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Bearing Fault Diagnosis by Wavelet Techniques
Xxxxxxxxxx @ CMHT, McMaster
2Incipient Bearing Fault Diagnosis
Cause 40%(?) motor failure Difficulty in detection:
Highly contaminated by environment noise Incipient fault
Fault category Localized faults: cracks, pits, spalls, etc. Distributed faults: surface roughness,
waviness, misaligned races, etc.
Spalling at inner raceSingle-point defect at outer race
3Motor and bearing system
Siemens Brushless DC Motor
Single row deep groove . ball bearing
Non-stationary signals
Environmental Noise, masking signals
4Siemens Drive
Drive System Diagram
PC
Electrical Motor
Siemens Drive System Sensor
Data Acqusition Card
Speed Setpoint
Raw signal
5Accelerometer Arrangement
Non-stationary signal - rolling elements slippage
Faulty Bearing (1)A hole in outer race(EDM)
Faulty Bearing (2)A pit in outer race
Faulty Bearing (3)A pit in outer race
Sensing from motor case Sensing from bearing case
6Characteristic Frequency Calculation
Ball Pass frequency, outer race:
Ideal output by faulty condition
7Time and Frequency Analysis
0 20 40 60 80 100 120 140 160 180 2000
1
2
3x 10
-3 Single-Sided Amplitude Spectrum of y(t)
Frequency (Hz)
|Y(f
)|
0 0.5 1 1.5 2 2.5 3
-0.1
-0.05
0
0.05
0.1
0.15
Time (sec)
Vol
tage
Out
put
(V)
Vibration Signal in Waveform
8Frequency Spectrum - Faulty Bearing (3)
60 70 80 90 100 1100
2
4
6
8x 10
-3 Single-Sided Amplitude Spectrum of y(t), RPM = 1500
Frequency (Hz)
|Y(f
)|
Fault=89.133Hz
Healthy,Sensing Motor Case
Faulty, Sensing Motor CaseFaulty, Sensing Bearing Case
16 18 20 22 24 26 28 30 32 34
0
10
20x 10
-4 Single-Sided Amplitude Spectrum of y(t), RPM = 400
Frequency (Hz)
|Y(f
)|
Fault=23.7688Hz
Healthy,Sensing Motor Case
Faulty, Sensing Motor CaseFaulty, Sensing Bearing Case
9Frequency Spectrum - Faulty Bearing (1)
70 80 90 100 110 120 130 1400
5
10
x 10-4 Single-Sided Amplitude Spectrum of y(t), RPM = 1500
Frequency (Hz)
|Y(f
)|
Fault=89.133Hz
Healthy,Sensing Motor Case
Faulty, Sensing Motor Case
0 1 2 3 4 5 6 7 8 9 10
-0.02
0
0.02
Time (sec)
Sen
sor
Out
put
(V)
Vibration signals in Waveform
10Time-Frequency Analysis
Time (integer index)
Sca
le
Wavelet Scalogram
1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
300
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 1 2 3 4 5 6 7 8 9 10
-0.02
0
0.02
Time (sec)
Sen
sor
Out
put
(V)
Vibration signals in Waveform
11Wavelet Techniques
History – 1990s to 2009
relatively new technology
Advantages of Multi-Resolutional Analysis (MRA)
Time & Frequency non-stationary signals
Applications in fault diagnosis Signal de-noising Feature extraction
Science Citation Report for the keyword – “Wavelet fault diagnosis”
12
Fourier Transform
Wavelet Transform
Understand Wavelet
Breaks down a signal into constituent sinusoids of different frequencies
WHEN did a particular event take place ?
Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the constituent wavelet of the original signal
13
Short Time Fourier Transform (STFT)
Multiresolution Analysis
Wavelet v.s. STFT
Analyze the signal at different frequencies with different resolutions
Good time resolution and poor frequency resolution at high frequencies; good frequency resolution and poor time resolution at low frequencies
More suitable for short duration of higher frequency; and longer duration of lower frequency components
Comparing to Wavelet Transform Unchanged Window: Fixed-width Gaussian “window” Dilemma of Resolution
Narrow window -> poor frequency resolution Wide window -> poor time resolution
14Definition of Continuous Wavelet Transform
Wavelet Small wave, means the window function is of finite length
Mother Wavelet A prototype for generating the other window functions All the used windows are its dilated or compressed and
shifted versions
dtst
txs
ss xx
*1
, ,CWT
Translation(The location of
the window)
Scale Mother Wavelet
15Wavelet for De-noising
Steps 1. Decomposition 2. Nonlinear thresholding 3. Reconstruction
Foundations: White noise distributes itself uniformly across all scales of coefficients of a
wavelet transform
Due to its simplicity Wavelet Shrinkage became extremely popular: Thousands of applications. Hundreds of related papers (984 citations of D&J paper in Google Scholar). Little knowledge about noise character required! signals tend to concentrate most of the “energy” in a few scales
Hard Thresholding
Soft Thresholding
Linear Wiener Filtering
16
Further research Processing experimental data with wavelet de-noising and
feature extraction
Try using other signal sources, for example stator current
Combine Multi-Resolutional Analysis with model-based filtering techinques.
17
Thank you