### Vibration Glossary

**Heavy Point: **It is the angular position of the unbalance vector at a given lateral position on the shaft. The heavy spot typically does not change with the rotational speed.

**Received Signal Strength Indication(RSSI):**** **Shows the received signal strength. Larger Rssi value means stronger signal. It takes negative values due to the logarithmic formulation.

**Subharmonic:** Sinusoidal quantity of a frequency that is an integral submultiple of a fundamental frequency.

**Analog Signal:** Analog is a continuous flowing signal that changes with time in terms of vibration signal. This is the reverse of the digital representation of the vibration signal, which is a sampled and quantized signal, usually consisting of a series of numbers in binary representation.

**Analog to Digital Converter(ADC): **It is the name given to systems that perform the process of sampling an analog signal to produce a series of numbers that are digital representation of the same signal. In order to avoid aliasing, the sampling frequency should be at least 2 times the highest frequency in the signal according to the Nyquist theorem.

**Failure: **Conditions where any item or part does not work as specified or becomes inoperable.

**Asynchronous: **Vibration components that are not related to rotating speed, also referred to as nonsynchronous.

Fig. 1 Misalignment

**Discrete Fourier Transform:** It is the method used to calculate discrete frequency components like filters, lines from sampled time data.

**Misalignment:** Misalignment, which is one of the major faults that cause vibration, is the position of the machine, motor etc. related to another part in the system like pump, fan, etc. or incorrect connection of the connection element.

**Band Pass Filter:** It is a filter with a single transmission band extending from low frequencies to high cut-off frequencies. The width of the band is normally determined by separating the frequencies at which the amplitude is attenuated by 3 dB a factor of 0.707.

**Bode Diagram: **It is a rectangular coordinate chart consisting of 1x component amplitude and phase (with respect to a key phasor) versus operating speed. It gives information about the stability of systems depending on the frequency.

**BPFI(Ball Pass Frequency Inner): **Common abbreviations for ball pass frequency of defects on inner bearing races. It is also called the inner race defect frequency.

**BPFO(Ball Pass Frequency Outer):** Common abbreviations for ball pass frequency of defects on outer bearing races.

**BSF(Ball Spin Frequency): **The frequency with which the balls rotate around their centerline in a bearing. This frequency depends on the bearing geometry and the running speed of the bearing, and is rarely a harmonic of the rotational speed. It is difficult to predict accurately due to differences in bearing geometry, contact angle and load. The ball spin frequency is one of the fault frequencies specified in the machine vibration spectra.

**Impact Test: **It is a response test where the broad frequency range produced by an impact is used as the stimulus. Sometimes referred to as a bump test. The resulting spectrum will contain peaks corresponding to the natural frequencies or resonances of the equipment.

**Balancing:** A procedure for adjusting the radial mass distribution of a rotor so that the mass centerline approaches the rotor geometric centerline.

**Balanced Condition:**** **For rotating machinery, a condition where the shaft geometric centerline coincides with the mass centerline.

**Unbalance:** It is defined as the unequal distribution of mass that causes the mass axis to differ from the bearing axis. During rotation, radial acceleration due to unequal mass and rotation generates centrifugal force. This results in force on the bearings or vibration of the bearings.

**Resolution: **The smallest change in stimulus that will produce a detectable change in the instrument output.

**Displacement: **It is the change in distance or position of an object relative to the reference.

**Rectangular Window:**** **It is the relative motion vibration window function measured with respect to a selected reference. Creates a more scalloped, narrower peaks and a lower noise floor window.

**Dynamic Signal Analyzer(DSA): **Vibration analyzer that uses digital signal processing and the Fast Fourier Transform to display vibration frequency components. DSAs also display the time domain and phase spectrum, and can usually be interfaced to a computer.

**Stiffness: **It is the resistance of an object to resist deformation in response to an applied force. The complementary concept is flexibility. The more flexible an object is, the less rigid it is.

**Gear Mesh Frequency: **A potential vibration frequency on any machine that contains gears; equal to the number of teeth multiplied by the rotational frequency of the gear.

**Order:** In rotating machines, orders are multiples or harmonics of the rotation speed. When comparing vibration spectra of rotating machines, it is convenient to express the frequency axis of the spectra orderly, especially if the machine speed varies between measurements.

**Rolling Element Bearing: **It is bearing whose low friction qualities derive from rolling elements (balls or rollers), with little lubrication.

**Condition Monitoring: **Condition monitoring is the process of monitoring a parameter of condition in machinery (vibration, temperature etc.), in order to identify a significant change which is indicative of a developing fault. It is a major component of predictive maintenance. The use of condition monitoring allows maintenance to be scheduled, or other actions to be taken to prevent consequential damages and avoid its consequences.

**Impulse Response:** The response of a system to an impulse as input signal. The output then produces the impulse response that is the time domain equivalent to the Frequency Response Function(FRF).

**Low Pass Filter: **It is a filter that transmits signals with a frequency lower than a selected cut-off frequency and attenuates signals with a higher frequency than the cut-off frequency.

Fig. 2 Phase Difference

**Eccentricity Rate: **The vector difference between the bed centerline and the mean steady state centerline.

**Phase: **A measurement of the timing relationship between two signals, or between a specific vibration event and a keyphasor pulse. Phase is often measured as a function of frequency.

**Frequency: **The rate of repetition of a periodic event is usually expressed in cycles per second (Hz), revolutions per minute (rpm), or multiples of rotational speed. It is usually called 1x for spin speed, 2x for twice spin speed, etc.

**Frequency Modulation(FM): **The process where the frequency of the carrier is determined by the amplitude of the modulating signal. Frequency modulation produces a component at the carrier frequency, with adjacent components (sidebands) at frequencies around the carrier frequency related to the modulating signal.

**Fundamental Train Frequency(FTF): **FTF is the rotation speed of the cage or ball retainer in bearings. It is usually about 0.4 times the running speed. The FTF itself rarely appears in a vibration spectrum because the cage is not very large and is essentially unloaded.

**G:** It is the acceleration of gravity(G=9.81 m/s^{2}).

Fig. 3 Wavelength

**Amplitude: **The magnitude of dynamic motion or vibration. Amplitude is expressed in terms of peak-to-peak, zero-to-peak, or rms. DSAs generally read rms for spectral components, and peak for time domain components.

**Amplitude Modulation(AM): **The process where the amplitude of a signal is varied as a function of the instantaneous value of a another signal. The first signal is called the carrier, and the second signal is called the modulating signal. Amplitude modulation always produces a component at the carrier frequency, with components (sidebands) at the frequency of the carrier frequency plus minus the modulating signal.

**Power Spectral Density(PSD):** It shows the strength of variations (energy) as a function of frequencies. In other words, it shows which frequency changes are strong and which frequency changes are weak.

Fig. 4 Power Spectral Density

**Noise: **Noise, in its most basic sense, is unwanted interference that affects or distorts a vibration signal. Noise can interfere with both analog and digital signals.

**Harmonics: **It is frequency component at a frequency that is an integer multiple of the fundamental frequency.

**Hanning Window:** It is an FFT window function that normally provides better frequency resolution than the flat top window, but with reduced amplitude accuracy.

**Hertz(Hz):** The unit of frequency represented by cycles per second.

**Fast Fourier Transform(FFT):** A fast Fourier transform (FFT) is an algorithm that calculates the discrete Fourier transform (DFT) of some sequence. The discrete Fourier transform is a tool to convert specific types of sequences of functions into other types of representations. Another way to explain discrete Fourier transform is that it transforms the structure of the cycle of a waveform into sine components.

Fig. 5 Fourier Transform

**Alignment: **A condition of rectification whereby the axes of machine components are either coincident, parallel, or perpendicular, according to design requirements.

**Accelaration: **The time rate of change of velocity. Typical units are ft/s^{2}, meters/s^{2}, and G’s (1G = 32.17 ft/s^{2 }= 9.81 m/s^{2}). It shows the change in both the speed and direction intensity of the object.

**Accelerometer: **It is device that measure the acceleration applied to a mass.

**Gyroscope:** It is a device that detects angular velocity from the coriolis force applied to a vibrating element.

**Calibration: **It is a series of operations and settings that establish the relationship between the values indicated by a measuring instrument or measuring system and expressed by a scale under specified conditions and the system whose values are known as the reference that measures that system.

**Blade Pass Frequency(BPF):** In the case of a fan or turbine, the speed at which the blades pass through a fixed position is called the blade pass frequency. It is calculated as number of blades times the number of revolutions of the rotor. Blade pass frequency is one of the fault frequencies that attracts attention in machine vibration spectra.

**Bow: **A shaft condition in which the geometric centerline of the shaft is not straight.

**Cavitation:** A condition which can occur in liquid-handling machinery (i.e. centrifugal pumps) where a system pressure decrease in the suction line and pump inlet lowers fluid pressure and vaporization occurs. The result is mixed flow which may produce vibration.

Fig. 6 Cavitation of Impeller

**Journal Bearing**: It is a bearing that supports the shaft on a thin oil film. The liquid film layer can be produced by journal rotation (hydrodynamic bearing) or by externally applied pressure (hydrostatic bearing).

**Cut-off Frequency: **The cut-off frequency is a limit in a system’s frequency response at which the energy flowing through the system begins to be reduced rather than passing through it. In general, cut-off frequency in filters is applied to an edge with low pass, high pass, band pass or band stop feature.It is applied to reduce the noise in the system.

**Critical Speeds: **It is generally any rotational speed associated with high vibration amplitude. Often times the rotor corresponds to the natural frequencies of the system.

**Criticality Index:** The Criticality Index is often used to determine the purpose of the machine, redundancy (i.e. is there a standby machine that can take over if the machine fails), the cost of repairs, the degree of condition monitoring on a particular machine, taking into account downtime effects.

**Critical Machinery:** They are critical equipments for most of the plant process. Failure of these machines also affects other machines and causes downtime in the system.

**Mechanical Looseness:** It is a phenomenon caused by mechanical looseness or improper fit between component parts can often be characterized by abnormally high amplitudes long frequency harmonics or 1/2 rotating frequency harmonics.

Fig. 7 Mechanical Looseness

**Mechanical Eccentricity:** The change in the outer diameter of the shaft surface with reference to the true geometric centerline of the shaft.

**Mechanical Secretion:** It is the difference between the displacement probe and the position of the shaft center line caused by rolling and surface defects.

**MEMS Sensor: **The term MEMS stands for micro-electro-mechanical systems. Whenever the force is applied to the MEMS sensor, then a balanced mass makes a difference within the electric potential. MEMS accelerometers are low-cost, high precision inertial sensors that serve a wide variety of industrial applications.

**Modal Analysis:** It is the method applied to determine the dynamic character of a structure, including its natural frequency, damping values and mode shape, which is a value dependent on structural deformation.

**Mode Shape: **It is the shape that a structure takes while vibrating at its natural frequency.

Fig. 8 Mode Shapes

**Modulation:**** **Modulation is the replacement of a parameter of a signal by the effect of another signal.

**Nyquist Frequency: **In the process of converting from analog to digital, the input signal must first be sampled. If the signal contains any information at frequencies above half the sampling frequency, the signal will not be sampled correctly and the sampled version of the signal will contain false components due to the aliasing phenomenon. The maximum frequency that can be accurately sampled is called the Nyquist frequency and is equal to half the sampling rate.

**Root Mean Square(RMS):** It is a statistical criterion used to measure the size of varying amounts. It is particularly useful in waves where the change is positive and negative. DSAs perform digital averaging RMS relative to the frequency line in consecutive vibration spectra.

**Sample Size: **It is the number of samples used in a DSA (Dynamic Signal Analyzer) to calculate the Fast Fourier Transform. It is also the number of samples in a time indicator.

**Sampling Rate: **It determines how often the analog-digital conversion will occur. High sampling rate gives more precise values. According to the Nyquist Theorem, the Sampling Rate should be *f*s ≥ 2×*f*_{max}.

**Aliasing:** A phenomenon, which can occur whenever a signal is not sampled at greater than twice the maximum bandwidth of the signal. Causes high frequency signals to appear at low frequencies. Aliasing is minimized by filtering the signal to a bandwidth less than ½ the sample rate.

Fig. 9 Piezoelectric

**Windowing: **Each part of the signals before processing is called a window. Window functions are multiplier functions that highlight the middle of the signal segments. It is used to minimize spectral leaks.

**Period:** The time required for a complete oscillation or a single event cycle. (T = 1/*f*)

**Piezoelectric:** Any material that converts between mechanical and electrical energy. For the piezoelectric crystal, when mechanical stresses are applied to opposite sides, electrical charges are seen on the other pairs.

**Radial Vibration: **Shaft dynamic motion or body vibration in the direction perpendicular to the shaft centerline.

**Resonance: **It is the state of the vibration amplitude and phase change response caused by a system sensitivity corresponding to a certain forcing frequency when it coincides with the natural frequency of the system. Resonance is typically defined by a significant amplitude increase and associated phase shift.

**Degrees of Freedom: **It is a term used in mechanical vibrations to describe the complexity of the system. The number of degrees of freedom is the number of independent variables that describe the state of a vibrating system.

**Free Vibration:** A type of vibration that occurs in systems that are given an initial motion and then released to release freely.

**Finite Element Modeling: **It is a computer-aided engineering technique for predicting the dynamic behavior of a mechanical system before production. For example, FEM can be used to estimate the natural frequencies of a flexible rotor.

Fig. 10 Resonance

**Damping: **The effect on an oscillation system that has the effect of reducing, restricting or preventing its oscillations. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation.

**Spectral Leakage: **If it is desired to draw the frequency spectrum of a single frequency sinusoidal wave, there will be a single straight line on its frequency value. However, when samples of this wave are taken and processed with FFT, not a single line in the resulting frequency spectrum, but a curve covering frequencies close to the frequencies it has, is encountered. This situation is called “spectral leakage”.

**Baseline Spectrum: **It is a vibration spectrum taken when a machine is in good working order.It is used as a reference for monitoring and analysis.

**Trend:** Trend is a graph of vibration level versus elapsed time. Most of the trend vibration data is made by vibration monitoring software and is usually designed to display the vibration level at certain key frequencies over several months or years.

**Flattop Window:** It is the FFT window function that provides the best amplitude accuracy for measuring discrete frequency components.

**Oil Whirl/Whip:** It is a constant vibration where the unit load of the fluid film bed is insufficient. In this condition, the shaft centerline dynamic motion is generally circular in the direction of rotation. Oil vortex occurs at the oil flow rate in the bearing, usually 40% to 49% of the shaft speed. Oil Whip occurs when the rotation frequency coincides with a shaft resonance frequency and is locked.

**Fatigue: **Metal fatigue is a condition in which a metal will lose strength and eventually crack when subjected to too much flex near its elastic limit. If vibrations are not controlled it can cause metal fatigue.

**High Pass Filter:** It is a high-frequency pass filter with a transmission band starting at a lower cutoff frequency and extending (theoretically) to infinite frequency.

### How is Fault Detection Performed?

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)