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The
elements in various mechanical power transmission systems have a specific
pattern of vibration that depends on the construction and condition of the
machine. Any variation in vibration pattern indicates the initiation of fault
in machine. The main purpose of vibration analysis is to identify condition of
gearbox, to distinguish the good and faulty gear and to identify the defective
component.

Variation
in transmitted force is one of the most important mechanisms responsible for
the vibration.

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Various vibration
analysis techniques are Time Domain Techniques, Frequency Domain Technique,
Time Frequency Analysis and Envelope Analysis 3. The frequency domain methods
include Fast Fourier Transform (FFT), Hilbert Transform Method and Power Cestrum
Analysis, etc. 1. Vibration analysis of mechanical system can be based on an
on-line computer monitoring system. The type of analysis to be applied depends
on the type of fault/defect, and therefore it is an important criterion to
investigate the cause of faults in the vibration signal 4. In these papers
the authors have analyzed the effect of tooth breakage on the vibration signal
with the help of MATLAB software.

The
signals are taken from experimental setup consisting of two stage spur gear
system (fig. 2.0). The vibration signals are analyzed using fast Fourier
transform (FFT), a frequency domain technique. The method is defined in below
sections.

List
of Equipment used

For this
project, we not only require the use of Solidworks
which is used for modelling and simulation of the Gear parts ad assembly but
also the use of either Matlab or Excel which is used to create the Fast
Fourier Transforms (FFTs). In order to create the FFT, we have taken the
results we got from our experiments in the Lab on Helical Gears running at
1000, 3000 and 5000rpm and constructed a graph of the FFT on Excel

Frequency domain technique

The
vibration signals, logged from mechanical power show system with the help of an
accelerometer, are in time domain. But it is hard to detect clear symptoms of
any defect in the gear from only the time domain, particularly if the defect is
at an early stage 5. Incidence domain is the most general approach for the analysis
of gear faults. Occurrence domain techniques convert time-domain vibration
signals into discrete frequency components using a fast Fourier transform
(FFT). The fast Fourier transform of time domain signal into frequency domain
is shown in fig. 1.0. This is a method of taking a real world, time varying
signal and splitting it into components, each with amplitude, a phase and a
frequency 6. Frequency domain does not carry any information that is not in
the time domain. The frequency domain is simply another way
of looking at signal information. The main advantage of frequency-domain
analysis over time-domain analysis is that the repetitive nature of the
vibration signals is clearly displaced as peaks in the frequency spectrum and
it has ability to easily detect the certain frequency components of interest
3.

Fast
Fourier Transform (FFT)

The Fast Fourier Transform (FFT) is a class of
special algorithms which implement the discrete Fourier transform with
considerable savings in computational time. The FFT is not a different
transform from the DFT, but rather just a means of computing the DFT with a
considerable reduction in the number of calculations required 1. The discrete
Fourier Transform is defined as

?1

x(k) = ? x(n)-j2?nk/N

n=0

Here:

X : the frequency domain representation of time
series signal ‘x’.

K : the ‘k’ frequency component ; k = 0, 1,
2,…. N-1.

N : the total number of samples in signal ‘x’.

x : the time series signal.

n : the n’th sample (in the time domain).

J : the imaginary unit 8.

Experimental Set- Up

The experimental set up is shown in fig. 2.0.

It consists of a motor, compound (two stage reduction) gear box. The input
shaft of gearbox is connected to 0.5 HP, 1500 rpm electric motor through
Oldham’s coupling. All drive shafts are supported at its ends with antifriction
bearings. A dimmer is used to vary the speed of electric motor and speed of
motor or input shaft is measured with the help of tachometer. The vibration
data is composed from the drive end manner of gear box using the accelerometer.

The composed vibration data are managed in MATLAB software for signal
processing.

The vibration signals from a healthy gear are composed
at a shaft speed of 1000, 3000 and 5000 rpm. Tooth breakage Fault is induced in middle shaft gear and the

Tooth
Breakage Defect

When two gears meshes with each other to
transmit a load, the teeth of each gear are under bending action due to
periodic effect of the load, fatigue crack may occur near the tooth base
resulting in ultimate failure of the tooth 9. Tooth breakage fault is shown
in Fig. 3.0

Observations

Vibration signals at speed 1000 rpm

The time domain trembling signals for both
perfect working disorder and Breakage fault condition at 1000 rpm speed without
filling are taken and shown in figure 4.0 and figure 5.0 correspondingly

Gearbox
with breakage fault

The time domain vibration signals of both fit
gear and gear with breaking fault are converted into incidence domain with the
help of FFT. Which is shown in figure 6.0 and figure 7.0 correspondingly.

Vibration
signals at speed 3000 rpm

The time domain vibration signals for both
perfect working condition and Breakage fault condition at 3000 rpm speed

The time domain vibration signals of both fit
gear and gear with breakage fault are converted into frequency domain with the
help of FFT. Which is shown in figure 10.0 and figure 11.0 respectively

Vibration
signals at speed 5000 rpm

The time
domain vibration signals for both perfect working condition and Breakage fault
condition at 5000 rpm speed without loading are shown in figure 12.0 and figure
13.0 respectively. 