Estimation of misalignment in bearing shaft by signal processing of acoustic signal

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
International Journal of Mechanical Engineering
ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME
and Technology (IJMET), ISSN 0976 – 6340(Print)
ISSN 0976 – 6359(Online) Volume 2
IJMET
Number 1, Jan - April (2011), pp. 60-69 ©IAEME
© IAEME, http://www.iaeme.com/ijmet.html

ESTIMATION OF MISALIGNMENT IN BEARING SHAFT BY
SIGNAL PROCESSING OF ACOUSTIC SIGNAL
Naveen Rathi1, Amit Gupta2, B. Manpreet3, Rajesh Kumar4 , Vikas Kumar5
1
Pursuing M.Tech from NCCE ,Israna, Panipat, Haryana, India
er.naveenrathi@gmail.com
2
Department of Mechanical Engineering, NCCE ,Israna, Panipat, Haryana, India
eramit81@yahoo.co.in
3
Pursuing PHD from SLIET Longowal -148106 (Pb), India
bainscoolbains@yahoo.com
4
Department of Mechanical Engineering, SLIET Longowal -148106 (Pb.), India
5
Pursuing M.Tech from NCCE ,Israna, Panipat , Haryana, India
vikas4m@gmail.com
ABSTRACT

Acoustic Emission (AE) is being extensively used as a Non Destructive Technique (NDT) for
diagnosis of rotating components. The main theory behind this diagnosis is that while rotation,
acoustic energy level of defective portion in rotating element is different. In the present study a
signal processing technique is proposed to identify the variation in acoustic signal and results are
verified for misalignment of the bearing shaft. Two different functions Fast Fourier
Transformation (FFT) and Decomposition are used to represent the Acoustic signal at different
levels of misalignment. Result reveals that the proposed methods are effective in estimating the
misalignment present in the bearing shaft. Statistical parameters such as Standard deviation and
Shannon entropy are also increases with increase in misalignment in the bearing shaft.

Keywords: acoustic emission, condition monitoring, fault diagnosis bearing, misalignment of
bearing shaft, signal processing.

I. INTRODUCTION

Vibration analysis is widely used in diagnostics of faults in machinery. There are many analytical
techniques such as Resonance demodulation [1], Instantaneous power spectrum distribution[2] and
Conditional moments analysis[3] etc which have been developed for processing vibration signals
to obtain useful diagnostic information about processing gear faults. Over the last few decades the
vibration analysis by using acoustic condition monitoring of rotating component has received very
little attention. This was probably due to perception that monitoring of air borne sound from a
machine is noisy and complex in normal industrial environment. During the last few years a
significant process in the capability of acoustic instrumentation together with the signal processing
techniques has made it possible to extract useful diagnostic information from contaminated
acoustic signals. Number of signal processing techniques like by using Discrete wavelet
transform,, Morlet wavelets, and Wavelet transform etc have been developed to diagnose the
faults in bearing and removal of noise from the signal in other industrial and research applications
[4-10].

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In the present work experiments are conducted to identify misalignment of bearing shaft by
recording the acoustic signal in the computer. The recorded acoustic signal is processed in
Matlab6.0 by using two different functions ‘Fast Fourier Transformation ‘(FFT)’ and
‘Decomposition’ for the analysis purpose.

II. THEORY
A .Fast Fourier Transformation (FFT)
The FFT is essence, decomposes or separates a waveform on function into sinusoids of different
frequencies It identifies or distinguishes the different frequency sinusoids and their respective
amplitudes [4]. The Fourier transform f(s) of function f(x) is expressed as
f(s) = ∫ f (x) exp (-i 2πxs) do. (1)
Applying the same transform to f(s) gives
∫
f (w) =∫ f (s) exp (-i 2πws) ds. (2)
If f(x) is an even function of x, that is f(x) = f(-x), then f(w) = f(x). If f(x) is an odd function of x,
that is f(x) = -f (-x), then f(w) = f(-x). When f(x) is neither even nor odd, it can often be split into
even and odd parts. It is often useful to think of functions and their transforms are occupying two
domains which are called as upper and lower domains.

B. Wavelet decomposition
Many applications use the wavelet decomposition taken as a whole. The common goals concern
the signal or image clearance and simplification, which are parts of de-noising or compression.
When trying to classify the applications by domain, it is almost impossible to sum up several
thousand papers written within the last 15 years. The decomposition process can be iterated, with
successive approximations being decomposed in turn, so that signal is broken down into many
lower resolution components. This is called the wavelet decomposition tree. The original signal
‘S’ is broken down to lower resolution components like ‘cA1’ and ‘cD1’. Then is further broken
out ‘cA2’ and ‘cD2‘as shown in Figure 2.1. Looking at a signal’s wavelet decomposition tree can
yield valuable information as shown below in Figure 2.2
Since the analysis process is iterative, in theory it can be continued indefinitely. In reality, the
decomposition can proceed only until the individual details consist of a single sample or pixel. In
practice, you’ll select a suitable number of levels based on the nature of the signal.

Figure 2.1: Wavelet decomposition tree

Figure 2.2: Wavelet decomposition tree with valuable information

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In our work we have used Daubechies 4th order is used as mother wavelet, which is compactly
supported orthogonal wavelet. Daubechies wavelet allows specific parts of the spectrum to be
filtered and can potentially give more detail in the time series, compared to the conventional filter
[8].
III. EXPERIMENTAL SET UP
In this paper we diagnose the defect of misalignment in the bearing shaft. An experimental setup is
made for the analysis purpose. We have taken the cage bearing (NBC make, 6004)having 9 balls
for our study. A motor (200 watt) is used to drive bearing arrangement and a mike (Logitec make,
20 Hz to 16000 Hz frequency range) is used to record the acoustic signal generated by the bearing
housing by placing it 1cm apart from that. In first set of reading shaft is made to run at 1460 rpm
with he help of motor and without any misalignment by providing support at pulley which is
mounted at the other end as shown in figure 3.1. Later weight is applied to introduce the
misalignment in the shaft as shown in figure 3.2 at three different levels by own weight of shaft
and pulley, adding further 2kg and adding 5kg (in total), which is also measured in terms of angle
as 0.35, 0.72 & 1.04 degrees respectively. Signal (in wav format) generated by the bearing is
recorded for 2 sec duration with the help of mike and saved in the computer for the processing.
These signals then processed in the Matlab6.0 software for generating the raw signal, FFT(Fast
Fourier Transformation) and decomposition at 6th level by using db4 as mother wavelet. Which are
shown in the next section.

Figure 3.1 Experimental se up with support at the end

Figure 3.2: Experimental setup with induced misalignment

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IV. RESULTS AND DISCUSSIONS
Raw signal (amplitude vs time), Fast Fourier Transform FFT(energy vs frequency domain) are
drawn and compared in this section.
A simple raw signal of case having no misalignment is shown in Figure 4.1 and the other cases
of misalignment are having almost similar view of raw signal as in case of no misalignment.
FFT’s are also shown below for four different cases given below.
Case1: FFT of Shaft without misalignment rotated at 1460 rpm in figure 4.2(a)
Case2: FFT of Shaft with misalignment because of its own weight of shaft and pulley or
(Equivalent to 1 Kg point load at the pulley) at 1460 rpm in figure 4.2(b)
Case3: FFT of Shaft with misalignment with 1.5 Kg additional load at the pulley at 1460 rpm in
figure4.2(c)
Case4: FFT of Shaft with misalignment with 3.0 Kg additional load at the pulley at 1460 rpm in
figure 4.2(d)

Figure 4.1: Raw signal of without misalignment at 1460 rpm

Figure 4.2 (a): FFT of the signal without misalignment at 1460 rpm

Figure 4.2 (b): FFT of the signal having misalignment because of its own weight or Equivalent to
1Kg point load at 1460 rpm

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Figure 4.2 (c): FFT of the signal having misalignment because of its own weight and additional
1.5 Kg load at 1460 rpm.

Figure 4.2 (d) FFT of the signal having misalignment because of its own weight and additional 3
Kg load

The peaks are coming at the multiple of 24.3Hz which are the harmonics of fundamental
frequency of rotation,

S.No Case Respective Angle of 4th peak
height in Misalignment energy value
( mm)
1. Without 135.26 0° 155
misalignment
2. Misalignment by 133.00 0.35° 255
own weight of pulley
and shaft
1.5Kg additional load

3.0Kg additional load

Table 4.1

This can be calculated by
1460 / 60= 24.3 rotation per second (Hz)
We have marked the energy values corresponding to 4th consecutive peak of 24.3 Hz (ie 97.2Hz)
on each FFT graph and their respective values are measured as 155, 255, 650, and 780 for the

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Case1, Case2, Case3 and Case4 respectively, Which are described in Table 4.1 and shown in
Figure 4.3 (Graph between Energy of 4th consecutive peak of rotational frequency vs Angle of
misalignment ).
The trend shown by energy level at 97.2Hz (4th harmonic of 24.3Hz) frequency in FFT graph is
the clear indication of misalignment, as misalignment increases energy level increases. So the 4th
consecutive peak of rotational frequency must be observed very precisely to avoid the damages
caused by the misalignment.

900

y 800
c
n
e
u
q 700
e
r
f
l
a
n 600
o
i
t
a
t
o
r
f 500
o
k
a
e 400
p
e
v
i
t
u
c 300
e
s
n
o
c 200
h
t
4
f
o
y 100
g
r
e
n
E 0

0 0.2 0.4 0.6 0.8 1 1.2
Angle of misalignment

Figure 4.3: Graph between Energy of 4th consecutive peak of rotational frequency vs Angle of
misalignment

Decomposition up to 6th level using db4 as mother wavelet is drawn for the Case1 (Without
misalignment) and shown in Figure 4.4 Enlarged views for the 6th level decomposition i.e. ’a6’ for
the different cases are shown in the Figures 4.5(b), 4.5(c), 4.5(d) and 4.5(e) for the Case1, Case2,
Case3 and Case4 respectively. Impression of each ball can be clearly visible on these enlarged
graphs in terms of peaks as shown in Figure 4.5(a). Also for the case of without misalignment (at
1460 rpm) we have marked two point by writing their coordinates which represent the same ball
impression after completing one cycle shown in Figure 4.5(b). With the help of these data point
we can also calculate the time to complete one cycle and hence rpm of the bearing shaft. As 1 sec
signal is decomposed into 44100 data point so
Time to complete one cycle=(7568.85-5758.93) /(44100)=1809.92 / 44100=0.041041
So rpm of the shaft can be given by= [1 / 0.041041] * 60=1461.94

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Figure 4.4 Decomposition up to 6th level by using db4 as mother wavelet without misalignment at
1460 rpm.

Figure 4.5 (a): Enlarged view of 6th level Decomposition ‘a6’ for Case1 without misalignment
load at 1460 rpm

Figure 4.5 (b): Enlarged view of 6th level Decomposition ‘a6’ for Case1 without misalignment
load at 1460 rpm

66


Figure 4.5 (c): Enlarged view of 6th level Decomposition ‘a6’ for Case2 having misalignment
because of its own weight or Equivalent to 1 Kg pulley load at 1460 rpm

Figure 4.5(d): Enlarged view of 6th level Decomposition ‘a6’ for Case3 having misalignment
because of its own weight and additional 1.5 Kg load

Figure 4.5 (e): Enlarged view of 6th level Decomposition ‘a6’ for Case4 having misalignment
because of its own weight and additional 3 Kg load

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Each ball gives two peaks one to the upside and one to the lower side, actually lower side peak is
due to the blank space which is coming after ball and gives impression to the lower side. The
middle 6 peaks difference has been shown in Figure 4.5(b) with energy variation (upper peak and
lower peak) have been measured as 0.070, 0.050, 0.025, 0.020, 0.015 and 0.020 as shown in figure
4.5(b). The average of this is coming out to be 0.033 in the case of without misalignment.
In the Case-2 having misalignment due to pulley and shaft weight the 6 intermediate peaks energy
variation has been measured as 0.20, 0.12, 0.12, 0.10, 0.10, 0.12 and 0.05 respectively as shown in
Figure 4.5(c). The average of this is coming out to be 0.127. Similarly in the next two cases Case-
3 and Case-4. the average value of energy variation is coming out to be 0.148 and 0.227
respectively.

S.No Case Respective Angle of Average value of
height in Misalignment energy variation
( mm)
1. Without 135.26 0° 0.033
misalignment
2. Misalignment 133.00 0.35° 0.127
by own weight
of pulley and
shaft
3. Misalignment 130.58 0.72° 0.148
by 1.5Kg
additional load
4. Misalignment 128.50 1.04° 0.227
by 3.0Kg
additional load
Table 4.2

0.25
Average energy variation of 6 intermediate balls

0.2

0.15

Series1
Series2

0.1

0.05

0
0 0.2 0.4 0.6 0.8 1 1.2
Angle of misalignment

Figure 4.6: Graph between Average energy variation of 6 intermediate balls vs Angle of
misalignment

We can observe that as misalignment increases then 6th level decomposition of signal shows more
disturbances (more up and down). This is because of increase in energy at each individual ball of
the bearing because of the misalignment in bearing shaft. So we can represent the misalignment in

68


terms of average energy variation of individual balls shown in Table 4.2 and graph shown in
Figure 4.6. So this energy variation of individual balls must be monitored properly to avoid the
failures due to misalignment.
V. CONCLUSION
In this paper we have analyzed the fault of misalignment in bearing shaft by using acoustic signal
and developed a method to identify such defects. From the experiments following conclusions can
be drawn.
1.It is demonstrated that, although the environment influences acoustic signal for
condition monitoring, it does not significantly reduce the extraction of useful diagnostic
information. It has been demonstrated that acoustic condition monitoring can
effectively be used for detection of misalignment in bearing arrangement.
2.The graphs drawn by using FFT and Decomposition functions responded equally for
the fault misalignment. Also the signs of increasing misalignment can be noted down
clearly with both functions.
3.In vibration monitoring using acoustic signal have certain advantages over the
conventional vibration measuring techniques. Firstly in this sensors do not alter the
behavior of the machine due to its non contact nature. And time based information is
not lost in this method.
4.Acoustic based method provides considerable freedom in positioning of the
microphone. For instance, in this application, small variations in distance and plane of
the microphone with respect to the bearing had a little influence in detecting the main
characteristics of the bearing acoustics. On the other hand, small change in the location
of the accelerometers based method had a bigger impact in detecting the main
characteristics of the bearing vibration.
5.The method developed in the project can be used for the condition monitoring and for
predictive maintenance of the ball bearing for the misalignment.
REFERENCES
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spectrum distribution”, NDT&E International 36 (2003) 535–542.
3. Isa Yesilyurt, “The application of the conditional moments analysis to gearbox fault detection—
a comparative study using the spectrogram and scalogram”, NDT&E International (2004).
4. MATLAB User Guide, The Math Works, Inc. (1999).
5. Prabhakar S., Mohanty A. R., and Sekhar A. S., “Application of discrete wavelet transform for
detection of ball bearing race faults”, Tribology International 35, 793-800 (2002).
6. Nikolaou N. G., and Anthoniadis I. A., “Demodulation of vibration signals generated by defects
in rolling element bearing using complex shifted morlet wavelets”, Mechanical systems and
signal processing 16, 677-694 (2002).
7. Jena D. P., Kumar Navneet, and Kumar Rajesh, “Defect detection in bearing using wavelet
transform”, NCMC-2003, Patiala (India) 31 October to 01 November 2003.
8. Daubechies I., “Ten lectures on wavelets”, Society for Industrial and Applied Mathematics,
Philadelphia (1992).
9. Wu Jian-Da, Huang Chin-Wei, and Huang Rongwen, “An application of a recursive Kalman
filtering algorithm in rotating machinery fault diagnosis”, NDT&E International, (2004).
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Estimation of misalignment in bearing shaft by signal processing of acoustic signal

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