1. ANALYSIS OF VIBRATION
SIGNALS TO IDENTIFY CRACKS
IN A GEAR UNIT USING
WAVELET TRANSFORMS
UNDER THE GUIDANCE OF
B. A. SUJATHA KUMARI SUSHANTH J
ASST PROF, DEPT of E&C 4JC09LIE18
SJCE, Mysore INDUSTRIAL ELECTRONICS
SJCE, Mysore
1

2. WHAT SHALL WE KNOW ABOUT
 INTRODUCTION TO CRACK DETECTION
 DATA ANALYSIS METHODS AND TECHNOLOGY
USED
 DESIGN AND IMPLEMENTATION
 RESULTS
 CONCLUSION AND FUTURE ENHANCEMENTS
 REFERENCES
2

3. INTRODUCTION TO CRACK DETECTION
 Vibration analysis is important tool for fault
identification.
3

4.  Signals in practice, are TIME-DOMAIN signals in their
raw format.
 Mathematical transformations are applied to signals to
obtain a further information from that signal that is
not readily available in the raw signal. 4

5. REVIEW OF DATA ANALYSIS METHODS
TIME
DOMAIN
ANALYSIS
• FOURIER TRANSFORMS
FREQUENCY • Butterfly algorithm
• Bluestein algorithm
DOMAIN • STFT
• WAVELET TRANSFORMS
ANALYSIS • CWT
• DWT
5

6. Fourier Transforms
 The frequency spectrum of a signal shows what
frequencies exist in the signal
BUTTERFLY ALGORITHM BLUESTEIN ALGORITHM
• Highly efficient • Used for Prime sizes
• Computation time is less • Reduces memory requirement
• Cannot be used for prime sizes
6

7. Continuous Wavelet Transforms
 CWT was developed as an alternative approach to
the STFT to overcome the resolution problem.
 CWT gives good time resolution and poor
frequency resolution at high frequencies and good
frequency resolution and poor time resolution at
low frequencies.
 The width of the window is changed as the
transform is computed for every single spectral
component.
7

8. At s = 1
At s = 5
At s = 20
8

9. WAVELET BASIS - MORLET
 Morlet wavelet, which is a complex sinusoid windowed
by a Gaussian function.
 Mother wavelet
 Real part
 Imag part
9

10. TECHNOLOGY USED
 C# an object oriented programming language.
I. C# does not allow multiple inheritance or use of pointers.
II. Power of the C# programming language, combined with the
simplicity of implementing Windows Form applications in Visual
Studio .NET
III. Versatile and flexible tool for creating Charts, graphics, and
graphical user interfaces.
 Common language Runtime
Framework layer that resides above the OS and handles the execution
of all the .Net applications.
 Microsoft Intermediate Language
When we compile our .Net Program our source code does not get
converted into the executable binary code, but to an intermediate code
10

11. TECHNOLOGY USED
 Just in time compilers
Compiles the IL code to native executable code(.exe or .dll).
 The Visual Studio .NET IDE
I. Keyword and syntax highlighting.
II. Solution explorer helps us to manage applications consisting of
multiple files.
III. Building user interface with simple drag and drop support.
IV. Properties tab that allows setting different properties for multiple
windows controls.
V. Standard debugger that allows us to debug our program using
putting break points for observing run-time behavior.
 WinForms and Win Applications
I. Windows applications are 'event driven‘.
II. A windows form may contain text labels, push buttons, text
boxes, list boxes, images, menus and vast range of other
controls.
III. all windows controls are represented by base class objects
contained in the System.Windows.Forms namespace. 11

12. DESIGN AND IMPLEMENTATION
Shaft rotational The Five Basic Frequencies
frequency( fs )
Fundamental train
frequency( fFTF )
Ball pass outer raceway
frequency( fBPOF )
Ball pass inner raceway
frequency( fBPIF )
Ball rotational
frequency( fB )
12

13. • n = number of samples
Input • fs = Input frequency = 1/(speed in rpm)
• Dc = cage diameter in inches
• Db = ball diameter in inches
Parameters • Theta = Contact angle of bearing
• Nb = Number of balls
13

14. Damage detection using FFT
 We construct basic frequency amplitude vectors to
represent different bearing vibrations.
 These vectors are created from the power spectrum of
the vibration signal and consist of the five basic
frequencies; with varying amplitudes based on the
defect present.
 Since the spectral components near the five basic
frequencies are also important, when generating the
vector we consider a frequency band of 1OHz for each
basic frequency
14

15.  Time taken for the inner/outer race to rotate one
revolution time = (1 / fs)
Condition - Inner Race Running(fi= fs, fo=0)
 Time for the inner race ball frequency
ie time_inner_outer = Math.Round((1 / fBPIF),5);
 Number of balls that pass over the defect each
revolution
ie ball_passes = (time / time_inner_outer);
 Percentage of the balls are passing over a point on
the outer race each revolution.
ie ballpass_Percentage = (ball_passes / Nb) * 100;
15

16. Condition - Outer Race Running(fi= 0, fo=fs)
 Time for the inner race ball frequency
ie time_inner_outer = Math.Round((1 / fBPIF),5);
 Number of balls that pass over the defect each
revolution
ie ball_passes = (time / time_inner_outer);
 Percentage of the balls are passing over a point on the
outer race each revolution.
ie ballpass_Percentage = (ball_passes / Nb) * 100;
16

17. The basic frequency amplitude vector
 Frequency band = [f-5, f+5], where f= basic freq
ie f can be fs, fFCF, fBPO, fBPIF, fB.
 Where P = weighted sum of spectral magnitude
 Accordingly 5 basic frequencies are
calculated for both normal and
abnormal conditions
The Basic frequency amplitude
vector
 Damage percentage can be calculated using
X(f) %= [( X(f)normal – X(f)abnormal )/ X(f)normal ] *100
17

18. Damage detection using wavelet
transforms
 For each scale factor s, it creates a “real” & “Complex” wavelet whose
period is that many samples long.
 The morlet wavelet that is used is a cosine function multiplied by a
guassian(For real part) and with sine multiplied by a guassian(for imag
part)
 Once wavelets are created, it convolves the wavelet with the signal.
 To speed up the algorithm, convolution is done by multiplying Fourier
transform of the signal and the Fourier transform of the wavelet.
 After the convolution we end up with the strength of wavelet in the
signal at each point in time.
 Process is repeated for each scale value starting from 2 upto sample
length in steps of 2n.
 We will get “real” and “complex” data samples. Their magnitudes are
taken and plotted.
18

19. START Multiply the contents of buffer
B1 and B2 point wise and store it in
Load the input signal and buffer B3
sample the input N of any
desired frequency Perform IFFT on buffer B3 and store
it in buffer B4 which gives the
Initialize buffers B1, B2, strength of the wavelet.
B3 and B4
Perform FFT on the input signal Check if scale
and S<N
store it in a buffer B1 ?
Yes No
Generate real and imaginary
parts of the morlet wavelet Increment scale S Display
logarithmically results
Set scale, S = 2
STOP
Perform FFT on the morlet wavelet
and
Store it in a buffer B2
19

20. CLASS DIAGRAM OF VIBRATION
ANALYZER
20

21. NEXT
FFT RESULTS Damage Percentage
Readings Normal Chipped tooth Worn gear
Horizontal - 15.95% 19.30%
Vertical - 32.72% 35.59%
Axial - 93.96% 95.94%
Horizontal readings from normal gear unit.
Horizontal readings from one chipped tooth in a gear unit.
Horizontal readings from a worn out gear unit.
Vertical readings from normal gear unit.
Vertical readings from one chipped tooth in a gear unit.
Vertical readings from a worn out gear unit.
Axial readings from normal gear unit.
Axial readings from one chipped tooth in a gear unit.
Axial readings from a worn out gear unit.
21

22. Go Back
X (fs) = 0.210833307850984
X (fFTF) = 0.0848194179103509
X (fBPOF) = 0.763374761193158
X (fBPIF) = 1.1341250094657
X (fB) = 0.518925198775527
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23. Go Back
X (fs) = 0.141840234995413
X (fFTF) = 0.0570631191589598
X (fBPOF) = 0.513568072430639
X (fBPIF) = 0.762994042528083
X (fB) = 0.349112163014516
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24. Go Back
X (fs) = 0.135794081591682
X (fFTF) = 0.0546307178580059
X (fBPOF) = 0.491676460722053
X (fBPIF) = 0.730470273603089
X (fB) = 0.33423073185528
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25. Go Back
X (fs) = 0.196820373885154
X (fFTF) = 0.0791819362699359
X (fBPOF) = 0.712637426429423
X (fBPIF) = 1.05874593853696
X (fB) = 0.484435086
25

26. Go Back
X (fs) = 0.165417749488167
X (fFTF) = 0.0665484849933834
X (fBPOF) = 0.598936364940451
X (fBPIF) = 0.889823380453054
X (fB) = 0.40714363118952
26

27. Go Back
X (fs) = 0.15882249755219
X (fFTF) = 0.0638951782844781
X (fBPOF) = 0.575056604560303
X (fBPIF) = 0.854345873409405
X (fB) = 0.390910700744437
27

28. Go Back
X (fs) = 0.233919896929374
X (fFTF) = 0.0941072817072259
X (fBPOF) = 0.846965535365033
X (fBPIF) = 1.25831353699934
X (fB) = 0.575748349484808
28

29. Go Back
X (fs) = 0.00948287012500394
X (fFTF) = 0.0038150116427087
X (fBPOF) = 0.0343351047843783
X (fBPIF) = 0.0510107263406572
X (fB) = 0.0233402412300918
29

30. Go Back
X (fs) = 0.00948762844870156
X (fFTF) = 0.00381692594292233
X (fBPOF) = 0.034352333486301
X (fBPIF) = 0.051036322552013
X (fB) = 0.0233519529187988
30

31. Wavelets RESULTS
Next
Horizontal readings from normal gear unit.
Horizontal readings from one chipped tooth in a gear unit.
Horizontal readings from a worn out gear unit.
Vertical readings from normal gear unit.
Vertical readings from one chipped tooth in a gear unit.
Vertical readings from a worn out gear unit.
Axial readings from normal gear unit.
Axial readings from one chipped tooth in a gear unit.
Axial readings from a worn out gear unit.
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32. Go Back
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40. Go Back
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41. CONCLUSION
 The success of the FFT and wavelet algorithm
introduced in this project relies on the properties of
inner and outer race bearing fault signals.
 FFT with energy diagram technique.
 Wavelets with time-frequency distribution diagrams.
 WA does provide good resolution in frequency at the
low frequency range, and fine resolution in time at the
high frequency range.
 WA is a simple visual inspection method and it does
not require the analyst to have a lot of experience in
Fault diagnosis.
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42. FUTURE EMHANCEMENTS
 Choice of mother wavelets
 Scale parameters of the wavelet technique will require
further investigations .
 Numerous families of wavelet basis with different
properties which can be used in crack detection.
 Artificial neural network method of automatic fault
detection.
 Comprehensive software package should be written as
a standalone program.
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43. REFERENCES
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(2004) 14-21.
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Ultrasonic’s 27 (1980) 317-328.
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with localized faults, Journal of Vibration and Acoustics 125 (2003) 282-289.
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diagnosis: a review with bibliography, Mechanical Systems and Signal Processing 18 (2004) 199-221.
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of local bearing defects in rotating machines, Mechanical Systems and Signal Processing 19 (2005) 509-535.
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 [12] Bo Li, Gregory Goddu, Mo- Yuen chow, Detection of common motor bearing faults using frequency
domain vibration signals and a neural network based approach, proceedings of American control conference
(1998) 43

44. Thanks FOR YOUR ATTENTION
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