# Vibration Analysis Dictionary

The field of vibration analysis is filled with technical terms, jargon, acronyms, and definitions. We hope you find this glossary useful!

## Acceleration

The time rate of change of velocity, usually measured in Gs in the English system of measurements, and in meters per second per second (m/s^{2}) in the SI system. It is interesting to note that the G is not actually a unit of acceleration, but is the magnitude of the acceleration due to gravity at the earth’s surface. This causes some undue complexity in converting parameters between acceleration, velocity, and displacement. The value of G amounts to 32.2 feet per second per second.

## Accelerometer

A transducer whose electrical output is directly proportional to acceleration over a fairly wide frequency range. The high-frequency response of an accelerometer is limited by its inevitable internal mechanical resonance. Most common accelerometers respond down to one or two hertz, and some special accelerometers respond all the way down to zero frequency, sometimes called “D. C. response”.

## Algorithm

An algorithm is simply a specific procedure for solving a mathematical problem. In digital computers, algorithms for different purposes are stored and called into play when needed for certain operations. The procedure for calculating the FFT spectrum is an algorithm.

## Aliasing

To digitize an analog signal for processing in digital instruments such as FFT analyzers, it first must be periodically sampled, and the sampling process occurs at a specific rate called the sampling frequency. As long as the sampling frequency is more than twice as high as the highest frequency in the signal, the sampled waveform will be a proper representation of the analog waveform. If, however, the sampling frequency is less than twice as high as the highest frequency to be sampled, the sampled waveform will contain extraneous components called “aliases”. The generation of aliases is called aliasing.

An example of aliasing sometimes occurs in motion pictures, as for instance when the wagon wheels in a Western seem to be going backward. This is optical aliasing, caused by the fact that the frame rate of the movie camera (24 frames per second) is not fast enough to resolve the positions of the spokes. Another example of optical aliasing is the stroboscope, where a moving object is illuminated by a flashing light and can be made to appear stationary, or move backward.

Aliasing must be avoided in digital signal analysis to prevent errors, and FFT analyzers always contain low pass filters in their input stages to eliminate frequency components higher than one-half the sampling frequency. These filters are automatically tuned to the proper values as the sampling frequency is changed, and this occurs when the frequency range of the analyzer is changed.

## Alignment

A condition where the components of a machine are coincident, parallel, or perpendicular, according to design requirements. Misalignment is the condition where the desired coincidence, parallelism, or perpendicularity is not achieved, and it causes abnormally high wear and power consumption in the machine. The procedure to correct misalignment is also called “alignment”.

## AM

See Amplitude Modulation.

## Amplitude

The magnitude, or amount, of displacement, velocity, or acceleration, measured from the “at rest” value. The amplitude of a vibration signal can be expressed in terms of “peak” level, “Peak-to-peak” level, or RMS level. It is somewhat of a de facto standard that Displacement is peak-to-peak, Velocity is peak, and Acceleration is RMS.

Amplitude Units

## Amplitude Modulation

Amplitude modulation, or AM for short, is the fluctuation in amplitude of one signal component due to the influence of another signal component called the modulating frequency. The modulating frequency is usually much lower in frequency than the modulated frequency. Amplitude modulation is a non-linear process, and gives rise to new frequency components in the spectrum which would not be there without the modulation. These new spectral components are called sidebands.

Amplitude Modulated Signal

Amplitude modulation occurs often in vibration signals generated by rotating machines. It is usually recognized by the presence of sidebands in the vibration spectrum. The most common modulating frequency is the turning speed, or 1X vibration component, and common modulated frequencies are gear mesh and bearing tones. See also Demodulation.

## Analog

If quantities in two separate physical systems have a consistently similar relationship to each other, they are called analogous, and one is called the analog of the other. The electrical output of a vibration transducer is an analog of the vibration input to the transducer, and bears a continuous similarity to the vibration itself. This is in contrast to a digital representation of the vibration signal, which is a sampled and quantized signal consisting of a series of numbers, usually in binary notation.

## Analog to Digital Conversion

The process of sampling an analog signal to produce a series of numbers that is the digital representation of the same signal. The sampling frequency must be at least twice as high as the highest frequency present in the signal to prevent aliasing errors.

## Analysis Parameters

The specific characteristics of spectrum analysis, such as frequency range, frequency resolution, windowing function, averaging type and number, etc., are called analysis parameters. They may be different for individual measurement points.

## Angular Frequency

The frequency of sinusoidal motion expressed as the rate of change of angle.

## Anti-Aliasing Filter

The low pass filter in the input circuitry of digital signal processing equipment such as FFT analyzers that eliminates all signal components higher in frequency than one-half the sampling frequency. See Aliasing.

## Apodize, Apodization

Literally, “to remove the foot”. To apodize is to remove or smooth a sharp discontinuity in a mathematical function, an electrical signal, or a mechanical structure. An example of apodization is the use of the Hanning window in the FFT analyzer to smooth the discontinuities at the beginning and end of the sampled time record. When stopping your car, if you reduce the brake pedal force just as you come to a stop, you will not feel a “jerk” and the car will come to a smooth stop. This is a form of apodization.

## Asynchronous

Frequency components in a vibration signature that are not integral multiples of, or harmonics of, the turning speed. Also called non-synchronous components. Belts and rolling element bearings, among other things, generate asynchronous components.

## Attenuation

Attenuation is the reduction in level of a signal when passing through a circuit element, or the reduction in level of vibration energy as it passes through a structure. Attenuation is commonly measured in Decibels, although it may be measured in percent. Attenuation is usually frequency dependent, i.e. the amount of attenuation present varies as a function of frequency. Attenuation of vibration energy in mechanical structures generally increases as frequency rises, but it can be a very complex function of frequency.

## Auto correlation

Auto correlation is a time-domain function that is a measure of how much a signal shape, or waveform, resembles a delayed version of itself. It is closely related to the Cepstrum. The value of auto correlation can vary between zero and one. A periodic signal, such as a sine wave has an auto correlation which is equal to one at zero time delay, zero at a time delay of one-half the period of the wave, and one at a time delay of one period; in other words, it is a sinusoidal wave form itself. Random noise has an auto correlation of one at zero delay, but is essentially zero at all other delays. Auto correlation is sometimes used to extract periodic signals from noise. Certain dual-channel FFT Analyzers are able to measure auto correlation.

## Averaging

In performing spectrum analysis, regardless of how it is done, some form of time averaging must be done to determine the level of the signal at each frequency. In vibration analysis, the most important type of averaging employed is linear spectrum averaging, where a series of individual spectra are added together and the sum is divided by the number of spectra.

Averaging is very important when performing spectrum analysis of any signal that changes with time, and this is usually the case with vibration signals of machinery. It is especially important for low-frequency measurements, which require long averaging times to achieve a good statistically accurate estimate of the spectrum. Linear averaging smoothes out the spectrum of the random noise in a spectrum making the discrete frequency components easier to see, but it does not actually reduce the noise level.

Another type of averaging which is important in machinery monitoring is time domain averaging, or time synchronous averaging, which requires a tachometer to synchronize each “snapshot” of the signal to the running speed of the machine. Time domain averaging is very useful in reducing the random noise components in a spectrum, or in reducing the effect of other interfering signals such as components from another nearby machine.

In the DLI Alert software, the baseline spectrum or reference spectrum can be defined as an average of spectra from several machines. This type of average is an average of previously averaged spectra.

## Axial

Parallel to the centerline of a shaft or turning axis of a rotating part. Axial vibration measurements are an important part of machinery analysis. See also Orientation.

## Background Noise

In machine vibration measurement, there will always be components in the spectrum that are not of interest and may be caused by processes external to the machine being analyzed. These components are collectively called background noise, and can sometimes mask the data of interest. An estimate of the background noise can be made by making a vibration measurement with the machine turned off. Some noise is contributed by the instrumentation itself, and consists usually of random signals and line frequency and its Harmonics. One way to reduce the effect of background noise is to use time synchronous averaging.

## Balancing

The adjustment of the mass distribution of a rotating member so that the forces on the bearings due to centrifugal effects are reduced to small values. The rotor is balanced if the center of the mass distribution is coincident with the center of rotation. Balancing reduces power consumption in machines, reduces vibration levels, and increases bearing life, sometimes greatly.

## Ball Pass Frequency

The frequency corresponding to the rate at which balls or rollers in a bearing pass a particular location on one or other of the races. The inner race and outer race ball pass frequencies are different from each other, and are dependent on the geometry of the bearing and the rotation speed of the bearing. They are generally not harmonics of the turning speed, and are difficult to predict exactly due to variations in bearing geometry, contact angle, and load. The two frequencies are abbreviated BPFI for inner race and BPFO for outer race. Ball pass frequencies are some of the fault frequencies which are noted in the spectra of machine vibration.

## Ball Spin Frequency

The frequency at which the balls or rollers revolve about their own centerline in a bearing. This frequency is dependent on bearing geometry and the running speed of the bearing, and is seldom a harmonic of turning speed. It is difficult to predict accurately because of variations in bearing geometry, contact angle, and load. Ball spin frequency is one of the fault frequencies that are noted in the spectra of machine vibration.

## Band Pass Filter

A filter that only passes energy between two frequencies which are called the lower and upper cutoff frequencies. Band pass filters can be fixed, where the cutoff frequencies are constant, and can be variable, where the cutoff frequencies are varied with time. Variable band pass filters are sometimes used for spectrum analysis, but the FFT analyzer has largely supplanted them.

## Bandwidth

The difference in frequency between the upper and lower cutoff frequencies of a band pass filter or other device is called the bandwidth of the filter or device.

## Baseline Spectrum

A vibration spectrum of a machine that is considered in good condition. In the DLI Alert software, the baseline spectrum may be an average of spectra recorded from several machines of the same type. The baseline spectrum is also sometimes called a reference spectrum, and is used as a basis for comparison to spectra recorded as the machine continues to operate.

## Bearing Tones

Anti-friction bearings, i.e. bearings containing rolling elements like rollers or balls, produce vibration excitation forces at specific frequencies dependent on the bearing geometry and rotation speed. These vibration frequencies are called bearing tones. All such bearings, regardless of their condition, will produce some level of bearing tones — the important fact is that they increase in level as the bearing deteriorates.

Four bearing tones are defined for rolling element bearings:

__The Fundamental Train Frequency__, abbreviated FTF, is the rotation rate of the cage or ball retainer. It is usually about 0.4 times the running speed. The FTF itself is seldom seen in a vibration spectrum because the cage is not very massive and caries essentially no load. The FTF is seen as a modulating frequency, for instance in the case of a defective roller being carried in and out of the bearing load zone will produce bursts of noise amplitude modulated at the FTF rate, causing sidebands in the spectrum spaced apart by the FTF.

__The Ball Spin Frequency__** **(BSF), which is the rotation rate of the balls or rollers. A defect such as a pit or spall on a ball will introduce the BSF into the vibration spectrum. The BSF is strongly dependent on bearing geometry.

__The Ball Pass Frequency Outer Race__ (BPFO), is the rate at which a ball passes over a fault in the outer bearing race. It is very commonly found in bearing signatures. The BPFO will be about 0.4 x RPM x No. of rollers.

__The Ball Pass Frequency Inner Race__ (BPFI), which is the rate at which a defect in the inner race encounters a ball. BPFI usually is lower in level than BPFO because the vibration source is farther from the transducer — the vibration excitation must pass through the rolling elements and the outer race before being detected. The BPFI will be about 0.6 x RPM x No. of rollers.

## Beat Frequency

If two vibration components are quite close together in frequency, they will combine in such a way that their sum will vary in level up and down at a rate equal to the difference in frequency between the two components. This phenomenon is known as beating, and its frequency is the beat frequency.

There is confusion in some areas between beating and amplitude modulation**,** which also can produce an undulating vibration level. Amplitude modulation is a different effect, and is caused by a low-frequency component being multiplied by a higher-frequency component and is thus a non-linear effect, whereas beating is simply a linear addition of two components whose frequencies are close to one another.

## Bin

In an FFT spectrum, the individual “lines”, or frequency indicators, are sometimes called bins.

## Bit

Short for Binary Digit. A number expressed in binary notation utilizes the digits 1 and 0, and these are called bits.

## Blade Pass Frequency

In the case of a fan or turbine, the rate at which the blades pass by a fixed position is called the blade pass frequency. It is equal to the number of blades times the rpm of the rotor. Blade pass frequency is one of the fault frequencies of interest in machine vibration spectra**.**

## Bode Plot

A type of spectrum plot which consists of a graph of amplitude vs frequency and a graph of phase vs frequency. In most vibration analysis work the phase spectrum is not important and is either ignored or not recorded. In two-channel vibration measurements, such as transfer functions and frequency response measurements used for modal analysis, phase is of vital importance.

## Bow

A shaft with a simple circular curve is said to be bowed. In electric motors, one cause of shaft bow is uneven heating of the rotor laminations due to broken or cracked rotor bars. A bowed shaft will exhibit a large degree of imbalance if the shaft RPM is above the first critical speed.

## BPI, BPFI

For rolling element bearings, the Ball Pass Frequency Inner Race (BPFI), is the rate at which a defect in the inner race encounters a ball. BPI usually is lower in level than BPFO because the vibration source is farther from the transducer – the vibration excitation must pass through the rolling elements and the outer race before being detected. The BPI will be about 0.6 x RPM x No. of rollers.

## BPO, BPFO

For rolling element bearings, the Ball Pass Frequency Outer Race (BPFO), is the rate at which a ball passes over a fault in the outer bearing race. It is very commonly found in bearing signatures. The BPFO will be about 0.4 x RPM x No. of rollers.

## BS, BSF

The Ball Spin Frequency (BSF), is the rotation rate of the balls or rollers in a rolling element bearing. A defect such as a pit or spall on a ball will introduce the BS frequency into the vibration spectrum. The BSF is strongly dependent on bearing geometry.

## Brinnelling

The indentation of a race in a ball bearing due to a large static force or continuous vibratory force applied to the bearing when stationary. A brinnelled bearing will show large amounts of ball pass frequencies in its vibration spectrum and will fail prematurely.

## Broad band

An overall vibration level which encompasses a wide range of frequencies is called a broad band measurement, as opposed to a narrow band or FFT measurement where the energy in narrow frequency bands is measured.

## Buffer

A memory location in a computer or digital instrument which is set aside for temporarily storing digital information while it is waiting to be processed. For instance, an FFT analyzer will have one or more input buffers where the digital words representing the samples of the input signal are kept.

## Bump Test, Impact Test

A bump test is a type of vibration test that is normally run on a non-operating machine. The machine is instrumented with one or more vibration transducers, and it is then impacted with a massive object such as a hammer. The machine will respond to the impact by a vibration that will die away, and the signals from the transducers are recorded and fed into a spectrum analyzer. The resulting spectrum will contain peaks that correspond to the natural frequencies, or “resonances” of the machine. In any machine, the vibration excitation forces from its normal operation should be well away from the natural frequencies to avoid resonant responses that can cause very high and destructive vibration levels.

## Calibration

The verification of the accuracy and repeatability of transducers and measurement electronic systems is called calibration. Vibration transducers are calibrated by subjecting them to a known motion and accurately measuring the electrical output. They are normally routinely calibrated at one-year intervals, and more often if they are subjected to damaging stresses.

## Carrier Frequency

In a signal which is generated by modulation, the frequency being modulated is called the carrier frequency, by analogy to radio broadcasting, where a very high frequency signal called the carrier is modulated by the audio signal. In machinery vibration analysis, an example of a carrier might be a gear mesh frequency which is being amplitude modulated by the turning speed of the gear.

## Cavitation

Cavitation is a condition that often occurs in pumps and water turbines where reduced fluid pressure results in bubbles forming near the surface of the rotor. When these bubbles collapse, relatively large forces are transmitted to the rotor, and eventually it will cause pitting of the surface. Cavitation in pumps commonly happens when the inlet pressure is too low. It causes high-frequency random noise in the spectrum of the machine.

## Center of Gravity

In a mechanical structure, the center of gravity is the point within the structure where the mass seems to be concentrated. If suspended from the center of gravity, the structure would be in equilibrium, and would not tend to rotate due to gravitational attraction. If the center of gravity of a rotor lies on its axis of rotation, the rotor is said to be statically balanced.

## Centrifugal Force

When you swing a stone on a string around in a circle, you apply an inward directed radial force to it through the string to keep it moving in a circle. Otherwise, it would continue to move in a tangential direction in accordance with Newton’s laws of motion. The force applied through the string is called the centrifugal force.

The stone also produces a reaction force equal to the centrifugal force in the outward radial direction, and this is the so-called centripetal force. There exists much confusion concerning these two forces — what is popularly called centrifugal force is usually actually centripetal force. The centripetal force is the force which causes 1X vibration in machines with out of balance rotors.

## Centripetal Force

See Centrifugal Force**.**

## Cepstrum

The Cepstrum is the forward Fourier Transform of a spectrum**.** It is thus the spectrum of a spectrum, and has certain properties that make it useful in many types of signal analysis. One of its more powerful attributes is the fact that any periodicities, or repeated patterns, in a spectrum will be sensed as one or two components in the cepstrum. If a spectrum contains several sets of sidebands or harmonic series, they can be confusing because of overlap. But in the cepstrum, they will be separated similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes lend themselves especially well to cepstrum analysis. The cepstrum is closely related to the auto correlation function.

## Charge Amplifier

A charge amplifier is a special type of preamplifier used with non-ICP piezoelectric accelerometers**.** Its purpose is to convert the extremely high output impedance of the accelerometer to a low value suitable for transmitting the vibration signal over cables to other signal processing instruments. The charge amplifier is sensitive to the amount of electric charge generated by the accelerometer rather than the voltage the accelerometer generates. Because the charge is independent of the cable attached to the accelerometer, the sensitivity of the accelerometer does not vary with cable length as it does when using a voltage amplifier**.**

## Coherence

Coherence is a number between one and zero, and is a measure of the degree of linearity between two related signals, such as the input force of a structure related to the vibration response to that force. Coherence is thus a two-channel measurement, and does not apply to single-channel measurements of vibration signatures. In a frequency response measurement of a mechanical structure, if the structure is linear, the coherence will be one, but if there is some non-linearity in the structure or if there is noise in one or the other measurement channel, the coherence will be less than one.

The dual-channel FFT analyzer is able to measure the coherence between the two channels, and this is a useful tool in determining good from noisy or meaningless data.

## Correction Weight

The correction weight is the added mass applied to a rotor to bring it into a state of balance. To balance some rotors, several correction weights may be needed, and the procedure required to determine the correction weights and their location is called multiple-plane balancing.

## Coulomb Damping

Coulomb damping is mechanical damping that absorbs energy by sliding friction, as opposed to viscous damping, which absorbs energy in fluid, or viscous, friction. Sliding friction is a constant value regardless of displacement or velocity. Damping of large complex structures with non-welded joints, such as airplane wings, exhibit coulomb damping.

## Couple Imbalance

See Imbalance

## Crest Factor

The crest factor of a waveform is the ratio of the peak value of the waveform to the RMS value of the wave form. It is also sometimes called the “peak-to-RMS-ratio”. The crest factor of a sine wave is 1.414; i.e. the peak value is 1.414 times the RMS value. A typical vibration signal from a machine with a large imbalance will have a crest factor similar to this, but as the bearings begin to wear, and impacting begins to happen, the crest factor will become much greater than this. The crest factor is one of the important measures of machine condition.

## Critical Damping

Critical damping is the minimum amount of damping which will prevent a resonant structure from oscillating. The frequency response function of a critically damped system will show no peak at the natural frequency. It is common to express the degree of damping of a system as a percent of critical damping.

## Critical Speed

The critical speed of a rotor is an operating range where turning speed equals one of its natural frequencies due to bending or torsional resonances. If a rotor is operated at or near a critical speed, it will exhibit high vibration levels, and is likely to be damaged. Much rotating equipment is operated above its lowest critical speed, and this means it should be accelerated relatively rapidly so as not to spend any appreciable time at a critical speed.

## Cross Correlation

Cross correlation is a measure of the similarity in two time domain signals. If the signals are identical, the cross correlation will be one, and if they are completely dissimilar, the cross correlation will be zero. Certain dual-channel FFT analyzers are able to measure cross correlation.

## Cycle

One complete period of a periodic waveform is called a cycle. The units for frequency used to be called “cycles per second” until the ISO standardized on the term “hertz”, in honor of Heinrich Hertz, the noted German scientist who was an early investigator of radio wave transmission.

## Damped Natural Frequency

If a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency known as its natural frequency, or “damped natural frequency”. This will be a little lower in frequency than the resonant frequency**,** which is the frequency it would assume if there were no damping. The resonant frequency is also called the “undamped natural frequency”.

## Damping

Damping is the dissipation of energy within a mechanical structure and its conversion ultimately into heat. There are several different mechanisms for damping, the most important two of which are coulomb damping and viscous** damping.**

## Degree of Freedom

In the description of the motion of structures or objects, a degree of freedom is one of several orthogonal components that can be used to completely characterize the motion. For instance, a free object in space has six different degrees of freedom — it can translate in three mutually perpendicular directions, and it can rotate about the three mutually perpendicular axes. Any motion of the object, no matter how complex, can be resolved into these 6 basic motions.

Some objects may not have all 6 degrees of freedom available to them; for instance an elevator in an elevator shaft is constrained to 1 degree of freedom. When describing the motion of a complex structure, different parts may be constrained in different ways, and a great many degrees of freedom may be required to fully describe the overall motion of the structure. In performing modal analysis of a structure or in finite element modeling of a structure, it is not uncommon to consider hundreds of degrees of freedom.

## Demodulate, Demodulation

Demodulation is the process of recovering the modulating signal from an amplitude modulated (AM) or frequency modulated (FM). The demodulator is also called a detector. In the field of vibration analysis, it is sometimes found that certain signal components, such as 1X or run speed, will modulate other components such as gear mesh frequencies or bearing tones. A demodulator can be used to detect and recover these modulating signals. See also Amplitude Modulation and Frequency Modulation.

## Detector

An electronic circuit that determines the amplitude level of a signal in accordance with certain rules. The simplest type of detector consists simply of a resistor and capacitor, and it measures the average value of a continuous fluctuating DC signal. A more complex but must more useful detector is the RMS detector, which is almost always used in vibration analysis systems. Any type of detector performs an average over time, and the averaging time can theoretically be of any length. It is typically set to be several times longer than the slowest fluctuation period of the signal being detected. Most detectors in vibration analysis equipment have an averaging time of about one second. Detectors are used to determine the levels of frequency domain signals (spectra) as well as time domain signals. Time domain detectors are usually of the analog type, while detectors used in FFT analyzers are digital in operation.

Demodulators used in radio receivers are also called detectors.

## Deterministic

A type of signal whose spectrum consists of a collection of discrete components, as opposed to a random signal, whose spectrum is spread out or “smeared” in frequency. Some deterministic signals are periodic, and their spectra consist of harmonic series. Vibration signatures of machines are in general deterministic, containing one or more harmonic series, but they always have non-deterministic components, such as background noise.

## Differentiation

In vibration analysis, differentiation is a mathematical operation that converts a displacement signature to a velocity signature, or a velocity signature to an acceleration signature. It is performed electronically on an analog signal, or can be performed digitally on a spectrum. Differentiation is an inherently noisy operation, adding a significant amount of high frequency noise to the signal, and is generally not used very much in machinery vibration analysis. See also integration **, **which is the inverse of differentiation .

## Digital

Digital instrumentation consists of devices that convert analog signals into a series of numbers through a sampling process and an analog to digital converter. They then perform operations on the numbers to achieve such effects as equalization, data storage, data compression, frequency analysis, etc. This process in general is called digital signal processing, and is characterized by certain advantages and disadvantages. One advantage is that the converted signals can be manipulated, transformed, and copied without introducing any added noise or distortion.

The disadvantage is that the digital representation may not be truly representative of the original signal. Care must be taken that the sampling rate is high enough to encode all the information of interest, and that artifacts are not introduced by aliasing.

## Discrete

With reference to a spectrum, discrete means consisting of separate distinct points, rather than continuous. An example of a discrete spectrum is a harmonic series. An FFT spectrum, which consists of information only at specific frequencies (the FFT lines), is actually discrete regardless of the input signal. For instance, the true spectrum of a transient is continuous, and the FFT of a transient appears continuous on the screen, but still only contains information at the frequencies of the FFT lines.

The input signal to an FFT analyzer is continuous, but the sampling process necessary to implement the FFT algorithm converts it into a discrete form, with information only at the specific sampled times.

## Discrete Fourier Transform

The mathematical calculation which converts, or “transforms” a sampled and digitized wave form into a sampled spectrum. The Fast Fourier Transform, or FFT, is an algorithm that allows a computer to calculate the discrete Fourier transform very quickly.

## Displacement

In machinery vibration, the displacement is the actual distance the vibration causes the part in question to move. It is oscillatory and is measured in thousandths of an inch (mils) in the English system and in millimeters (mm) in the SI system. By popular convention, displacement measurements are made in peak-to-peak units.

## Displacement Transducer

See Proximity Probe.

## Distortion

Distortion is the presence of frequency components in the response of a system that are not present in the excitation of the system, and it is caused by non-linearity in the system. An example is an imbalance in a rotor in a machine that generates a sinusoidal excitation force at the turning speed. If the machine is linear, the resulting vibration will be only at the turning speed, but if there are non-linearities in the machine, such as looseness, then harmonics of the turning speed will also be generated. In other words, the looseness of the machine parts distorts the driving force signal. This property is used to diagnose machine non-linearities such as looseness in machines.

## Domain

A domain is a set of coordinates in which a mathematical function resides. A wave form, for instance, has dimensions of amplitude vs. time, and it is said to exist in the time domain, while a spectrum has dimensions of amplitude vs. frequency, and is said to exist in the frequency domain.

## Dynamic Imbalance

See Imbalance

## Dynamic Range

The dynamic range of an instrumentation device such as an amplifier or an analyzer is the ratio between the smallest signal it will sense without noise contamination to the largest signal it will accept without an overload occurring. Dynamic range is usually expressed in decibels, and most instrumentation used for vibration analysis has a dynamic range of 70 to 80 dB. An overload in any instrument is a gross non- linearity, causing spurious components to appear in the signal, and must be avoided at all costs. For this reason, most vibration instruments have overload indicators that warn the operator of possible data contamination.

## Eccentricity

Eccentricity is the deviation from circularity of a part, such as a rotor or a shaft. In electric motors, eccentricity of the rotor causes undue vibration of the motor due to non-symmetrical magnetic effects. Eccentricity of the stator also causes magnetic effects which increase the vibration level.

## Eddy Current

Eddy currents are electric currents induced in electrically conducting materials by fluctuating magnetic fields. They cause heating of the metal, and are thus wasters of power. A practical use for eddy currents is the eddy current probe, or proximity probe.

## Eddy Current Probe

See Proximity Probe**.**

## Engineering Units, EU

The units in which a measurement is made; for instance velocity may be expressed in millimeters per second, miles per hour, or furlongs per fortnight, depending on the use the data will be put to. Modern instrumentation, such as FFT analyzers allow you to specify what the engineering units are and to apply conversion factors if needed.

## EU

See Engineering Units

## Excitation

In a vibrating mechanical system, the force, or forces, which cause the vibration are called the excitation forces. If a mechanical system such as a machine is excited at a particular frequency, it will vibrate at that frequency, and the vibration can be sensed almost anywhere on it. Machinery analysis uses this basic fact, i.e. when a cracked bearing race causes a force on the bearing housing at its characteristic frequency, this can be sensed by a vibration transducer and the crack thus detected.

## Expert System

The portion of Predictive Maintenance software that automatically examines recorded vibration data, performs a diagnosis of machine problems, and writes a report is called an expert system, or EADS (Expert Automated Diagnostic System) for short.

## Fast Fourier Transform (FFT)

The FFT is an algorithm, or digital calculation routine used in the FFT analyzer, which calculates a spectrum from a time waveform. In other words it converts, or “transforms” a signal from the time domain into the frequency domain. See also **DFT**.

## Fatigue

Metal fatigue is a condition in which a metal will lose its strength and will eventually crack when subjected to too many flexings near its elastic limit.

## FEM

FEM stands for Finite Element Modeling, which is a computer technique that models or simulates a mechanical structure in software. Its physical characteristics such as resonances and deflections under loads are calculated. The FEM model assumes that the structure can be represented by a large number of single degree of freedom spring-mass systems. The purpose of FEM is to perform testing on a structure without having to actually build the structure, saving time and money. When the computer model does what the designer wants it to do, only then is a physical structure constructed.

## FFT

See **Fast Fourier Transform.**

## FFT Analyzer

The FFT analyzer is a device that uses the FFT algorithm to calculate a spectrum from a time domain signal, and is the most common type of spectrum analyzer available today. The FFT analyzer is a very useful device, and is available in a great variety of models with varying complexity. It is the heart of any machinery predictive maintenance program.

## Filter

A filter is an electrical circuit that allows signals of certain frequency ranges to pass through, and blocks all other frequencies. There are many types of filters, such as low pass filters, high pass filters, and band pass filters. Examples of filters used in machinery monitoring instruments are low pass filters to reject high frequency noise and to prevent aliasing, and high pass filters to reject low frequency noise. Variable band pass filters were used in the past to perform spectrum analysis, but they have been largely supplanted by the FFT analyzer.

## Flattop Window

The flattop window is a special window used in some FFT analyzers in addition to the more common Hanning window and rectangular window. The flattop window does not allow as fine a frequency resolution as the Hanning window, but it will accurately measure the level of a signal at any frequency, even if the frequency is between the lines of the FFT analysis. It is used in transducer calibration systems to increase amplitude accuracy.

## Fluid-Film Bearing

A fluid film bearing is a sleeve bearing which supports the shaft, or journal, on a thin film of oil. The oil film layer may be generated by the rotation of the journal itself (hydro-dynamic bearing), or it may be generated by externally applied pressure (hydro-static bearing).

## Forced Vibration

The vibration of a structure or system in response to an applied force. If the system is linear, the vibration will be at the same frequency as the force, but if it is non-linear, the vibration will also occur at other frequencies, especially at harmonics of the forcing frequency. Vibration of machines is typically forced vibration, and the forces result from such things as imbalance and misalignment of rotating parts, and from bearing faults, etc.

## Forcing Frequencies

In a rotating machine, the moving parts impart vibratory forces into the structure, and these forces occur at specific frequencies determined by the dynamics of the moving element. The resulting vibration of the machine will occur at these frequencies and other frequencies that are related to them. The most important forcing frequencies of interest to the maintenance engineer and vibration analyst are the ones related to various faults such as bearing problem, misalignment, mechanical looseness, etc. These frequencies should be identified and kept at hand by the analyst when examining vibration spectra. One of the most important uses of the VTAG is the listing of the forcing functions present in each machine.

## Foundation

The supporting structure for a machine is generally called the foundation, and it is vitally important to the proper operation of the machine. Loose, flexible, or cracked foundations are the cause of many machine problems, especially misalignment.

## Fourier, Jean Baptiste

The famous many-talented French engineer, one time president of Egypt, and mathematician who devised the Fourier series and Fourier Transform for the conversion of time functions into frequency functions and vice versa.

## Fourier Transform

The mathematically rigorous operation that transforms from the time domain to the frequency domain and vice versa. See Fourier Analysis.

## Fourier Analysis

Fourier analysis is another term for spectrum analysis, although it generally refers to analysis using an FFT analyzer.

## Free Running

Free running is an operating mode of an FFT analyzer, and it means the analyzer is set to continuously accept data and perform analyses rather than to wait for a trigger to initiate data acquisition.

## Free Vibration

Free vibration is the continuing oscillation of a structure after the excitation force is stopped. The vibration will then be at the natural frequency of the system and will gradually die away due to the damping in the system.

## Frequency

Frequency is the reciprocal of time. If an event is periodic in time, i.e. if it repeats at a fixed time interval, then its frequency is one divided by the time interval. If a vibrating element takes one tenth of a second to complete one cycle and return to its starting point, then its frequency is defined to be 10 cycles per second, or 10 hertz (Hz). Although the SI standard unit of frequency is the Hz, when analyzing machinery vibration we often find it more convenient to express frequency in cycles per minute, which corresponds to rpm. Frequency in rpm is simply frequency in Hz times 60. Another common frequency representation used in machinery monitoring is multiples of turning speed, or “orders”. Frequency in orders is frequency in rpm divided by the turning speed of the machine. The second order is then the second harmonic of turning speed, etc. This is especially convenient if the machine is varying in speed, for the frequency representation on a spectrum will be the same regardless of speed. Two machine spectra can therefore more easily be compared if they are both expressed in orders. Conversion of the frequency axis of a spectrum to orders is called “order normalization”, and is done by the monitoring software.

## Frequency Domain

Vibration exists in time, and it is said to be in the “time domain”. The representation of a vibration signal in the time domain is a “wave form”, and this is what you would see if the signal were displayed on an oscilloscope. If the waveform is subjected to a spectrum analysis, the result is a plot of frequency vs amplitude, called a spectrum, and the spectrum is in the frequency domain. The waveform is said to be “transformed” from the time domain to the frequency domain. Most detailed analysis of machinery vibration data is done in the frequency domain, but certain information is more easily interpreted in the time domain.

## Frequency Response

The frequency response is a characteristic of a system that has a measured response resulting from a known applied input. In the case of a mechanical structure, the frequency response is the spectrum of the vibration of the structure divided by the spectrum of the input force to the system. To measure the frequency response of a mechanical system, one must measure the spectra of both the input force to the system and the vibration response, and this is most easily done with a dual-channel **FFT analyzer. Frequency response measurements are used extensively in modal analysis of mechanical systems.**

The frequency response function is actually a three-dimensional quantity, consisting of amplitude vs. phase vs. frequency. Therefore a true plot of it requires three dimensions, and this is difficult to represent on paper. One way to do this is the so-called Bode plot, which consists of two curves, one of amplitude vs. frequency and one of phase vs. frequency. Another way to look at the frequency response function is to resolve the phase portion into two orthogonal components, one in-phase part (called the real part), and one part 90 degrees out of phase (called the “quadrature” or “imaginary” part). Sometimes these two phase parts are plotted against each other, and the result is the so-called Nyquist plot.

## FT, FTF

FT stands for “fundamental train frequency”, and is the rotation rate of the “cage” supporting the rollers in a rolling element bearing. The FT is always less than one-half the rpm of the shaft, and is one of the fault frequencies which is monitored in machines. If the vibration spectrum of a machine shows a high amplitude of the FT, it does not mean the bearing has a bad cage, but rather means that one of the rollers is cracked or otherwise deformed. This causes a vibration component to occur each time the roller enters the load zone of the bearing, which is at each revolution of the cage, giving rise to a vibration at that rate. Frequently other fault frequencies in bearings are amplitude modulated by the FT. This means there will be sidebands around these frequencies spaced at the interval of the FT.

## Fundamental Frequency

The spectrum of a periodic signal will consist of a fundamental component at the reciprocal of the period and a series of harmonics of this frequency. The fundamental is also called the “first harmonic”. It is possible to have a periodic signal where the fundamental is so low in level that it cannot be seen, but the harmonics will still be spaced apart by the fundamental frequency.

## Fundamental Train Frequency

See FT, FTF

## G

G is the acceleration due to gravity at the surface of the earth, and it is used as a unit of acceleration in the English system of measurements. G is not exactly constant, but varies a little over the earth’s surface, so an average value of 32.2 feet per second per second is used. In the SI system, G is 9.81 meters per second per second, but is not usually used as a unit of acceleration. Because we use inches per second as a unit of velocity, it would make more sense to use inches per second per second as an acceleration unit, but G has a long tradition behind it.

## Gear-Mesh Frequency

The gear mesh frequency, also called “tooth mesh frequency”, is the rate at which gear teeth mate together in a gearbox. It is equal to the number of teeth on the gear times the rpm of the gear. A gearbox will always have a strong vibration component at the gear mesh frequency, and it is one of the fault frequencies used in machinery monitoring.

## Ghost Frequency

Sometimes the vibration spectrum of a gearbox will contain components which cannot be related to any known geometry of the gearbox. These are called “ghost frequencies”, and are caused by irregularities machined into the gears in the manufacturing process. Ghost components are independent of loading, and tend to disappear as the gears wear.

## GPIB

GPIB stands for General Purpose Interface Bus, and is a method of connecting digital instruments such as FFT analyzers and plotters, etc., together according to the IEEE-488 standard. It is also known as the HPIB, which is a version of it used by Hewlett-Packard.

## Ground Loop

In instrumentation systems, such as vibration measurement data collection systems, it is often required to mount a transducer on a machine whose structure or “ground” may have an electrical voltage present on it caused by current leakage in motor windings, etc. The transducer cable shield is normally connected to the housing, and is then electrically connected to this voltage when the transducer is mounted. If the instrument to which the transducer is connected is connected to a different ground, such as a power line neutral, this difference in the ground potentials will cause a current in the shield, and this will add interference to the measured signal. The interference will be at 60 Hz and its harmonics, and it reduces the signal to noise ratio of the measurement. This condition is called a ground loop, and there are several ways to avoid it. One is to use an insulating disc between the transducer and the machine, and another is to use a battery-operated instrument which is not connected to a power line.

## Hanning Window

The Hanning window, also called “Hanning weighting”, is a digital manipulation of the sampled signal in an FFT analyzer which forces the beginning and end of the time record to zero amplitude. This compensates for an inherent error in the FFT algorithm that would cause the energy at specific frequencies to be spread out rather than well-defined in frequency. The Hanning window causes a distortion of the waveform used by the analyzer to calculate the spectrum resulting in the measured levels being too low. When processing continuous data, this effect is compensated for, but an error is introduced if the Hanning window is used for transient data.

## Hamming Window

Named after its originator, the Hamming window is a Hanning window sitting on top of a small rectangular pedestal. Its function is similar, but has its first side lobes 42 dB down, whereas the Hanning window’s first side lobes are only 32 dB down. Thus the Hamming has better selectivity for large signals, but it suffers from the disadvantage that the rest of the side lobes are higher, and in fact fall off slowly at 20 dB per octave like those of the rectangular window. The Hamming window had some advantage in the days when FFT analyzers only had 50 dB or so of dynamic range, but nowadays it is essentially obsolete.

## Harmonics

Harmonics, also called a harmonic series, are components of a spectrum which are integral multiples of fundamental frequency. A harmonic series in a spectrum is the result of a periodic signal in the wave form. Harmonic series are very common in spectra of machinery vibration.

## Hertz

The unit of frequency in the SI measurement system is the hertz, abbreviated Hz. One hertz is equal to one cycle per second. The name is in honor of Heinrich Hertz, an early German investigator of radio wave transmission.

## High-Pass Filter

A filter that passes signal frequencies above a specific frequency called the “cut-off” frequency. High pass filters are used in instrumentation to eliminate low-frequency noise, and to separate alternating components from direct (DC) components in a signal.

## HTF

See Hunting Tooth.

## Hunting Tooth

The hunting tooth frequency (HTF) is the rate at which a particular tooth on one gear mates with a particular tooth on the other gear. If the numbers of teeth on the gears are a simple ratio such as 1:2 or 1:3, the HTF will be equal to the RPM of the larger gear, but if the numbers of teeth have no common factors, the HTF may be very low. Gear pairs with low HTFs will wear more evenly and last longer than ones with a relatively high HTF. The HTF is equal to the gear mesh frequency divided by the least common multiple of the numbers of teeth on the gears.

## Hysteresis

Hysteresis is a condition that exists in certain systems where a small change in input level does not result in a change in the output of the system. It is also sometimes called “deadband”. Hysteresis exists in many types of systems; i.e. in the magnetization of magnetic media as well as mechanical systems, especially ones that have excessive looseness.

## Hz

See **Hertz.**

## ICP Accelerometer

ICP stands for Integrated Circuit Piezoelectric, and an ICP accelerometer contains within its housing a small integrated circuit which effectively isolates the piezoelectric element from the outside world. A power supply is needed at the signal-conditioning device to supply a constant current of a few milliamperes to the IC. This current is in the same conductor as the signal coming back from the accelerometer, and there must be a series capacitor to isolate the DC source from the signal current.

## Imbalance

A condition of a rotating part where the center of mass does not lie on the center of rotation. Imbalance of a rotor causes a centripetal force at the frequency of the rotation rate to be applied to the bearings. If it is large, it can severely shorten the life of the bearings, besides causing undue vibration of the machine. Forces caused by imbalance are proportional to the square of the RPM, and this means that high-speed machines must be balanced to a higher standard than low-speed machines.

Imbalance exists in several forms. Static Imbalance is the condition where the principal inertia axis of a rotor is offset from and parallel to the axis of rotation. A rotor with static imbalance will seek a position with the heavy spot at the bottom if placed on level knife-edges. Static imbalance can theoretically be corrected by the addition of a single correction mass.

Couple imbalance is the condition where the principal inertia axis intersects the rotation axis of the rotor at the center of gravity. A rotor with couple imbalance will be stable in any position on knife edges, but will produce out-of-phase imbalance forces on the bearings when rotated. Correction of couple imbalance requires the addition of two correction masses.

Dynamic imbalance is a combination of these two types, and is the most common type found in practice. In dynamic imbalance, the principal inertia axis neither intersects nor is parallel to the axis of rotation. Correction of dynamic imbalance requires at least two correction masses.

## Impact Test

See Bump Test.

## Impedance, mechanical

The mechanical impedance of a point on a structure is the ratio of the force applied to the point to the resulting velocity at the point. It is a measure of how much a structure resists motion when subjected to a given force, and it is the reciprocal of mobility. The mechanical impedance of a structure varies in a complicated way as frequency is varied. At resonance frequencies, the impedance will be low, meaning very little force can be applied at those frequencies. Mechanical impedance measurements of machine foundations are sometimes made to insure their suitability for the machine in question. For instance, it would not be good to have a foundation resonance near the turning speed of the machine.

## Inertia

Inertia is the tendency of a mass to remain stationary when it is not moving and to remain in motion when it is moving. Mass is actually a quantitative measure of inertia.

## Integration

Integration is the mathematical operation that is the inverse of differentiation. In vibration analysis, integration will convert an acceleration signal into a velocity signal, or a velocity signal into a displacement signal. Integration can be done with excellent accuracy with an analog integrator in the time domain or can be done digitally in the frequency domain, and for this reason the accelerometer is the best choice of vibration transducer because velocity and displacement can so easily be derived from its output. An analog integrator is actually a low pass filter with 6 dB of attenuation per octave.

## Integrator

The integrator, sometimes called an “analog integrator”, is a simple electronic circuit which performs a mathematical integration on a signal which passes through it. It is most often used to convert the acceleration signal output of an accelerometer to a velocity signal. Integrators are common in signal processing equipment, including FFT analyzers.

## Isolation

Vibration isolation is the reduction in the tendency of a mechanical system to respond to, or to transmit, an excitation, and it is accomplished by a system of resilient supports. The design of such supports is somewhat complex, and depends on the mass of the unit to be isolated, among other things.

## Jerk

Jerk is the rate of change of acceleration, and can be measured by differentiating the output of an accelerometer. It is not normally used in vibration analysis of machinery, but is measured by elevator makers because it is the quantity most easily felt by elevator riders.

## Keyphasor

The keyphasor is an electric pulse, or trigger, which is derived from a point on a rotating shaft. It serves as a zero phase reference for determining where imbalance is on a rotor. Keyphasor is a trademark owned by the Bentley Nevada Company, but has almost become a generic term by popular usage.

## Kurtosis

Kurtosis is a statistical measure of the amplitude distribution of a signal, and heavily weights the fourth power of the signal amplitude. It is strongly affected by the crest factor of the signal, and if trended, is a sensitive indicator of crest factor changes over time. It has been used in machinery monitoring, especially for reciprocating compressors, but has not become commonplace.

## Leakage

In an FFT analyzer, the input signal is recorded in blocks, called time records, and the spectra are computed from the blocks of data. Because the input signal is not synchronized with the length of the block, it will be truncated at the beginning and end of the block. This truncation causes an error in the calculation that effectively spreads out, or “smears” the spectrum in the frequency domain. This phenomenon is called leakage; the signal energy essentially “leaks” from a single FFT line to adjacent lines. Leakage reduces the accuracy of the measured levels of peaks in the spectrum, and reduces the effective frequency resolution of the analysis. Leakage is worst for continuous signals and rectangular window, and it is greatly reduced by use of the Hanning window, which forces the signal level to zero at the ends of the data block.

## Level

In common usage the level of a signal is simply its amplitude, but strictly speaking, the term should be reserved for the amplitude expressed on a decibel scale relative to a reference value.

## Line Spectrum

A line spectrum is a spectrum where the energy is concentrated at specific frequencies (lines or bins), as opposed to a continuous spectrum where the energy is smeared out over a band of frequencies. A deterministic signal will have a line spectrum, and a random signal will have a continuous spectrum. Spectra generated by machine vibration signatures are always a combination of the two types.

## Linear, Linearity

A system is said to be linear if it meets the two following conditions: If input A to the system results in output B, and input 2A results in output 2B AND if input A results in output B and input C results in output D, then input A+C results in output B+D. A linear system generates no spurious signals of its own, and its output frequency is always the same as its input frequency. It is non-linearities in stereo systems that result in harmonic and intermodulation distortions. While mechanical systems tend to be linear, they always exhibit non-linearities when driven at very high levels.

## Low Pass Filter

A low pass filter is a filter that passes signal components at frequencies lower than a specific frequency called the cut-off frequency. An example is the anti-aliasing filter.

## Magnetostriction

Magnetostriction is a property of magnetic materials that causes them to change shape in the presence of magnetic fields. This causes a vibration at the frequency of the field fluctuations, and this is part of the cause of 120 Hz vibration found in electrical machines such as motors and transformers.

## Mask

In predictive maintenance software, a mask (often called alarm envelope) defines the alarm level across the frequency span. You may decide that the vibration level should not increase by more than 6 dB (that is, where the level will double), so you will design the mask so that it is 6 dB above all of the peaks in the reference trace. Every spectrum measurement point on a machine should have its own mask.

## Mechanical Impedance

See Impedance, Mechanical

## Micrometer

The micrometer, or micron as it is sometimes called, is a unit of length in the SI system equal to one millionth of a meter. 25.4 micrometers equals one mil.

## MIL-STD-167-1

This is the military standard that defines acceptable vibration levels. This limit will be used if no average data is available for expert system analysis. This sets the alarm level at 107 VdB above a frequency of about 1000RPM:

## Mils

The mil is the English system abbreviation for one thousandth of an inch. Vibration displacement is usually measured in mils in the English system.

## Mobility

Mobility is the inverse of Mechanical impedance. It is the ease with which a structure is able to move in response to an applied force, and is a function of frequency as well as a function of the location on the structure.

The vibration measured at a point on a machine is the result of a vibratory force acting somewhere in the machine. The magnitude of the vibration is the equal to the magnitude of the force times the mobility of the structure. From this it follows that the value of the destructive forces acting on a machine are not determined directly by measuring the vibration if the mobility is not known. For this reason, it is a good idea to measure the mobility at the bearings of a machine in order to find out the levels of the forces acting on the bearings due to imbalance or misalignment.

## Modal Analysis

Modal analysis is generation of a computer model of a mechanical system from measured frequency response functions of the system. Once the model exists in the software, it can be displayed on the screen and all its modes of vibration can be animated. The model can also be modified by adding or subtracting masses and stiffnesses to evaluate the effect of doing this on the actual system. Modal analysis is an experimental technique, and is often used to verify the accuracy of an **FEM**.

## Mode of Vibration

A mode of vibration is a characteristic pattern or shape in which a mechanical system will vibrate. Most systems have many modes of vibration, and it is the task of modal analysis to determine these mode shapes. The actual vibration of a structure is always a combination or mixture of all the vibration modes. But they need not all be excited to the same degree. For instance, if a bell is rung softly, we hear primarily the fundamental mode of vibration, but if it is hit harder, other modes are excited, and we hear the upper partials of the tone.

## Mode Shape

A mode shape is a specific pattern of vibration executed by a mechanical system at a specific frequency. Different mode shapes will be associated with different frequencies. The experimental technique of modal analysis discovers these mode shapes and the frequencies.

## Modulation

Modulation is the variation of one parameter of a signal by the action of another signal. A common type of modulation is amplitude modulation, where the amplitude of one signal (called the “carrier”) is caused to fluctuate in response to a modulating signal. This is the way AM radio transmission works; a high-frequency wave called the carrier is caused to fluctuate in level in accordance with the voice or music signal being transmitted. The radio receiver picks up the modulated carrier and performs a demodulation to extract the audio signal. Frequency modulation is another type where the frequency of the carrier is varied rather than the amplitude. Modulation of a carrier causes new components to appear in the spectrum and they are called sidebands. The frequencies of the sidebands are equal to the carrier frequency plus and minus the modulating frequency.

In rotating machinery there are many fault mechanisms which can cause amplitude and frequency modulation, and vibration analysis exposes the sidebands. Demodulation can be performed to detect the modulation frequencies directly.

## Narrow band Analysis

Narrow band analysis is technobabble for FFT analysis.

## Natural Frequency

The natural frequency is the frequency at which a mechanical system will continue to vibrate after the excitation signal is removed. It is sometimes called the resonant frequency, but this is inaccurate, for the resonant frequency is the frequency at which it would vibrate if there were no damping. See also Free Vibration.

## Node

In a vibration mode shape the locations where the motion is zero are called nodes. Each mode shape will have its nodes in different places on the structure, and there may be some nodes that are common to several mode shapes.

## Noise

Strictly speaking, noise is any unwanted signal, but the term generally is used to indicate a random signal. Noise is caused by electrical effects as well as mechanical ones, and there are many different types.

## Noise Floor

The noise floor is the residual noise level of an instrumentation system when nothing is being measured. The smallest measurable signal must be above this noise floor if it is to be measured accurately.

## Non-Linear

A non-linear process is defined as any process that violates the rules of linearity. Most properly running machines are essentially linear in their response to vibration excitation, but certain defective conditions introduce non-linearity, and this greatly affects the vibration signature. This fact is the major reason for the success of vibration monitoring as an effective tool for machine condition determination. Non-linearities caused by looseness account for the generation of harmonics of running speed, and defective gears and bearings create non-linearities that cause running speed sidebands to appear in the vibration spectra.

## Non-Linear Damping

Non-linear damping is damping in a mechanical system where the damping force is not proportional to velocity. Many complex structures exhibit non-linear damping, and their behavior at various excitation levels is difficult to predict.

## Normal Mode of Vibration

A normal mode of vibration of a mechanical system is vibration in a mode shape as described under modal analysis. It is difficult to excite a system to vibrate in only one mode at a time unless it is a very simple system; usually all modes are excited at least to some extent.

## Normalization

With regard to vibration spectra of rotating machines, normalization is the process of dividing the frequency values along the x-axis by the turning speed of the machine. After this is done, the machine speed will appear at a frequency of 1, the second harmonic will be at a frequency of 2, etc. A glance at the spectrum is all that is needed to find the harmonics of turning speed, and any other components are thus easily seen, especially non-synchronous components.

## Nyquist frequency

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

In all digital signal processing systems, including FFT analyzers, the sampling rate is made to be significantly greater than twice the Nyquist frequency in order to be certain the aliasing will not occur.

## Nyquist Plot

The Nyquist plot is representation of a frequency response function by graphing the “real” part versus the “imaginary” part. In the Nyquist plot, a resonance shows up as a circle, but there is no indication what its frequency is – the Nyquist plot is like sighting down the frequency axis at the real and imaginary parts of the function.

## Octave

An octave is a frequency interval having a ratio of two. It is called an octave from the music tradition where an octave spans eight notes of the scale. The second harmonic of a spectral component is one octave above the fundamental. In acoustical measurements, sound pressure level is often measured in octave bands, and the center frequencies of these bands are defined by the ISO. Vibration measurements are seldom expressed as octave band levels.

Octaves and 1/3 Octaves

## Oil Whip

Oil whip is a potentially destructive condition where a shaft is operating at a speed where the vibration excitation due to oil whirl corresponds to a shaft critical speed. The result is violent vibration of the shaft.

## Oil Whirl

A vibration of a shaft within a sleeve bearing caused by the oil film whirling around the inside of the bearing and moving the journal around with it. It occurs at between 40 and 48 percent of the shaft rpm, and is non-synchronous with the shaft. It can be caused by excessive clearance in the bearing and/or by insufficient radial loading of the bearing. Oil whirl is never desirable, but if it causes oil whip, it becomes much more serious.

## Orbit

The orbit is a plot of the position of the centerline of the journal in a sleeve bearing, and it is measured by two proximity probes mounted in the bearing housing 90 degrees apart from each other. It can be displayed on an oscilloscope if the two probe outputs are connected to the horizontal and vertical inputs respectively, and it is a good indicator of the presence of oil whirl in the bearing.

## Orders

In rotating machines, orders are multiples or harmonics of the turning speed. In comparing vibration spectra of rotating machines, it is convenient to express the frequency axis of the spectra in orders, especially if the machine speed varies between measurements.

## Order Analysis

Order analysis is simply frequency analysis where the frequency axis of the spectrum is expressed in orders of rpm rather then in Hz or rpm.

## Orthogonal

Orthogonal refers to independent dimensions of a measured quantity. For instance, on a map, it is possible to locate a point by its longitude and latitude. These two measures are independent of each other, and both are required to locate the point. They are said to be orthogonal. In vibration measurement for machine monitoring, we measure acceleration in three orthogonal directions, and from these three measurements, the actual orientation in space of the vibration can be determined. In three-dimensional space, orthogonal directions are 90 degrees from each other.

## Oscillation

Oscillation is another term for vibration.

## Overall Level

The overall level of vibration of a machine is a measure of the total vibration amplitude over a wide range of frequencies, and can be expressed in acceleration, velocity, or displacement. The overall level can be measured with an analog vibration meter, or it can be calculated from the vibration spectrum by summing up all the amplitude values over a frequency range. In comparing overall vibration measurements, it is important that they encompass the same frequency range.

## Overlap Processing

In the FFT Analyzer, the time signal is stored in a buffer before being processed to form the spectrum. If the buffer is continually being updated with new information, and if the FFT algorithm is allowed to process the signal before all the data is replaced, overlap processing is the result. Overlap processing is desirable when using a Hanning Window because it ensures against loss of data for parts of the signal that occur near the beginning and end of the window. Most FFT-type data collectors use 50% overlap processing as a default.

## Peak

The peak value of a signal is the maximum excursion in one direction from the zero point. The actual value can be displacement, velocity, or acceleration, or could simply be expressed as a voltage.

In a spectrum, a peak is simply a sharp maximum.

## Peak-to-Peak (Pk-Pk) Value

In measuring the level of a signal waveform, the peak-to-peak value is the difference between the highest positive peak level and the lowest negative peak value. In machine vibration, displacement is generally measured in peak-to-peak units.

## Pendulum

A pendulum is a simple mechanical system consisting of a mass suspended on a pivoted rod such that it can vibrate in one direction under the influence of gravity. It is generally considered to be a single degree of freedom system, and has been used for centuries as the timing mechanism for clocks. If a pendulum has a constant length of swing, it will always vibrate at exactly the same frequency; i. e., it is said to be isochronous. A pendulum swinging in a circular arc is not isochronous if the arc length changes, a fact which has caused much gnashing of teeth among clock makers over the years. A truly isochronous pendulum would have to swing in a cycloidal rather than circular arc, a fact that was recognized by Christian Huygens, who built the first pendulum clock in the 15th century.

## Period

A signal which repeats the same pattern over time is called periodic, and the period is the length of time encompassed by one cycle, or repetition. The period of a periodic waveform is the inverse of its fundamental frequency.

## Periodic

A signal is periodic if it repeats the same pattern over time. The spectrum of a periodic signal is always a series of harmonics.

## Phase

Phase is a relative time difference between two signals. It is usually measured in units of angle rather than units of time, and it makes sense only if the two signals being compared are of the same frequency. One cycle of a periodic signal represents a complete circle, or 360 degrees of phase angle. A phase difference of 180 degrees is thus a difference of one half cycle. Phase measurement is a two-channel measurement, and has no meaning when considering a single signal. In balancing of rotating equipment, phase measurement relative to the shaft position is of vital importance, and a tachometer pulse derived from a position on the shaft is used as a reference for zero phase angle. Phase is also an important part of the frequency response measurement.

## Phase Angle

See Phase

## Phase Shift

The phase shift of one signal in relation to another is simply a time delay expressed in degrees of angle where a full circle (360 degrees) is equal to one cycle of the signal, or one rotation of the rotor in a rotating machine.

## Phasor

A sinusoidal signal can be thought of as a rotating vector whose length represents its magnitude and angle represents its phase. Its rate of rotation is then the frequency of the signal. Such a vector is called a phasor.

Phasor notation is sometimes used when describing amplitude and frequency modulation.

## Picket Fence Effect

See Resolution Bias Error.

## Pickup

“Pickup” is instrumentation people’s slang for a vibration transducer. It is not specific for any particular type.

## Piezo-electric

Certain substances, especially some crystals such as quartz, will develop an electric charge on their surfaces when they are mechanically squeezed and they are called piezoelectric. The word piezo comes from the Latin word meaning to squeeze. This characteristic is utilized in the design of many different transducers, especially accelerometer**s**.

## Piezo-electric Transducer

Any transducer that uses a piezoelectric substance as an active element. Examples are force transducers, accelerometers, pressure transducers, and phonograph pickup cartridges.

## Pink Noise

A type of random noise in which its energy content is attenuated by 3 dB per octave of frequency is called pink noise. It is often used as a test signal in acoustical testing.

## Power Factor

In the 60 Hz alternating current power distribution system, the voltage and the current have the same sinusoidal wave form. Ideally, these two waves would be exactly in phase, and this will be true in the case of a purely resistive load. If the load is reactive, i.e., if it has either capacitive or inductive reactance, then the current will either lead the voltage or lag behind the voltage. When this happens, the power transmitted is reduced, even though the voltage and current levels are the same. (Since power is current times voltage, if the two are not in phase the produce will be smaller than if they are in phase.) The power factor is the amount that the power is reduced because of reactive loads, and it is measured in percent.

Most industrial plants have many electric motors, and this presents a highly inductive load to the power line, reducing the power factor and the efficiency of the power lines. Because capacitive and inductive reactance shift the current in opposite directions, a reactive load can be compensated by connecting a large capacitor across the line. This is frequently done in practice.

An interesting characteristic of synchronous electric motors is that they behave like capacitors if the rotor excitation current is larger than normal. This is called “over excitation”, and is sometimes used to correct power factor in plants with many induction motors.

## Power Spectral Density

Power spectral density, or PSD, is a method of scaling the amplitude axis in certain spectra which consist of random rather than deterministic signals. Because a random signal has energy spread out over a frequency band, it is not meaningful to speak of its RMS value at any specific frequency. It only makes sense to consider its amplitude in a fixed frequency band, usually 1 Hz. PSD is defined in terms of amplitude squared per hertz, and is thus proportional to the power delivered by the signal in a one-hertz band.

## Preload

A preload is a static axial force applied to a rolling element bearing to assure that the rolling elements and the races are always in contact. Too little preload can cause the elements to lose contact momentarily and then skid with consequent damage. Too much preload will also cause premature bearing failure.

## Pressure Waves

Vibratory motion in a mechanical system is seldom uniform in all parts of the system especially at high frequencies, but travels in the metal at high speeds by pressure waves. Any material or structure cannot transmit a force instantaneously, but does so at the speed of sound in the material. Because this speed is not infinite, if the force being transmitted is oscillatory, pressure waves will travel through the medium, and their wavelength will be the speed of sound divided by the frequency of oscillation of the force.

The speed of sound in steel is about 17 times the speed of sound in air.

## Prime Mover

A machine which converts chemical or electrical energy into mechanical motion, such as a steam engine or an electric motor.

## Principal Inertia Axis

In reference to a rotor, the principal inertia axis is a hypothetical axis, on which the center of mass is located, and around which the rotor would spin if it were in free space unencumbered by bearing or gravitational forces. See Imbalance.

## Proximity Probe

The proximity probe is a displacement transducer. It consists of a small coil of wire around a metal rod, which is connected to a special preamplifier. The voltage output of the preamplifier is proportional to the displacement between the end of the probe and a conducting surface. The response of the system is from DC, i.e. it measures static displacement, and dynamic displacement up to about 1000 Hz. Proximity probes are used extensively in instrumenting sleeve bearings, where they measure the thickness of the oil film and can detect **oil whirl** and other bearing defects. They are also sometimes called eddy current probes.

## PSD

See Power Spectral Density.

## Q

Q stands for “quality factor”, and is a measure of the sharpness, or frequency selectivity of a mechanical or electrical resonance. A high Q means a sharply tuned resonance and low damping. Q is numerically equal to the resonant frequency divided by the difference in frequency between the half power points, or the frequencies where the response is 3 dB below the maximum.

## Quasi-Periodic

A quasi-periodic signal is a deterministic signal whose frequency components are not a harmonic series, but are nevertheless discrete frequencies. The vibration signal of a machine which has non-synchronous components resembles a quasi-periodic signal.

## Radial

Radial means in a direction toward the center of rotation of a shaft or rotor. In machine vibration measurements, radial measurements are made with the transducer oriented so its sensitive axis is in the radial direction. Radial measurements are best for detecting imbalance in rotors.

## Random

A random signal contains energy spread over a band of frequencies rather than concentrated at discrete frequencies. Random signals are commonly called random noise, and a good example is the noise heard on an FM radio receiver when tuned off station. Most vibration signals from machines contain a certain amount of random noise in addition to the desired vibration signature.

## Rectangular Window

In the FFT analyzer, the rectangular window is actually no window at all. It is also called rectangular weighting, or uniform weighting, and is selected when the signal to be analyzed is a transient rather than a continuous signal. See also Hanning Window.

## Resolution Bias Error

The FFT spectrum is a discrete spectrum, containing information only at the specific frequencies that are decided upon by the FFT analyzer analysis parameters. The actual spectrum of the analyzed signal may have peaks between the lines of the FFT spectrum, and the peaks in the FFT spectrum will not be at exactly the correct frequencies. This is called Resolution Bias Error, or the Picket Fence Effect. By a process of interpolation, it is possible to increase the apparent resolution and amplitude accuracy of the FFT by a factor of ten.

## Resonance

A vibratory condition where a natural frequency and an excitation frequency coincide. Resonance results in high vibration, and may reach damaging levels. It is of paramount importance that a machine not be operated at a speed that corresponds to a natural frequency of the structure!

## Resonant Frequency

See Natural Frequency.

## Response Spectrum

See Frequency Response.

## Rigid Rotor

A rotor that does not deform significantly at its running speed.

## RMS

RMS stands for Root Mean Square, and is a measure of the level of a signal. It is calculated by squaring the instantaneous value of the signal, averaging the squared values over time, and taking the square root of the average value. The RMS value is the value which is used to calculate the energy or power in a signal. The RMS value of a sine wave is .707 times the peak value, but the RMS value of a complex signal is difficult to predict without measuring it. It is the accepted convention to measure the RMS value of acceleration when performing vibration analysis of machines.

## Roll Off, Rolloff

The attenuation of a high-pass or low-pass filter is called the roll off. The term is mostly used for high-frequency attenuation.

## Running Speed

The speed, usually expressed in revolutions per minute (rpm) at which a rotating machine runs. It may also be expressed in Hz.

## Runout

Runout, also called TIR for Total Indicator Reading, is the apparent radial motion of the surface of a turning rotor or shaft. It can be caused by the part not being round, or it can be caused because the center of rotation is not coincident with the geometric center of the part. When a proximity probe is used to sense the position of a shaft, it reads the location of the surface, and is therefore sensitive to runout, introducing an error in the measurement.

## Scalar

A scalar quantity has magnitude only, as opposed to a vector, which has a direction and a magnitude.

## Seismic

Literally, seismic means caused by an earthquake, but in vibration instrumentation, it means related to an inertial mass. A seismic transducer utilizes the inertia of a small mass to generate a force when accelerated, or to generate a relative motion which is then sensed. Examples are the piezoelectric accelerometer and the velocity transducer.

## Selectivity

Selectivity is a measure of the narrowness of a band pass filter. The greater the selectivity, the narrower, or more selective, the filter. The term is also used to describe the ability of a radio receiver to separate transmitting stations that are close together on the dial.

## Sensitivity

The sensitivity of a transducer is the numerical value of the output signal resulting from one unit of the quantity being sensed. The sensitivity of a velocity transducer is expressed in millivolts per inch per second, and the sensitivity of an accelerometer can be expressed in millivolts per G or Pico coulombs per G. Typically, the sensitivity of a transducer will vary significantly with frequency, and the purpose of the calibration of a transducer is to determine this relationship and an accurate value of the sensitivity.

## Shock

Mechanical shock is a non-periodic, or transient, excitation of a mechanical system, and it typically excites all or most of the system resonances.

## Shock Pulse Meter

The Shock Pulse Meter is a proprietary device which evaluates rolling element bearing condition by very high frequency vibration. It uses a resonant transducer, and relies on the excitation of the resonance by the bearing vibration signal.

## Shorting Ring

The shorting ring is the circular conductor, usually of copper or aluminum, which electrically connects the ends of the rotor bars in induction motors. There are two shorting rings — one at each end of the rotor. One of the problem areas in induction motors is the degradation of the shorting rings, causing loss of torque and heating of the rotor.

## SI

SI stands for Système Internationale, which is the successor to the metric system of weights and measures. The United States has the distinction of being the only industrial country in the world which does not use it.

## Sidebands

Sidebands are spectral components that are the result of amplitude or frequency modulation. The frequency spacing of the sidebands is equal to the modulating frequency, and this fact is used in diagnosing machine problems by examining sideband families in the vibration spectrum. For instance, a defective gear will exhibit sidebands at the gear rpm around the gear mesh frequency.

## Signal

In vibration analysis, a signal is an electric voltage or current which is an analog of the vibration being measured. The signal is usually meant to be the desired part of the quantity, and the accompanying undesired part is called noise. The signal to noise ratio is an important parameter in any measurement system.

## Signal Conditioning

Signal conditioning is the manipulation of a signal from a transducer by such instruments as preamplifiers, filters, etc., in preparation for its final destination, which might be an FFT analyzer or recording device.

## Signature

The signature, usually called the vibration signature, is the overall pattern of a vibration of a machine. It is said that the vibration signature contains more information about the machine than any other non-destructive test can discover.

## Single Degree of Freedom

A single degree of freedom system is the simplest mechanical system possible. It can move by translation along one direction only, or can rotate about one axis. The motion of a single degree of freedom system is a sinusoid, having only a single frequency. Mechanical structures are always more complex than the single degree of freedom system, but they can be though of a being built up of a collection of single degree of freedom systems. This is somewhat analogous to a complex waveform being considered as a collection of sinusoidal components. The disciplines of modal analysis and finite element modeling treat mechanical systems in this way, and the number of degrees of freedom they possess determines their complexity.

## Simple Harmonic Motion

Simple harmonic motion is the simplest possible motion of a vibrating system, and it consists of a single frequency at constant amplitude. An example of simple harmonic motion is a mass oscillating up and down on a spring. The waveform of simple harmonic motion is a sine wave. A single degree of freedom mechanical system would exhibit simple harmonic motion.

## Sine Wave

A sine wave, also called a sinusoid, is the graph of the mathematical sine function from trigonometry. It consists of a single frequency at constant amplitude. A mechanical system of one degree of freedom would vibrate with a sinusoidal wave form, but this is never found in the real world.

Sine Wave

## Sinusoid

See sine wave.

## Ski Slope

In a vibration spectrum, a “ski slope” is an artifact consisting of rising very low-frequency content. It could be the result of actual data, but this is rare. It is usually caused by a problem with the vibration transducer, such as a temperature transient or a loose mounting. When applying power to an ICP accelerometer, you have to wait until the circuitry is stabilized before taking data., This usually takes about 10 seconds or so. Another cause can be noise introduced by the integration process if the spectrum is velocity derived from acceleration. When you see a ski slope, it is a good idea to look at the time wave form and see if there is an exponentially sloping curve extending over the entire time record. This indicates an instrumentation problem, usually not enough time delay between applying power to the transducer and the taking of the data.

Slip is the difference between the actual speed of an induction motor and the synchronous speed, which is the speed at which a similarly wound synchronous motor would run. For instance, the slip of a motor turning 1760 RPM would be 1800 – 1760 = 40 RPM. The slip is dependent on the load on the motor, greater loads producing more slip, and hence lower speeds.

## Slip Cycle

The slip cycle of an induction motor is the synchronous speed divided by the slip. For instance, a motor turning 1740 RPM would have a slip cycle of 1800¸ 60 = 30. This means that every thirty revolutions, the rotor will be in the same relationship with the rotating magnetic field inside the stator. In other words, it takes thirty revolutions of the rotor for the magnetic field to migrate all the way around it. If there is a discontinuity in the rotor, such as a broken rotor bar, it will encounter the maximum of magnetic force twice each slip cycle, once for the North end of the rotating pole, and once for the South end.

## Spectra

Spectra is the plural of spectrum.

## Spectrum

The spectrum is the result of transforming a signal from the time domain to the frequency domain. It is the decomposition of a time signal into a collection of sine waves. The plural of spectrum is spectra. Spectrum analysis is the procedure of doing the transformation, and it is most commonly done with an FFT analyzer.

## Spectrum Analyzer

A spectrum analyzer converts a signal from the time domain into the frequency domain, and the FFT analyzer is the most common type today.

## Spike Energy

Spike energy is a measurement of acceleration in a high-frequency range, usually to 20 kHz, for the detection of rolling element bearing problems. The name is a trademark of the IRD company, but the technique is generic.

## Squirrel Cage Motor

Another term for Induction Motor, which comes from the resemblance of the rotor bar assembly to a rotating cage used to exercise pet squirrels.

## Standard Deviation

In a vibrating quantity, the instantaneous deviation from the equilibrium position, if considered over a long time interval, will have an average, or mean value. If these deviation values are squared and then averaged, the result is called the *variance* of the vibration. The square root of the variance is defined as the standard deviation of the vibration. It can be thought of as the RMS value of the deviation. A vibration with a small standard deviation never strays very far from its equilibrium position, while one with a large standard deviation does make larger excursions.

## Stationary Signal

A stationary signal is a signal whose average statistical properties over time are constant, and it can be deterministic or not. In general, the vibration signatures of rotating machines are stationary.

## Strain

Strain is physical stretching of a mechanical member as a result of an applied force. The amount of resultant strain for a given force depends on the stiffness of the material. Strain is a dimensionless quantity, usually expressed in “micro strain”, i.e. micro inches per inch, etc.

## Strain Gage

A strain gage is a small transducer that measures strain. It consists of a series of fine wires, or other conductors, which are glued to the surface being measured. Strain in the material stretches the wires and reduces their resistance, and this change in resistance is sensed by an external circuit that outputs a voltage proportional to the strain. Strain gages are used extensively in mechanical structural testing.

## Sub harmonic

Sub harmonics are synchronous components in a spectrum that are multiples of 1/2, 1/3, or 1/4 of the frequency of the primary fundamental. They are sometimes called “sub-synchronous” components. In the vibration signature of a rotating machine, there will normally be a component at the turning speed along with several harmonics of the turning speed. If there is sufficient looseness in the machine so that some parts are rattling, the spectrum will usually contain sub harmonics. Harmonics of one-half turning speed are called “one-half order sub harmonics”, etc.

## Sub synchronous

See Sub-Harmonic.

## Synchronous

Synchronous literally means “at the same time”, but in spectrum analysis, synchronous components are defined as spectral components which are integral multiples, or harmonics, of a fundamental frequency. They may in some cases exist as multiples of an integral fraction of the fundamental frequency, in which case they are called sub harmonics.

## Synchronous Averaging

A type of signal averaging where successive records of the time wave form are averaged together. This is also know as time domain averaging. The important criterion is that the start of each time record must be triggered from a repetitive event in the signal, such as 1X rpm. The triggering assures that the phase of the wave form components that are synchronized with the trigger are the same in each record. Then in the averaging process, these in-phase components will add together while the rest of the signal components will gradually average out because of their random relative phases. The technique is excellent for extracting signals from noisy environments.

## Tangential

In measuring tri-axial vibration in rotating machines, one of the sensitive axes of the transducer is tangent to the rotating shaft in question. It is perpendicular to the radial transducer, which is a direction toward and away from the center of the shaft.

## Temperature Transient

When a piezo-electric accelerometer is subjected to a different temperature, as will be the case when it is attached to a hot surface, it will take a certain time before the active elements reach a constant temperature. During this time, the accelerometer will produce a slowly varying output voltage that can be relatively large. If it is connected to a spectrum analyzer or other instrumentation, the measured vibration signal will be contaminated with this low-frequency noise component. The usual result is a so-called “ski-slope” at the low end of the frequency scale. In some accelerometers, especially of the compression type, the temperature transient is so large that the internal preamplifier is momentarily overloaded, causing gross distortion of the data.

Whenever an accelerometer is mounted to a surface having a different temperature than the accelerometer itself, you should wait a half-minute or so to be sure the temperature transient has died away before taking any vibration data.

## Thermography

Thermography is the art and science of utilizing infrared sensing devices to determine the surface temperature distribution of a device that may not be readily accessible. Typically, an infrared video camera is used, and the video image is digitized and fed into a computer that assigns different colors to different temperatures so one can see at a glance if there are hot spots in the device. Thermography is extensively used to check electrical breaker panels, fuses, etc., for local heating.

## Thrust

Thrust is a force in the axial direction of a rotating shaft or part. If significant thrust forces are generated in rotating equipment, such as is the case in a vertically mounted motor/pump assembly, a special thrust bearing is required to bear the thrust load. The term is sometimes misused to refer to axial motion of a shaft.

## Time Domain

Vibration is an oscillation in position as a function of time, and is said to exist in the time domain. The signal from a transducer is also in the time domain, and when it is displayed on the screen of an oscilloscope, it is called a wave form. Although most diagnosis of machine vibration problems is done via spectrum analysis, some types of information are more easily seen in the wave form; for example when looking at repetitive impacting in a rolling element bearing.

## TIR

Short for Total Indicator Reading. See Runout.

## Tone

A signal at a specific frequency, which would be heard as a specific musical pitch, is called a tone, by analogy with music. Sometimes a peak in a spectrum is also called a tone, such as a “bearing tone”.

## Torque

Torque is defined as a force that causes rotation about a centerline. The rotational force exerted on a shaft by an electric motor is a torque.

## Torsional Resonance

A torsional resonance is a resonance where the spring is the twisting of a shaft and the mass is polar inertia of a component connected to the shaft, such as a coupling or a rotor of some type. Torsional resonances occur when a torsional natural frequency corresponds to a torsion excitation frequency, and can result in high levels of torsional vibration. They can cause severe damage to rotating machines.

## Torsional Vibration

Torsional vibration is an oscillation of angular position about a centerline, and is caused by oscillating torque forces. For instance, a motor coupled to a shaft that is driving a pinion gear in a gearbox will experience a torque variation as each tooth meshes with the tooth of the other gear. This causes a torsional vibration to exist in the shaft. It is important to see to it that such forces do not occur near the frequencies of torsional resonances, or the vibration levels can be very high.

## Transducer

A transducer is a device that converts one type of energy, such as vibration or sound, into a different type of energy, usually an electric current or voltage. Transducers are the hearts of instrumentation systems, and are usually also the weakest links. They contribute noise to the measured signals and also generate distortion because of non-linearities. They are subject to changes in their sensitivity, and therefore require regular calibration. Some types of transducer are much more reliable and linear than others; an example is the piezoelectric accelerometer, which is by far the best type for general vibration measurement.

## Transient

A transient is a signal or waveform which begins at zero amplitude, lasts for a certain time, and ends at zero amplitude. An example is the sound of a gunshot, or the vibration due to a hammer blow. When transients are subjected to spectrum analysis, they usually do not generate a harmonic series, but generate a continuous spectrum where the energy is smeared out over frequency. When analyzing transients with an FFT analyzer, care must be taken that the entire transient is included in the time record of the analyzer, and also that the rectangular window rather than the Hanning window be used.

## Transform

A transform is a mathematical operation that converts a function from one domain to another with no loss of information. For example, the Fourier transform converts a function of time into a function of frequency.

## Transmission Loss

See attenuation.

## Trend

A trend is a plot of vibration level versus elapsed time. The trend is made by most vibration monitoring software from stored vibration data, and is usually designed to display the vibration level at certain important frequencies over a period of several months or years.

## Trial Weight

In the performance of balancing, which is the determination of the magnitude and location of balance weights for a rotor, it is the usual practice to attach a known trial weight to the rotor and to measure the change in vibration level and phase that it causes.

## Triaxial

Literally, with three axes. The vibration transducers often used by machine vibration measurement systems consist of three accelerometers oriented at 90° from each other enclosed in a single housing. This is called a triaxial accelerometer.

## Trigger

A trigger is an electrical impulse that is used to initiate a process, such as data collection with an FFT analyzer or oscilloscope. The trigger can be generated by a machine event such as a once per revolution tachometer pulse, or can be generated manually. The once per rev trigger is essential in performing time synchronous averaging of vibration spectra.

## True RMS

True RMS is the actual RMS value of a signal as calculated by squaring the signal level instantaneously, averaging the squared values, and taking the square root of the average, and this is what is done in a true RMS meter. In the case of a sine wave, the RMS value is 1.11 times the average value, and many AC voltmeters use this relationship to calculate the RMS value from the average value, which is much easier to sense. This works only with sine waves, so such meters give the wrong answer when measuring any other wave forms.

## Tunable Filter

A tunable filter is simply a filter whose cutoff frequencies, either high pass, low pass, or band pass, are adjustable. The term comes from the practice of tuning musical instruments, which is a frequency adjustment. Someone once said that a tunable filter is a filter that is never at the correct frequency.

## Turning Speed

In a rotating machine, the turning speed is the frequency of rotation, and it can be expressed in Hz, or RPM. In vibration analyst slang, the turning speed is called “1 X”, the second harmonic “2 X”, etc.

## Uniform window

The same as rectangular window.

## Vane Pass Frequency

In a centrifugal pump or a fan, the vane pass frequency is the number of fan blades or impeller vanes times the turning speed of the rotor. The vane pass always shows up as a relatively strong component in the vibration spectrum of a pump or fan. Thus, a pump with 7 vanes will have a spectral component at 7 times the RPM, or “7 X”.

## Vector

A vector quantity is a quantity that has a direction as well as a magnitude. For example a thrust is a vector, as it is a force in the axial direction on shaft or rotor.

## Velocity

Velocity is defined as the time rate of change of position, and has units of distance per unit time. In vibration signals, velocity is also the rate of change of displacement, and is expressed usually in inches per second or millimeters per second. Velocity is also the time integral of acceleration, and it is often calculated in practice by integrating acceleration.

## Velocity Transducer

The velocity transducer is one of the oldest types of vibration transducer, and even though it has many drawbacks, is still in fairly common use. It is a seismic transducer that contains either a moving coil of wire in a magnetic field, or a moving magnet inside a coil of wire.

The velocity transducer has moving parts, and is therefore subject to wear. It requires frequent calibration, and its response depends on temperature and the orientation of the transducer. Its frequency response extends from about 15 Hz to 1500 Hz, and its phase response can be erratic, especially at low frequencies.

A newer type of velocity transducer, called a “velometer”, consists of a piezoelectric accelerometer with a built-in integrator to convert the signal to velocity, and it is much better in all respects than the traditional velocity transducer.

## Vibration

Vibration is the oscillation of a point, an object, or a part of an object around a fixed reference, or rest, position. An object can vibrate as a unit, in which case it is called “whole body vibration”, or, as is usually the case, an object can vibrate in a complex way where it deforms and different parts of it vibrate at different frequencies and amplitudes.

## Vibration signature

The vibration signature of a machine is the characteristic pattern of vibration it generates while it is in operation. The actual signal from a vibration transducer can be considered the signature, but the spectrum of the vibration signal is usually referred to as the signature. It has been said that of all the non-destructive tests that can be made on a machine, the one containing the most information is the vibration signature.

## Viscous Damping

Viscous damping is a type of mechanical damping where the damping force is proportional to the velocity of vibration, as opposed to Coulomb damping, where the damping force is constant. A good example of viscous damping is the damping provided by the shock absorbers in cars. Most mechanical systems exhibit a combination of the two types of damping.

## Vortices

Vortices are eddies, or “whirlpools” sometimes formed at the ends of airplane wings, fan blades, propeller blades, pump vanes, and the edges of other structures in a fluid flow. Vortices absorb energy, and they cause turbulence and reduced efficiency in many fluid handling machines. The vibration signature of a machine with turbulent flow will exhibit a strong random component.

## Wave

A wave is a disturbance propagated in a medium, and it results in local oscillatory motion of the medium. Waves transmit energy in the medium, and travel at characteristic speeds depending on the medium. The speed of sound is the speed of pressure wave propagation in air. Sound waves are longitudinal waves, meaning that the direction of propagation is the same as the direction of the oscillation of the medium. Ocean waves, on the other hand, are an example of transverse waves, for the direction of wave transmission is at 90 degrees to the direction of motion of the water; the energy moves horizontally, but a floating cork simply moves up and down as the waves pass. Mechanical structures can have both kinds of vibration waves, and they travel at different speeds, and the result is that most such structures, when excited by a complex force, will vibrate in a very complicated pattern.

## Waveform

The waveform is the shape of a time domain signal as seen on an oscilloscope screen. It is a visual representation or graph of the instantaneous value of the signal plotted against time. Inspection of the waveform can sometimes reveal information about the signal that the spectrum of the signal does not show. For instance a sharp spike or impulse and a randomly varying continuous signal can have spectra that look almost identical, while their waveforms are completely different. In machine vibration, mechanical impacting usually causes spikes, while random noise can be caused by the advanced stages of bearing degradation.

## Wavelength

The wavelength of a wave traveling in a medium is the distance in the medium spanned by one repetition of the wave motion. The wavelength is the wave velocity divided by the frequency of the waves. The velocity of wave motion is usually constant in a medium, and the wavelength thus depends only on the frequency of the waves. The speed of a vibration compression wave in steel is very fast, about 17 times as fast as the speed of sound in air, and this means the wavelengths are extremely short.

## Wear Particle Analysis

Wear particle analysis is a type of lubricating oil analysis where the particles found in the oil are analyzed to see what process caused them to be there.

## Weighting

See Hanning Window, and Window.

## White Noise

White noise is defined as random noise that contains a constant energy at each frequency, or more precisely, a uniform distribution of energy over the frequency spectrum. The noise heard in an FM radio when tuned off station is approximately white noise.

## Whole Body Motion

Whole body motion is the vibration of an object as a unit, where all parts of it are moving in the same direction at the same time. An example is a mass oscillating up and down on the end of a spring.

## Window

The FFT analyzer does not operate in a continuous manner, but is instead a batch processing device, taking samples of the time domain signal and transforming them into the frequency domain. The time interval during which the signal is sampled and recorded is called the window. In order to compensate for certain limitations of the FFT process, the time data in the window is often multiplied by a weighting curve, such as a Hanning or Flattop weighting. These weighting curves are also called Hanning window and flattop window respectively.

## X

Abbreviation for run speed. X refers to the speed of the shaft nearest the measurement point, so a machine with more than one shaft will have several values of X.

## Xm

Abbreviation for motor speed. See also X.