Although the great differences in the nature of maintenance operations in industrial facilities, it contains the processes where similar quantities such as; vibration, temperature, oil quality, etc. are measured. During these processes, data from sensors are converted into different units with transducers and comments are made about system health. RMS (Root Mean Square) is generally used in vibration analysis. It is widely used because the RMS vibration profile gives information about the energy content and thus the destructive capacity of the vibration. However, it is not correct to deduce about the system with a single parameter. Therefore, various parameters are used in troubleshooting, and a multi-parameter approach gives the best results to help identify the root cause of the problem. Sensemore provides outputs by adopting this procedure with various parameters in its interface for accurate detection in vibration analysis, while also allowing the user to add different telemetry.

The biggest advantage of vibration analysis is that it can detect developing problems of machinery and equipment before they become too serious and cause downtime. This can be achieved by monitoring machine vibrations regularly or in certain intervals. Fault detection can be performed in various ways. We can examine the methods used in predictive maintenance under 2 main headings:

1. Time Waveform Analysis

2. Frequency Domain Analysis

**Time Waveform Analysis**

The waveform is created when the vibration signal is taken from an accelerometer and then converted into a digital signal and then imaged. This signal is in the time domain. The time domain is the amplitude plotted against time. While the vibration problem in most machines is detected using spectrum analysis, some types of waveforms can also be used effectively to enhance spectral information. Time waveform can be used effectively for low speed applications, assessing the severity of bearing failures, showing true amplitude, improving spectral information in situations where looseness and beats occur.

*Rolling elements in roller bearings *create periodic effects when they encounter a small crack or wear. In the presence of external noise, the spectrum of this signal may not show a well-defined peak, but when acceleration occurs, they will usually form peaks with repetition rates equal to the race’s defective frequency or bearing ball pass frequency period.

Fig. 1 Typical Faults a)Imbalance b)Outer Ring Damage c)Beat Phenomenon d)Looseness

When there are two or more adjacent machines operating at almost the same speed, a *beating phenomenon* occurs with the current sum and difference frequencies. The beat frequency may not be clearly visible in the spectrum as it corresponds to an exceptionally low frequency. However, it is clearly seen in the time record as an amplitude modulated signal.

In many cases of *looseness*, such as a bearing block that rises slightly during part of the rotation causing the vibration and then touches the base for the rest of the cycle, the waveform flattens above a certain value. It will manifest in the spectrum as harmonics that are indistinguishable from other types of waveform distortion that also produce harmonics. Such looseness in which movement from the time waveform is constrained in one direction can be quickly identified.

When a loose machine component impacts a piece of equipment at a speed unrelated to machine speed, it generates random vibrations, often non-periodic. Although this spectrum is similar to other broadband noise sources, the effects are very clearly visible in the time domain waveform.

Some indexes can be extracted from the time record of a vibration signal that are useful in diagnosis. The most commonly used indices are statistical parameters that can be calculated from the raw signal, highlighting differences between logs and making them useful for diagnostics and trend. Since these parameters are affected by the vibrations of all the components of the machine, they cannot exactly identify the faulty component in the machine but allow us to take action against faults. Some of these parameters are RMS, crest factor, skewness, kurtosis factor and clearance factor. Creating these features at regular intervals (trend tracking) is a common situation monitoring technique. The fact that these properties differ significantly from the reference or baseline values (measured under normal conditions) will indicate that there are malfunctions in the system.

The *RMS *value is calculated by taking into account the time history of the wave. It is a measure of the energy content in the vibration sign and therefore one of the most accurate statistical parameters for the severity of machine failure. This feature is good for monitoring the overall vibration level but does not provide any information about which component is faulty. The RMS value can be highly effective in detecting a major imbalance in rotating equipment systems. The RMS value also increases with the occurrence of shock pulses. The following equations can be used to calculate RMS values for discrete and continuous time signals.

Fig. 2 RMS Formula

*Crest Factor *is defined as the ratio of the peak value of a waveform to its RMS value and is therefore a dimensionless quantity. The expression on the figure 3 defines the crest factor. The crest factor of a sine wave is 1.414. When a typical vibration signal is received from a machine with a large imbalance, no other problem, a crest factor of 1.5 is achieved, while the crest factor becomes much greater as the bearings start to wear and result in impacts. The basis of the approach is that when a bearing breaks down, peak levels of acceleration increase faster than RMS levels due to the increase in impulsivity. The crest factor is easily calculated and is relatively insensitive to bearing speed and load. In the initial stage of bearing damage, the inner race of the bearing, bearing housing, rolling elements, and cage can generate periodic impact signals. This causes the crest factor value to increase. However, as the damage worsens, the RMS value will increase and cause the crest factor value to decrease.

Fig. 3 Crest Formula

The* skewness *measures the asymmetry behavior of the vibration signal through the probability density function. The skewness of a distribution is defined as the absence of symmetry. Skewness is a dimensionless measure and measures how unsymmetrical the signal is around the mean. If the signal is symmetrical, the skewness is zero. For most vibration signals, the probability distribution is symmetrical about the mean like the normal distribution. So, the non-zero skew in most cases indicates that something is wrong.

Fig. 4 Skewness Formula

The* kurtosis factor *is a statistical indicator used to characterize the pulse condition of a signal. A high kurtosis factor indicates the presence of repetitive impulses. It contributes to determining whether the spectrum includes small peaks scattered over a wide frequency range or a few peaks located at specific locations. It is particularly suitable for monitoring the bearings of low-speed rotating shafts where frequency-based techniques are limited. Kurtosis is also widely used to detect non-periodic shocks. The kurtosis factor of a normal bearing is 3. Signals with a larger kurtosis value have more peaks; these are the peaks that are greater than three times the RMS value of the signal.

Fig. 5 Kurtosis Factor

**Frequency Domain Analysis**

Time signals are more easily interpreted using mathematical transformations to obtain processed signals that reveal information that is not easily visible in the raw signal. The most common of these is the conversion to the frequency domain. The time domain is transformed into the frequency domain by applying Fourier Transform to the vibration signal. In this method, the energy in the original signal is divided into various frequency components and the amplitude versus frequency representation of this signal is obtained. The main advantage of this format is that any periodicity in the vibration signal is clearly displayed as peaks in the spectrum at corresponding frequencies. This allows early detection of faults that often create certain characteristic frequency components in the vibration signal and to trend over time as the situation worsens. However, the disadvantage of frequency domain analysis is that a significant amount of information (transitions, non-repetitive signal components) can be lost during the conversion process. This technique is the most widely used technique in machine diagnosis and 85% of mechanical problems in rotating equipment can be detected.

Fig. 6 Signal View from Time and Frequency Domains

Each equipment that makes up the machines has characteristic frequencies against the driven force. These frequencies are also used in the diagnosis of machine failures. Various faults create specific spectra. After the signals received in time form are transformed into frequency domain, they can be compared with characteristic fault spectra, and interpretation can be made about which equipment and why the fault occurred. The characteristics of the failure are the rotation speed of the rotating element, the bearing inner/outer race transition frequencies, the gear network frequency, etc. determines equipment specific frequencies. For example, if we examine the parallel misalignment problem in a motor-pump system connected to each other by a coupling, a radial peak occurs at the motor rotation frequency in the spectrum. While peaks are formed at the 2^{nd} and 3^{rd }times of the motor rotation frequency, the 2^{nd} harmonic can be seen predominantly. However, this spectrum can also be observed at the start of the fault. In order to measure the severity of the situation, the amplitude values of the characteristic frequencies that make up the fault are used. In this way, threshold values that show the severity of the situation can be established with reference to various standards. Therefore, in the spectrum, we look at the frequency axis to find the cause of the failure, and the amplitude axis to determine the severity of the failure.

Fig. 7 Characteristic Parallel Misalignment Spectrum

Sensemore offers various solutions for vibration analysis in Time Waveform and Frequency Domain. You can observe the raw data you receive from the accelerometer in G_{RMS} and V_{RMS} format. You can create alarms by observing the trend of periodic measurements of your equipment in total G_{RMS}, V_{RMS}, temperature values according to time. You can also receive these alarms by mail or mobile notification. It allows you to monitor the situation by creating trends according to various statistical parameters such as crest factor, kurtosis, skewness in order to analyze your data in time domain more easily. In spectrum analysis, you can easily observe the harmonics of the peak-forming frequencies and make comparisons with the common fault spectra in our library.

Fig. 8 Sensemore LAKE Facility Dashboard

**References:**

- C. Scheffer, P. GirdharMachinery Vibration Analysis & Predictive Maintenance(Oxford:Elsevier, 2004) –
- A. Brandt, Noise and Vibration Analysis(New Delhi: Wiley, 2011)
- C. Sujatha, Vibration and Acoustics(New Delhi:Mc Graw Hill Education, 2010)