4.4 Vibration Analysis Method
4.4.1 Time Domain Analysis
The time domain is measurement of the vibration signal as a function of time and can be used for mechanical fault detection. The most commonly used parameters of the vibration signal levels are the peak values (PV), root mean square (RMS), crest factor and kurtosis (Alguindigue 1993). The time domain analysis is used to process the collected vibration signals by an accelerometer attached to the machine, component or rig. There are indicators called “condition indices” which are used to indicate whether the machine’s condition is acceptable or not.
Time domain methods are appropriate when the faults in the system produce wideband frequencies due to periodic impulses. Use of the waveform enables changes in the vibration signature allowing the faults to be detected, but it is often difficult to diagnose the source of faults. The condition indices are used to describe the machine’s condition and are expected to increase in the presence of faults and further increase as the fault severity increases. The procedure consists either of visual inspection of the time domain signal, or to analytically examine the time domain vibration signal and extract statistical parameters (Alguindigue 1993; Sait 2011).
Figure 4.5, shows the raw time domain waveform with the effect of varying degrees of installation shaft misalignment of planetary gearbox at (Healthy, 0.4mm, 0.7mm and 1.0mm respectively). The amplitude in Figure 4.5, does not give any clear information which makes the fault detection and fault locating very difficult. In general, time domain analysis is not
112 DEGREE OF DOCTOR OF PHILOSOPHY (PHD)
useful for the identification of the gear faults, and this method has had limited success for detecting localised defects in planetary gearboxes (Alguindigue 1993).
Figure 4.5 Waveform of the vibration signal for a planetary gearbox: healthy and with misalignment faults
4.4.1.1 Filters Classifications
A pass band filter is a device for passing only a band of frequencies; signal frequencies lying outside the pass band are removed or weaken. Filters fall into one of the following categories, based on the overall shape of their pass band (Zhang-Cheng and Jia-Sheng 2010). Generally, there are four types of filters, see Figure 4.6, low-pass filters which pass low frequency signals; high-pass filters which pass high frequency signals (up to infinity); band stop filters which reject signals occurring between two given frequencies (band-stop filters are also called notch filters when the stop band is narrow); and band-pass filters which pass only signals between two given frequencies, blocking lower and higher signals and are often
0 0.1 0.2 0.3 0.4 0.5 0.6 -100 0 100 Time(s) A m p lit u d e (m /s 2)
Planetary gearbox vibration at S40L90-2-Healthy
0 0.1 0.2 0.3 0.4 0.5 0.6 -100 0 100 Time(s) A m p lit u d e (m /s 2)
Planetary gearbox vibration at S40L90-2-0.4mm
0 0.1 0.2 0.3 0.4 0.5 0.6 -100 0 100 Time(s) A m p lit u d e (m /s 2)
Planetary gearbox vibration at S40L90-2-0.7mm
0 0.1 0.2 0.3 0.4 0.5 0.6 -100 0 100 Time(s) A m p lit u d e (m /s 2)
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characterised as having a bandwidth that is symmetric around a centre frequency (Sait 2011; Ramsden July/2001).
The band-pass filter should be set where the effect of the bearing fault is predominant in the spectrum. It could be anywhere in the middle range of the spectrum where there are no other significant contributors except for background vibrations (Stack 2004).
Figure 4.6 Type of filters reproduced from (Stack 2004)
The structure and the machine of which the bearing or gear are part will have natural frequencies or resonances that are very sensitive to excitation. It can happen that the bearing or gear fault will have a frequency that is close to one of these resonances and may well excite that resonance, thus the resonance will amplify the line spectrum, giving at least, a better signal or noise ratio, but there are drawbacks, for example;
1. The vibration level measured is very sensitive to the placement of the sensor and the measured values may represent the structural properties rather than the bearing condition. 2. If the resonances are very narrow or very lightly damped, they may contaminate the signal
envelope. With low damping, the resonance may cause the pulse to “ring”, broadening out the envelope of the pulses (Stack 2004).
114 DEGREE OF DOCTOR OF PHILOSOPHY (PHD)
4.4.1.2 Root Mean Square (RMS)
The RMS value is the square root of an average of squared values of the waveform. In a sinusoidal wave, the RMS value is 0.707 times the peak value of the wave. From the figure below it can be seen that it is the area under the curve. If the negative area under the curve is rectified by changing it into the positive area, the resultant wave will show a constant level and this level is proportional to the root mean square value (Steve Sabin 2006; Bruel.V 2009; M. P. Norton 2013).
Figure 4.7 RMS and Peak-Peak Value reproduced from (Steve Sabin 2006; Bruel.V 2009;
M. P. Norton 2013).
Determination of the RMS value of particular vibration amplitude of a certain signal is vitally important. The value of RMS of the amplitude of the acceleration can be expressed as (2010).
2 1 1 N n RMS x n M N
(4.1) 1 1 ( ) N n M X n N
(4.2) where; 𝑁 -is the number of samples taken from the signal. 𝑥(𝑛) -is the amplitude of the signal for the 𝑛 sample. 𝑀 -is the average amplitude of the N the sample.
115 DEGREE OF DOCTOR OF PHILOSOPHY (PHD)
4.4.1.3 Peak Value (peak –peak)
Peak Value (Peak-Peak) is the peak amplitude of the wave. Peak is the maximum distance the wave deviates from the zero or equilibrium point. Peak from zero to positive value is known as the positive peak and peak from the minimum value to zero is known as the negative peak as in Figure 4.7 .The vertical distance from positive peak and negative peak is called peak to peak value. In a sinusoidal wave, positive peak distance and negative peak distance are exactly the same but this is not necessarily the case for every waveform (Stack 2004; 2010).
4.4.1.4 The Crest Factor
The Crest Factor (CF) can be defined as the peak-to-RMS ratio of the measured vibration see Equation (4.3) and Figure 4.8 it gives a first indication of bearing failure. The lower curve in the figure shows a typical trend for the CF as a bearing condition deteriorates. At the beginning healthy component shows a relatively constant ratio of peak to RMS value. As a localised fault develops, the resulting short bursts of vibration increase the peak level substantially but have little influence on the RMS level, therefore the CF increases (Bruel.V 2009). As the fault develops, the peak level will typically grow to a certain limit and, as the gears deteriorate further, more spikes will be generated in the vibration signal and the RMS value increases relatively (Bruel.V 2009; M. P. Norton 2013).
116 DEGREE OF DOCTOR OF PHILOSOPHY (PHD)
* Peak value CF RMS (4.3) 4.4.1.5 Kurtosis
The kurtosis is a statistical calculation of signal, (see Equation 4.4). The kurtosis is a statistical measure of the number of peaks in a signal and their amplitudes, the more and sharper the peaks in a signal the greater the value of the kurtosis (Bruel.V 2009).
4
1 1
/ [ ]
kurtosis enhance the RMS
N N