 HSS harmonics at various levels of zoom (a) the first 25 harmonics (b) A zoom showing harmonics17–24 (c) A zoom around the 20th HS harmonic (3rd stage GMF).

Figure 7.5 ISS harmonics at various levels of zoom (a) the first 130 harmonics (b) A zoom showing harmonics103–122 showing the HS GM frequency at order 113 (c) A zoom on the first 26 IS harmonics, showing the IS GM frequency at order 25 (d) A zoom around the 113th IS harmonic.

Figure 7.6 Comparison of residual signals using different methods [4] (a) Linear prediction (b) Editing spectrum.

Figure 7.7 Illustration showing that as a planet gear passes a particular point on the annulus gear, a particular tooth is in contact with the annulus, and another with the sun gear [5].

Figure 7.8 Demodulation of the second harmonic of the toothmesh frequency for a cracked gear [9]. (a) Time signal after TSA (b) Amplitude modulation signal (c) Phase modulation signal.

Figure 7.9 Transmission error for a gear with a simulated tooth root crack (a) Phase of Gear 1 (b) Phase of Gear 2 (c) TE by subtraction (d) Simulated crack.

Figure 7.10 Enhancement of the fault indication from Figure 7.9c. (a) Forming residual by removing toothmesh harmonics (b) Removing low frequency drift by highpass filtration at half mesh frequency (c) Squared envelope after (a) and (b).

Figure 7.11 Measurement of gear transmission error by phase and frequency demodulation of shaft encoder signals from each gear by zoom demodulation and pulse timing [10]. (Upper) Time signals (Lower) Frequency spectra.

Figure 7.12 Measurement of TE and combined encoder error for 1 : 1 ratio gears [11] (Left) Spur gears (32 teeth) (Right) Helical gears (29 teeth).

Figure 7.13 Measurement of encoder error for gear ratio 32 : 49 [11]. (Upper) TEs measured with swapped encoders for two rotations of the 32 tooth gear. (Lower) Time record and its spectrum of the combined encoder error, extracted by synchronous averaging with respect to the 32 tooth gear.

Figure 7.14 Results of demodulation of the TE signal for a simulated tooth root crack (a) Demodulated amplitude (b) Tacho signal (c) Demodulated phase (d) TE signal.

Figure 7.15 Comparison of demodulation results for TE and acceleration signals (a) Amplitude demodulated TE (b) Tacho signal (c) Amplitude demodulated acceleration (d) Phase demodulated acceleration.

Figure 7.16 Illustration of how a transfer function can change the distribution of amplitude and phase modulation.

Figure 7.17 Spectra of (a) the TE signal and (b) the Acceleration signal.

Figure 7.18 Variation of TE with wear and load for case of tooth pitting.

Figure 7.19 Effect of ‘high‐spots’ on TE under load with mild and severe pitting.

Figure 7.20 Original and filtered TE for a range of speeds and loads (shown). (a–d) Original (e–h) Filtered (Left) 2 Hz (Right) 20 Hz.

Figure 7.21 (a) Differential TE with increasing load at 2 Hz (b) Corresponding differential deflection vs load, and mesh compliance.

Figure 7.22 Illustration of wear depth as absolute geometric transmission error.

Figure 7.23 Absolute TE (low speed, low load) at different wear stages with respect to healthy gear condition (Test 0‐14).

Figure 7.24 Comparison of combined average wear depth calculated using GTE, STE and DTE signals, and from mass loss of the gears.

Figure 7.25 Measured TE for three different faults on one planet gear.

Figure 7.26 Comparison of spectra and cepstra for a worn and reconditioned gearbox. Source: Courtesy Brüel & Kjær.

Figure 7.27 Comparison of spectra and cepstra just after and four years after repair. Source: Courtesy Brüel & Kjær.

Figure 7.28 Spectra and cepstra for two truck gearboxes, one with a fault. Source: Courtesy Brüel & Kjær.

Figure 7.29 Editing in the spectrum to increase the diagnostic power of the cepstrum. (a) original spectrum and cepstrum (b) Spectrum edited to remove low order harmonics (c) Edited spectrum one month later with increased misalignment of the 121 Hz shaft.

Figure 7.30 Editing in the cepstrum to remove a particular family of harmonics. Source: Courtesy Brüel & Kjær.

Figure 7.31 Spectra and cepstra for two measurement points on a gearbox. Source: Courtesy Brüel & Kjær.

Figure 7.32 Use of liftering in the cepstrum to remove the forcing function component from the low quefrency part of the cepstra for a gear with and without cracked teeth, leaving the part dominated by the structural transfer functions [20]. This illustrates that resonance frequencies have changed little.

Figure 7.33 Cepstrum for (a) Noise (b) Positive echo (c) Negative echo.

Figure 7.34 Moving cepstrum integral for an actual spall in a gear tooth [22].

Figure 7.35 Simulated TE for tooth cracks and spalls along with the first and second derivatives to approximate acceleration [23].

Figure 7.36 MCI and echo delay times for two crack depths, using simulation [23].

Figure 7.37 MCI and echo delay times for three spall sizes, using simulation [23].

Figure 7.38 Detection of a tooth root crack from the phase demodulation of the gearmesh frequency for ±10% and ± 25% speed variation: (a, b) 10% case, (c, d) 25% case, (a, c) demodulated amplitude, (b, d) demodulated phase (from [2]).

Figure 7.39 Procedure for envelope analysis using the ‘Hilbert transform’ method [35].

Figure 7.40 Potential aliasing given by squaring and rectifying a sinusoidal signal. With just squaring, but not rectification, aliasing can be avoided by doubling the sampling frequency before squaring.

Figure 7.41 Generation of spectrum of squared envelope (or signal) for three cases (a) Analytic signal (b) Equivalent real signal (c) Frequency shifted real signal Downward arrow indicates complex conjugate [34].

Figure 7.42 Two models for the variation in period of pulses from a localised bearing fault.

Figure 7.43 Frequency spectra for the two models (a) Model 1 (b) Model 2 [40].

Figure 7.44 Generation of a modulating signal by an extended inner race fault in a bearing supporting a gear.

Figure 7.45 Spectral correlation evaluated for cyclic frequency equals shaft speed (a) Localised fault (b) Extended fault.

Figure 7.46 Comparison of spectral correlation evaluated for cyclic frequency equals zero (normal power spectrum) and shaft speed Ω for the depicted extended inner race spall. The fault is only apparent at α = Ω. Discrete frequency components were removed using DRS before the spectral correlation analysis.

Figure 7.47 Semi‐automated procedure for bearing diagnostics.

Figure 7.48 Time signals (one rotation of the carrier), (a) Order tracked signal, (b) Residual signal – passage of the three planets is seen.

Figure 7.49 Wavelet kurtogram for 4 filter banks; namely (3, 6, 12, 24) filters/octave.

Figure 7.50 Squared envelope spectra showing two fault frequencies (a) Cage speed (9.8 Hz) (b) BPFI (117.7 Hz).

Figure 7.51 Damaged planet gear bearing after final disassembly (a) faulty bearing (b) spalled inner race (c) spalled rollers.

Figure 7.52 Wavelet kurtograms (a) Before application of MED (b) After MED.

Figure 7.53 Envelope spectrum of signal of Figure 5.35c showing harmonics of BPFI 1398 Hz, and harmonics and sidebands spaced at shaft speed 196 Hz.

Figure 7.54 Results of applying DRS to signal with faulty bearing (a) Original signal (b) Deterministic part (c) Random part.

Figure 7.55 Effect of optimal SK filtering (a) Time signal (b) Envelope spectrum.

Figure 7.56 Comparison of spectral correlation vs spectral coherence for enhancing the squared envelope spectrum (a) Spectral correlation (b) spectral coherence (c) Squared envelope spectrum (d) Enhanced envelope spectrum.

Figure 7.57 Spectrograms (a) Acceleration point A (b) tacho signal, decimated by 8.

Figure 7.58 PSD spectra over run‐up range (a) Acceleration point A (b) Acceleration point C.

Figure 7.59 Signal envelopes for different methods (Row 1) Original; (Row 2) SK filtered; (Row 3) MED; (Row 4) Exponential liftered.

Figure 7.60 Spectrograms of order tracked raw signals (a) Point A (b) Point C.

Figure 7.62 Envelope spectra at different positions along record; (a) Point A (b) Point C (c) C after MED (d) C after exponential liftering.

Figure 7.63 Gear test rig (a) Overall view (b) Schematic diagram.

Figure 7.64 Application of various techniques in time or angle domains.

Figure 7.65 Speed profile for one variable speed test.

Figure 7.66 Result of applying exponential lifter (light) original (dark) liftered.

Figure 7.67 Order domain cepstra before and after notch liftering to remove discrete components. (a) Quefrency range including three rahmonics of HSS (b) Zoom around HSS.

Figure 7.68 Order domain spectra before and after notch liftering to remove discrete components.

Figure 7.69 SES for 20 Hz variable speed (21 seconds period) after exponential and notch lifters.

Figure 7.70 Squared envelope spectra (SESs) for 20 Hz variable speed (20 second period) after second stage processing of the envelope signal (a) not using kurtogram (b) using kurtogram.

Figure 7.71 Advantage of WVS for diesel engine diagnostics (a) WVD for normal condition (including deterministic components) (b) WVS for normal condition (deterministic components removed) (c) WVS with blocked injector in one cylinder (d) WVS with open injector.

Figure 7.72 Diagnostics of a reciprocating compressor (a) WVS (b) STFT (c) Pressure on forward and backward strokes (d) Accelerometer signal (e) WVD for one cycle. Legend: a – forward stroke, b – backward stroke. 1, 2 – opening, closing of discharge valve. 3, 4 – opening, closing of suction valve.

Figure 7.73 Single cylinder air‐cooled diesel engine with accelerometer placement.

Figure 7.74 Typical pressure and acceleration signals and the time window used to extract them.

Figure 7.75 Coherence between pressure and acceleration at different measurement points.

Figure 7.76 Results of inverse filtering for 2400 rpm and three loads (a,d,g) Filter generated at 100% load (b,e,h) Filter generated at 75% load (c,f,i) Filter generated at 50% load (a,b,c) Signal recovered for 100% load (d,e,f) Signal recovered for 75% load (g,h,i) Signal recovered for 50% load.

Figure 7.77 Coherence for the FRF averaged over two speeds and three loads.

Figure 7.78 Results of inverse filtering for filter averaged over two speeds and three loads (a) 2400 rpm, 100% load (b) 3000 rpm, 100% load (c) 2400 rpm, 75% load (d) 3000 rpm, 75% load (e) 2400 rpm, 50% load (f) 3000 rpm, 50% load.

Figure 7.79 Reconstructed (dotted) and measured (solid) pressure signals for (a) Light knock (b) Medium knock (c) Heavy knock.

Figure 7.80 Recovered piston slap using faulty piston: a, b; Two of the three measured signals when there are fuel injection and combustion; c; Recovered piston slap; d, e; Two of the three measured signals when there is no fuel injection; f; Recovered piston slap.

Chapter 8

Figure 8.1 (a) Spur gear test rig (b) Schematic diagram of the test rig.

Figure 8.2 LPM of parallel shaft gearbox in Figure 8.1 for gear vibrations only.

Figure 8.3 Detail of LPM showing the meshing gears.

K

mb

(θ)

: Position dependent variable stiffness;

C

: Damping;

e

t

(θ)

: Combined effect of gear geometrical errors and misalignment;

h

t

(θ)

: A switch representing the contact status of the meshing gear.

Figure 8.4 Definitions of fault geometry (a) crack (b) spall.

Figure 8.5 The RMEs for gears with (a) a tooth crack and (b) a spall.

Figure 8.6 Measured properties for spall and crack.

Figure 8.7 Effect of load with spall and crack (a, b, c) Spall (d, e) Crack.

Figure 8.8 Definition of parabolic line defining the effective thickness of the tooth for different crack depths.

Figure 8.9 Lumped parameter model of a planetary gear (five planets) with both torsional and lateral DOFs.

Figure 8.10 The planetary gear test rig at UNSW. (a) photo; (b) schematic diagram ([12]).

Figure 8.11 Simulated vs measured TE for planetary gear faults (a, c, e) Simulations (b, d, f) Measurements (a, b) Spall – ring gear (c, d) Spall – sun gear (e, f) Crack.

Figure 8.12 Detail of a rectangular simulated spall in the load zone of the outer race. (a) spall geometry and loaded balls (b) trajectory of ball passing through spall.

Figure 8.13 Power spectrum comparison for good and outer race defect bearings. (a) simulated, (b) experimental.

Figure 8.14 Filtered response signals for an outer race fault and their envelope spectra (a, c) Simulated (b, d) Measured (a, b) Time signals (c, d) Envelope spectra.

Figure 8.15 Filtered response signals for a ball fault and their envelope spectra. (a, c) Simulated; (b, d) Measured; (a, b) Time signals; (c, d) Envelope spectra.

Figure 8.16 Extended rough inner race fault (a) ground surface (b) Modelled profile.

Figure 8.17 Cyclic spectrum comparisons. (a, b) measured. (c, d) simulated. (a, c)

α

 = 0, corresponding to power spectra; (b, d)

α

 = 10 Hz, rotation speed.

Figure 8.18 FE model – (a) gearbox casing (b) internals.

Figure 8.19 Evaluation of total response from reduced models.

Figure 8.20 Pre‐processed time signals from simulated data for localised faults. (a, c, e) Inner race fault; (b, d, f) Outer race fault; (a, b) Three consecutive fault impacts; (c, d) zoom on central event; (e, f) Trajectory of ball centre, showing that impact event occurs at lowest position.

Figure 8.21 Pre‐processed time signals from test data for localised faults. (a, c) Inner race fault; (b, d) Outer race fault; (a, b) Three consecutive fault impacts; (c, d) zoom on central event.

Figure 8.22 Casing suspension and accelerometer locations.

Figure 8.23 Relative thickness change in updated model.

Figure 8.24 Mode shape comparisons, test vs updated FE. (a) Mode shape pair 02; (FEA 350.77 Hz, EMA 345.68 Hz, MAC 88.7%). (b) Mode shape pair 10; (FEA 930.52 Hz, EMA 882.92 Hz, MAC 84.4%).

Figure 8.25 Comparison of PSD spectra and squared envelope spectra for local inner race fault. (a, b) Test results; (c, d) Simulation; (a, c) PSD spectra (b, d) Envelope spectra.

Figure 8.26 SCD comparisons for healthy case and extended inner race fault, before and after removal of discrete gear harmonics. (a, b) before removal (c, d) after removal.

Figure 8.27 Measured spectral correlation density before and after comparable extended inner race fault, though with shaft speed 15 Hz and with non 1 : 1 gear ratio.

Figure 8.28 Torsional model of crankshaft.

Figure 8.29 Mode shapes and natural frequencies. (a–d) Mode shapes 1–4, respectively. The table gives the estimated frequencies for modes 1–5, and compares them with observed frequencies (described above).

Figure 8.30 Torsional vibration resonances from run‐up (a) Spectrogram (b) Integrated power spectrum.

Figure 8.31 Wiebe model vs measured cylinder pressure.

Figure 8.32 Waveforms obtained by adjusting frequency and damping parameters.

Figure 8.33 Test engine (a) Photograph (b) Accelerometer layout.

Figure 8.34 Typical signals for the engine at constant speed.

Figure 8.35 Pressure curves for normal and misfire conditions.

Figure 8.36 Measured and simulated crankshaft angular velocities.

Figure 8.37 Polar diagrams of the experimental and simulated torsional vibration for two torques and misfires in cylinder 1 (for 1500 and 3000 rpm).

Figure 8.38 Measured and simulated pseudo angular accelerations of the block for healthy condition and misfire in Cylinder 1.

Figure 8.39 Polar diagrams of the experimental and simulated pseudo angular acceleration for misfires in cylinder1 (for 1500 and 3000 rpm).

Figure 8.40 Forces causing lateral piston motion after TDC.

Figure 8.41 Impact model between piston and cylinder wall.

Figure 8.42 Measurement of transfer paths for piston slap (a) and bearing knock (b).

Figure 8.43 Simulated and experimental envelope signals for two levels of excessive clearance (3× and 6×).

Figure 8.44 Modelled piston connecting rod system (a) oversized big end bearing clearance (b) expanded view showing forces.

Figure 8.45 Interaction between kinematic/kinetic system and lubrication system.

Figure 8.46 Experimental transfer function for bearing knock from cyl2 to acc5.

Figure 8.47 Comparison of measured and simulated envelope signals for first and second stage bearing knock, at 3000 rpm and 80 Nm load.

Chapter 9

Figure 9.1 A trend of the data from Figure 4.7 of Chapter 4.

Figure 9.2 Trend curves for two different speeds of a blower drive shaft.

Figure 9.3 Trending of a frequency band indicating a bearing fault.

Figure 9.4 Trending of frequency components from a bearing fault. (a) two individual harmonics (b) a band including several harmonics.

Figure 9.5 Spectra and cepstra for measurements on an auxiliary gearbox [10].

Figure 9.6 Trend of cepstrum values for the case of Figures 9.4 and 9.5.

Figure 9.7 (a) Accumulated metal wear debris. (b) Kurtosis of the filtered signal.

Figure 9.8 The development of kurtosis with and without MED for a high speed bearing, compared against fault size.

Figure 9.9 Typical trend of crest factor (and kurtosis) with fault development.

Figure 9.10 Trend of SK for another high speed bearing.

Figure 9.11 (a) Model of rolling element travelling into a fault. (b) A typical measured response [18].

Figure 9.12 Bandpass filtered trace from a helicopter gearbox [19].

Figure 9.13 Outer race bearing fault signal (a) before MED filtering (b) after MED filtering.

Figure 9.14 A single entry/exit event for a faulty bearing in the same test rig as Figure 9.13.

Figure 9.15 Simulated spalls in the inner race (a) Location in one race (b) Small spall (0.6 mm) (c) Large spall (1.1 mm).

Figure 9.16 Entry/exit events for small and large inner race spalls.

Figure 9.17 Effect of the first three processing stages.

Figure 9.18 Results from alternative procedure (a) small spall (b) large spall.

Figure 9.19 The proposed approach applied to a spall of size 1.6 mm (0.0045s in time): (a) WVS averaged over multiple ball pass occurrences; (b) instantaneous power; (c) WVS normalised by instantaneous power; (d) average frequency of the normalised WVS; (e) standard deviation of the normalised WVS. Source: From [24].

Figure 9.20 Comparison of spall size estimation methods. (a) The spall (aligned approximately according to the impact event in the centre) corresponding to the dotted lines in the remaining figures; (b) The measured vibration signal in time domain; (c) Sawalhi's method to reveal the entry and impact points; (d) Smith's method (gradient); (e) Moazen's method to reveal the entry and exit points; (f) The natural frequency variation method by using WVS.

Figure 9.21 Comparison of spall size estimation methods for extended spall (5.92 mm). (a) The size of extended spall; (b) The raw vibration signal, (c) Sawalhi's method to reveal the entry and impact points, (d) Smith's method (gradient), (e) Moazen's method to reveal the entry and exit points, (f) The proposed approach by using WVS.

Figure 9.22 Prognostic method types [30].

Figure 9.23 Illustration of how the uncertainty of estimation of RUL can be improved on the basis of an estimate of current degradation [31].

Figure 9.24 Graph of trended parameter vs Operating age for a particular case, and the prediction outputs of survival probability for the proposed prognostic model [33].

Figure 9.25 Structure of the three‐stage ANN system.

Figure 9.26 Output of MLP1 for the piston slap faults.

Figure 9.27 Output of MLP2 for the piston slap faults.

Figure 9.28 Output of MLP1 for the bearing knock faults.

Figure 9.29 Output of MLP2 for the bearing knock faults.

Figure 9.30 Simulated vs experimental wear profiles [42].

Figure 9.31 Proposed vibration‐based scheme for updating wear prediction [46].

Figure 9.32 Proposed flow diagram for processing.

Appendix

Figure A.2.1 Vibration spectra of an induction motor driving a screw compressor.

Figure A.3.1 Signals for Fourier series analysis.

Figure A.3.2

Figure A.3.3

Figure A.3.4

Figure A.3.5

Figure A.3.6

Figure A.3.7

Figure A.3.8

Figure A.3.9

Figure A.3.10

Figure A.3.11

Figure A.3.12

Figure A.3.13

Figure A.3.14

Figure A.3.15

Figure A.3.16

Figure A.3.17

Figure A.4.1 (upper) New CPB spectrum, September 81. (lower) dB difference spectrum from reference mask.

Figure A.4.2 Waterfall plot of a series of difference spectra ranging from July, 1981, when the first significant change was detected, at one month intervals until March, 1982.The baseline of each of these spectra is set at the tolerance of 6 dB, so that only components above this value are seen.

Figure A.4.3 Spectra and cepstra on linear x‐axes for the same case before the fault developed (March '81) and after it developed (November, '81).

Figure A.4.4

Figure A.4.5

Figure A.4.6 Crankshaft angular velocity vs time for two conditions of a spark ignition engine. The lower curve in each figure is a spark timing signal for cylinder 2. The vertical dotted lines indicate firing on the other cylinders, indicated by their number.

Figure A.6.1 Cepstra obtained from two zoom bands of the same spectrum.

Figure A.7.1 Spectrum and cepstrum for a gearbox with a fault on test in the manufacturing plant.

Figure A.7.2

Figure A.7.3

Figure A.7.4. Envelope spectrum from a bearing fault.

Figure A.7.5 Envelope spectrum from a helicopter gearbox.

Guide

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VIBRATION‐BASED CONDITION MONITORING

INDUSTRIAL, AUTOMOTIVE AND AEROSPACE APPLICATIONS

SECOND EDITION

Robert Bond Randall

University of New South Wales

Australia

This edition first published 2021

© 2021 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Robert Bond Randall to be identified as the author of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication Data

Names: Randall, Robert Bond, author.

Title: Vibration-based condition monitoring : industrial, automotive and aerospace applications / Robert Bond Randall, University of New South Wales.

Description: Second edition. | Hoboken, NJ : Wiley, 2021. | Includes bibliographical references and index.

Identifiers: LCCN 2020048411 (print) | LCCN 2020048412 (ebook) | ISBN 9781119477556 (cloth) | ISBN 9781119477693 (adobe pdf) | ISBN 9781119477655 (epub)

Subjects: LCSH: Vibration–Testing. | Nondestructive testing. | Vibration–Measurement.

Classification: LCC TA355 .R34 2021 (print) | LCC TA355 (ebook) | DDC 621.8/11–dc23

LC record available at https://lccn.loc.gov/2020048411

LC ebook record available at https://lccn.loc.gov/2020048412

Cover Design: Wiley

Cover Images: © Suriya Desatit/Shutterstock, Borya Galperin/Shutterstock, M101Studio/Shutterstock, PARETO/E+/Getty Images, Alexsey/E+/Getty Images

Dedicated to the memory of Professor Simon Braun, 1933–2020.

Foreword

About 10 years ago, when the first edition of Prof Randall's Vibration‐based Condition Monitoring was published, I enthusiastically welcomed it, because a book was finally published that presented a systematic approach to a subject, ‘Condition‐Based Monitoring’, which had grown in complexity over the years, with contributions from many important scholars, but in a non‐systematic way.

There were already books that dealt with partial aspects (e.g. Vibration and Acoustic Measurement Handbook (1972) by Michael P. Blake and William S. Mitchell, A Practical Vibration Primer (1979) by Charles Jackson and Fundamentals of Noise and Vibration Analysis for Engineers (1989) by Michael P. Norton), or they dealt with specific fields (including, among the many, Maurice L. Adams Jr.'s Rotating Machinery Vibration from Analysis to Troubleshooting in 2001). There was already a reference journal (i.e. Mechanical Systems and Signal Processing, founded in 1987 with foresight by the late and recently deceased Simon Braun), but it lacked an organic work, a book that presented a systematic approach and introduced both methods and techniques.

Certainly, in twenty‐first century society, one could reflect and debate for a long time whether a book still represents ‘the instrument’ for the transmission of knowledge. Today we have different media, but I remain personally convinced that, in the scientific field, the book is still a fundamental tool; what has certainly changed is the way it is used: probably many readers of this book are not doing it, right now, on paper media, but on a digital medium.

The scientific community and engineers were lucky because this book was written by Prof Randall. I do not think there is any need to present him, because he has a long career of research, of development of signal processing techniques, of case study analysis and of teaching. I was lucky enough to meet him in person 20 years ago, and my esteem for him has always grown, as a monotonic function, not only for its scientific aspects, but also human.

Now, this second edition fills in some inevitable gaps (when writing for the first time a wide‐ranging work like this, it is impossible to delve into all the topics or not neglect some, which appeared secondary at that time), but above all introduces and deepens new methods and techniques that have been fully developed in the last ten years, such as tacho‐less techniques.

Why is Condition Monitoring so important in engineering and, more generally, in today's world? Prof Randall explains very well the reasons in the introduction of this book: it is a fundamental component for some of the so‐called pillars of the technology paradigm of Industry 4.0, at least for IoT (‘Internet of Things’), but also for Big Data analytics. Condition Monitoring allows the full implementation of Condition‐Based Maintenance (CBM), with remarkable economic advantages, from a single machine to entire plants and industrial facilities, from manufacturing, to services and utilities. Finally, Condition Monitoring is the basis of a predictive – i.e. prognostic – approach to determining the residual useful life (RUL) of a component or a system.

It is certainly ambitious to define what the purpose of science is, and illustrious minds have applied themselves to this: from Greek philosophers to Galileo, from Descartes to Gödel, from Cantor to Popper. If we limit ourselves to the narrow sphere of Engineering and to its purpose, it is not possible to fail to recognise that it must explain ‘how’ one does something and ‘why’ it is done. In this case, in his book, Prof Randall explains very clearly the ‘how’, that is, the most well‐established methods and techniques for condition monitoring are analysed in detail and implemented. To do this, he uses one of the most natural signals generated by mechanical systems: vibrations, inextricably linked to the dynamic behaviour of the mechanical systems themselves. Prof Randall also explains in detail ‘why’ applying Condition Monitoring is so important.

There is also, however, another interesting ‘why’ to analyse, by limiting the scope to the foreword to a book: it concerns Condition Monitoring's rapid development in recent years and its pervasiveness in the modern world. Condition Monitoring is certainly a technological innovation, and as such, its genesis and evolution can be analysed by means of the mechanisms of generating innovation, starting from the more traditional ones, such as the ‘Technology‐Push’, theorised by Joseph A. Schumpeter way back in 1911, and the ‘Demand‐Pull’ most recently introduced by Jacob Schmookler in 1966.

Certainly, the ‘epic’ and ‘primordial’ phase of Condition Monitoring (we could call it the ‘Proto‐Condition Monitoring’) was governed by technology‐push: without the microprocessors (introduced in the Cold War, not so much for the space race as it is commonly believed, but for the guidance and control of intercontinental missiles), without the invention of miniaturised and reliable sensors (the switch from the strain‐gage to the piezoelectric accelerometer happened between the 1940s and the 1950s, with the starting up of manufacturers such as Brüel & Kjær, Columbia Research Laboratories, Endevco, Gulton Manufacturing and Kistler Instruments – some of which are still firmly on the market – or the introduction of the eddy‐current proximity probe in 1961 for rotary machines by Bently Nevada), without the personal computers and without the low‐cost storage systems, Condition Monitoring would have remained confined to laboratories. Very often, the hardware manufacturer also produced the necessary software and supplied the brainware: for example, minicomputers to collect data and run signal processing methods and rule‐based systems for the implementation of condition monitoring. Think, for example, to Hewlett‐Packard and Sohre's tables of 1968 or to Bently Nevada and their ADRE systems, and the signal processing methods developed by Donald Bently himself and Agnes Muszynska.

This phase was followed by a ‘maturity’ phase, governed mainly by the demand‐pull, which we could call the ‘Meso‐Condition Monitoring’, during which some large players immediately realised the benefits of Condition Monitoring and implemented it within a CBM approach, as an economic driver for cost reductions. At this stage, the leading roles were big companies and operators of ‘big fleets’, both in a physical and figurative sense, in various sectors: from the military (think the US Navy) to the transport and aerospace (as in the case of NASA), from the energy (first of all GE and Siemens) to the manufacturing.

However, the two traditional technology‐push and demand‐pull models do not explain, as it is often the case in technology, why what we might call the ‘Neo‐Condition Monitoring’ is growing so rapidly, in more recent years. The explanation, from a technological innovation point of view, is given by an interactive vision: on the one hand, technological evolution introduces new tools (hardware in the broadest sense: sensors, wireless systems, computers and memory) and new signal processing techniques are proposed, with a frequency if not weekly, at least monthly. On the other hand, as we said, the condition monitoring market, thanks in part to the IoT, has become immense.

In light of these considerations, it is clear how important it is that we have a reference and authoritative text for ‘Vibration‐based Condition Monitoring’ and all of us who work in science and technology should be grateful to Bob Randall (I now allow myself to move to a more confidential tone) for writing this second updated and expanded edition, which will certainly become a new milestone.

Paolo Pennacchi

Dept. of Mechanical Engineering

Politecnico di Milano – Milan, Italy

October 2020