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.

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

vibration readings are taken.

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

without loading are shown in figure 8.0 and figure 9.0 respectively.

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.