Bearing Fault Diagnosis by Wavelet Techniques

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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