1. Detection Of Roller Bearing Defects By Vibration Analysis
Presenting By: NASEEL IBNU AZEEZ M.P
Roll No:12
M-Tech MD AJCE-KANJIRAPALLY
Guided By: Mr.TOMS PHILIP
Ast. Professor Mechanical Engineering
AJCE-KANJIRAPALLY

2. BEARINGS
A bearing is a machine element that constrains relative motion between moving parts to only in the desired motion
The term "bearing" is derived from the verb "to bear; a bearing being a machine element that allows one part to bear (i.e., to support) another.

3. Bearing
Sliding Contact
Rolling Contact

4. Rolling Contact Bearings
Rolling Contact bearing carries a load by placing round elements between two bearing rings.The relative motion of the pieces causes the round elements to roll with very little rolling resistance and with little sliding.
Tapper Bearing
Ball Bearing
Cylindrical Bearing

5. Ball Bearing
Shaft
Outer Ring
Ball
Inner Ring

6. Bearing Defects Inappropriate use of bearings
Causes Of Rolling Bearings Defects
Inappropriate use of bearings
Faulty installation or improper processing
Improper lubricant, lubrication method or sealing device
Inappropriate speed and operating temperature
Contamination by foreign matter during installation
Abnormally heavy load

10. Roller Bearing Defect Detection
Magnetic particle testing
Artificial visual detection
Eddy current testing
Optical detection
Acoustics & Vibration analysis

11. Vibration Analysis
Cracks change the original vibration modal parameters of roller structure, so whether there are cracks defects in the roller can be distinguished by impulse response features. If there are cracks in the structure, theirs damping coefficient and stiffness will be changed, which will reflect on damping ratio and natural frequency. Damping ratio of the structure is increasing with the extension of the cracks, while natural frequency is reducing.

12. Condition Monitoring Sensor(s) Cables Signal Conditioning
Data Acquisition & Storage
Communications
Remote Analysis and Diagnostics

13. 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (2𝜋𝑓) 2
What to measure in vibration? Peak values of: 1. Displacement 2. Velocity 3. Acceleration Being related to each other, measurement of one leads to determination of the other two.
𝑥 = 𝑥 𝑑𝑡
𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (2𝜋𝑓) 2
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (2𝜋𝑓)
𝑥= 𝑥 =𝑑𝑡𝑑𝑡

14. Signal Processing
Input
Sampling
Anti-aliasing Filter
A/D Convertor
Windows
&
Input Buffer
FFT
Averaging
Display
Storage
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, or measurements of time-varying or spatially varying physical quantities. 
Digital Signal Processing(DSP)

15. Sampling
In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A sample refers to a value or set of values at a point in time and/or space.
A sampler is a subsystem or operation that extracts samples from a continuous signal.
A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. s
𝑆𝑎𝑚𝑝𝑖𝑛𝑔 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝑓 𝑠 = 1 𝑇 𝑠
𝑆𝑎𝑚𝑝𝑙𝑒𝑑 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛=𝑆 𝑛 𝑇 𝑠 ,𝐹𝑜𝑟 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 valu n

16. Anti-aliasing Filter
Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling. That fidelity is reduced when s(t) contains frequency components higher than 𝒇 𝒔 𝟐 Hz is known as aliasing of signal.
Any signal bandlimited to maximum frequency 𝑓 𝑚 can be perfectly reconstructed from its sample if the sample rate, 𝑓 𝑠 ≥2 𝑓 𝑚 (Nyquist rate)

17. Analog-to-digital converter
An analog-to-digital converter(ADC, A/D or A to D) is a device that converts a continuous physical quantity to a digital number that represents the quantity's amplitude. The result is a sequence of digital values that have converted a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete amplitude digital signal.
x(t)
Anti-aliasing
filter
DSP
ADC
x [n]

18. Signal Windowing
Most digital signals are infinite, or sufficiently large that the dataset cannot be manipulated as a whole. Sufficiently large signals are also difficult to analyze statistically, because statistical calculations require all points to be available for analysis. In order to avoid these problems, engineers typically analyze small subsets of the total data, through a process called windowing

19. Fast Fourier Transform(FFT)
This is a method of taking a real world,time-varying signal and splitting it into components, each with an amplitude, a phase, and a frequency. By associating the frequencies with machine characteristics, and looking at the amplitudes, it is possible to pinpoint troubles very accurately.
𝑥= 𝐴 1 𝑒 −ξ 𝜔 𝑛 𝑡 cos 1− ξ 𝜔 𝑛 𝑡+ 𝜑 𝑋 𝑠 sin⁡(𝜔𝑡−𝜑) [1− (1− 𝜔 𝜔 𝑛 ) 2 ] 2 +[ (2𝜉 𝜔 𝜔 𝑛 ) 2 ]

21. Averaging
Signal averaging is a signal processing technique applied in the time domain, intended to increase the strength of a signal relative to noise that is obscuring it.
Consider v(k) is the contaminated signal
Mathematically,
v(k) = vs(k) + vnoise(k),
vs(k) being the desired periodic signal
vnoise(k) the unwanted noise
Signal averaging is performed by accumulating and partitioning v(k), and adding the partitions with the hope that the noise adds destructively while the desired signal builds up.

23. Experimental Setup

24. Accelerometer Sensor
Sample Defect Is Shown as Red Spot

25. Outer Race
Inner Race
Cage
Bearing Pitch
Diameter (D)
Bearing Used in Test Motor
(SKF 6306)
No. of Balls = n = 8
Rotational Speed, N = 1480 rpm
Ball diameter, d = 12.3 mm
Bearing pitch dia, D = 50.8 mm
Ball contact angle = 0 0

26. Vibration Analysis Time Domain Frequency Domain FFT Amplitude

27. Time Domain Analysis
Time Domain Zooming

28. Time Domain Splitting
𝟐 𝐧𝐝 𝐝𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞

30. Frequency Domain Analysis

31. Characteristic Frequencies of Bearings
𝐹 𝐵𝑃𝐹𝑂 = 𝑛 𝑏 2 𝑁 60 1− 𝑑 𝐷 cos 𝛽
𝐹 𝐵𝑆𝐹 = 𝐷 𝑑 𝑁 60 1− 𝑑 𝐷 2 cos 𝛽
𝐹 𝐵𝑃𝐹𝐼 = 𝑛 𝑏 𝑑 𝐷 cos 𝛽
𝐹 𝐹𝑇𝐹 = 1 2 𝑁 60 1− 𝐷 𝑑 cos 𝛽
𝐹 𝐵𝑃𝐹𝑂 =Ball passing frequency outer race
n = no. of balls
N = rotational speed in rpm
d=ball diameter
D=bearing pitch diameter
𝛽=ball contact angle with the races
𝐹 𝐵𝑃𝐹𝐼 =Ball passing frequency inner race
𝐹 𝐵𝑆𝐹 =Ball spin frequency
𝐹 𝐹𝑇𝐹 =Fundamental train frequency

32. Characteristic Frequencies For SKF-6306
No. of Balls,n=8
Rotational Speed,N = 1480rpm
Ball diameter,d =12.3 mm
Bearing pitch dia,D=50.8 mm
Ball contact angle= 0 0
𝐹 𝐵𝑃𝐹𝑂 =74.77 Hz
𝐹 𝐵𝑃𝐹𝐼 = Hz
𝐹 𝐵𝑆𝐹 =47.95 Hz
𝐹 𝐹𝑇𝐹 =9.3 Hz

34. Positioning Of Bearing Defect

36. Conclusions
Trend of overall frequencies and vibration spectrum provide useful information to analyze defects in roller bearings.
This technique can provide early information about progressing malfunctions.As a result, the necessary control action can be taken on the machine in advance.
The distinct and different behavior of vibration signals from bearings with inner race defect and outer race defect helps in identifying the defects in roller bearings.

37. Reference
Prediction of Defects in Roller Bearings Using Vibration Signal Analysis
H. Mohamadi Monavar, H. Ahmadi and S.S. Mohtasebi
World Applied Sciences Journal 4 (1): , 2008 ISSN ,IDOSI
Publications,2008
Vibration Analysis using Time Domain Methods for the Detection of small Roller Bearing Defects
Tahsin Doguer,Jens Strackeljan
SIRM th International Conference on Vibrations in Rotating
Machines,Vienna, Austria, February 2009
Prediction of Defects in Antifriction Bearings using Vibration Signal Analysis
M Amarnath,R Shrinidhi,A Ramachandra,S B Kandagal
IE(I) Journal-MC
Monitoring and Analysis of Vibration Signal Based On Virtual Instrumentation
Sunita Mohanta1, Umesh Chandra Pati
International Journal of Advanced Computer Research
ISSN: ISSN: ) Volume-3 Number-1 Issue-8 March-2013

38. Reference Cont.
Experimental Study on Condition Monitoring of Low Speed Bearings : Time Domain Analysis
Eric Y. Kim,Andy C. C. Tan,Bo-Suk Yang and Vladis Kosse
5th Australasian Congress on Applied Mechanics, ACAM
December 2007, Brisbane, Australia
Text Books
Mechanical Vibrations:Theory and Practice
Author:Shrikant Bhave
Publisher:Pearson
Mechanical Vibrations
Author:V P Singh
Advanced Engineering Mathematics
Author:Erwin Caryzig
Publisher:Willey
Digital Signal Processing
Author:A Anand Kumar
Publisher:PHI Learning 

39. THANK YOU