Accelerance
The frequency response function of acceleration/force. Also known as inertance.

Accelerometer
A transducer whose output is n electrical/mechanical directly proportional to acceleration forces. The output is usually produced by force applied to a piezoelectric crystal which generates a current proportional to the applied force. This current is then amplified and displayed as a time waveform or processed by a Fourier transform to produce a frequency display. Single integration of the acceleration signal will produce a velocity display and double integration of the acceleration signal will produce a displacement display.

Accuracy
How close a measurement is to the absolute quantity.

Acoustic Emission
The detected energy that is generated when materials are deformed or break. For rolling element bearing analysis, it is the periodic energy generated by the over rolling of particles or flaws and detected by the display of the bearing flaw frequencies.

Algorithm
A specific procedure for solving mathematical problems. An FFT is an algorithm.

Aliasing
To digitize an analog signal for processing in digital instruments such as an FFT analyzer, it first must be periodically sampled, the sampling process occurring 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 wave 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 whereby the axes of machine components are either coincident, parallel or perpendicular, according to design requirements, during operation.

Amplification Factor (Q)
The amount of mechanical gain of a structure when excited at a resonant frequency. The ratio of the amplitude of the steady state solution (amplitude at resonance) to the static deflection for the same force F. The amplification factor is a function of the system damping. For a damping ratio  =0 (no damping) the amplification factor is infinite, for  =1 (critically damped) there is no amplification.

Amplitude
The measurement of energy or movement in a vibrating object. Amplitude is measured and expressed in three ways: Displacement (commonly in mils Pk-Pk); Velocity (commonly in In/Sec Pk); and Acceleration (commonly in gs RMS). Amplitude is also the y-axis of the vibration time waveform and spectrum, it helps define the severity of the vibration.

Analog
Quantities in two separate physical systems having consistently similar relationships to each other are called analogous. One is then called the analog of the other. The electrical output of a transducer is an analog of the vibration input of the transducer as long as the transducer is not operated in the nonlinear (overloaded) range. This is in contrast to a digital representation of the vibration signal, which is a sampled and quantisized signal consisting of a series of numbers, usually in binary notation.

Analog to Digital Conversion
The process of sampling an analog signal produces a series of numbers which 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.

Angularity
The angle between two shaft center lines; this angle is the same at any point along either centerline. It is normally specified in rise/run.

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

Apodize, Apodization
To apodize is to remove or smooth a sharp discontinuity in a mathematical function, an electrical signal or a mechanical structure. An example would be to use a Hanning Window in the FFT analyzer to smooth the discontinuities at the beginning and end of the sample time record.

Asymmetrical Support
A rotor support system that does not provide uniform restraint in all radial directions. This is typical in industrial machinery where stiffness in one plane may be substantially different than stiffness in the perpendicular plane. Occurs in bearings by design, or from preloads such as gravity or misalignment.

Asynchronous
Nonsynchronous
Frequencies in a vibration spectrum that exceed shaft turning speed (TS), but are not integer or harmonic multiples of TS. Also commonly refered to as non-synchronous.

Attitude Angle
The angle between the steady state preload through the bearing centerline, and a line drawn between the bearing center and the shaft centerline. (Applies to fluid film bearings).

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, q.v. The numerical value of auto correlation can vary between zero and one. A periodic signal, such as a sine wave has an auto correlation that 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 waveform 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 accurately 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. 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 that is important in machinery monitoring is time domain averaging, or time synchronous averaging, and it requires a tachometer connected to the trigger input of the analyzer 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.

Axial
In the same direction as the shaft centerline.

Axial Float (or End Float)
Movement of one shaft along its centerline due to the freedom of movement permitted by a journal bearing or a sleeve bearing. This adjustment should be set before performing vertical or horizontal moves. The degree of axial float can be adjusted by the position of the stops, or whatever limits the motion.

Backlash
A condition where a rotor can rotate freely for a certain angular distance before encountering any resisting force. It may be measured in degrees. This term normally applies to couplings and gears.

Band Pass Filter
The frequency range over which a filter passes a signal within 3 dB of full strength. Outside the filter bandwidth, the signal is attenuated. The further outside, the greater the attenuation.

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

Baseplate
The surface to which the feet of a machine are attached.

Bearing
Primarily two types, rolling element and sleeve or plain bearing. Rolling element bearings consist of four parts: an inner race, an outer race, balls or rollers, and a cage to maintain the proper separarion of the rolling elements. A sleeve bearing is a cylinder of alloy metal surrounding the rotating shaft. Contact between the shaft and sleeve is prevented by a lubrication film.

Bearing Frequencies
Faults in any of the four bearing components will generate specific frequencies dependent upon the bearing geometry and rotating speed.
BPFO - Ball Pass Frequency, Outer Race
BPFI - Ball Pass Frequency, Inner Race
BSF - Ball Spin Frequency
FTF - Fundamental Train Frequency

Bearing Misalignment
A misalignment that results when the bearings supporting a shaft are not aligned with each other. The bearings may not be mounted in parallel planes, cocked relative to the shaft, or distorted due to foundation settling or thermal growth.

Bearing Nomenclature
Each bearing manufacturer has specific codes applied as prefixes and suffixes to their bearings. These codes inform the user of the construction, materials, clearances, and other factors used in the construction of the bearing. Consult the individual manufacturer's handbook for specific code meaning.

Beat Frequency
If two vibration components are quite close together in frequency and if they are present at the same time at the same place, 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 different from beating, and is caused by a high-frequency component being multiplied by a lower-frequency component and is thus a nonlinear effect, whereas beating is simply a linear addition of two components whose frequencies are close to one another.

Bins
In an FFT spectrum, the individual frequencies at which the amplitudes are calculated, commonly called "lines."

Binwidth
Effective Binwidth
*these terms need more work*
The binwidth equals the frequency span divided by the number of lines.
Effective binwidth equals the binwidth times the window noise factor.

Bit
Short for binary digit. A number expressed in binary notation utilizes the digits 1 and 0, and these are called bits. Any number can be expressed with combinations of them.

Bode Plot
1. A plot of the frequency response function that includes log magnitude versus frequency plus phase versus frequency. For a single-degree of freedom, the magnitude is a maximum at the natural frequency and the phase shift is 90°.
2. A type of spectrum plot that 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.
The term is named after a man named Bode (pronounced Bo-day), who worked at the Bell Telephone Labs.

Bolt Bound
The situation whereby a machine cannot be moved in the desired direction because of mounting hole restrictions.

Bow
A shaft condition such that the geometric centerline of the shaft is not straight.

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.

Bump Testing
A single channel approximation to a two channel impact test. This method works because the impacting force approximates an impulse and imparts broadband excitation over a limited frequency range. Since the Fourier Transform of the impulse response function is the frequency response function, it provides a good method of estimating the natural frequencies of the structure.

Calculated peak
Term used to describe the spectral overall RMS level multiplied by sqrt (2). Sometimes referred to as "derived peak" or "pseudo peak."

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 specific 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 in a way similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes and rolling element bearing vibrations lend themselves especially well to cepstrum analysis. The cepstrum is closely related to the auto correlation function.

Characteristic Equation
The mathematical equation whose solution defines the dynamic characteristics of the structure in terms of its natural frequencies, damping, and mode shapes. The mathematical formulation of the characteristic equation is called the Eigenvalue problem. The characteristic equation is obtained from the equations of motion for the structure.

Circle Fit
A single-degree of freedom curve fitting routine that tries to fit a mode to a circle (Nyquist plot of a single-degree of freedom system). The modal coefficient is determined by the diameter of the circle and the phase by its location relative to the imaginary axis. For a real mode, it should be either completely above or completely below the imaginary axis.

Coefficient of Thermal Expansion
The constant value or factor of expansion of a material for a given increase in temperature, divided by the length of the material. This is different for each material.

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 nonlinearity in the structure or if there is noise in a 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 it is a useful tool in determining good from noisy or meaningless data.

Coherence Function
Coherence is a function of frequency that measures amount of power in the response (output) that is caused by the power in the excitation (input). If it is 100% coherent, the value is 1.

Co-Incident
Another name for the real part of the frequency response function.

Cold Alignment
Machine condition in which alignment procedures are normally performed. Changes in off-line to on-line running conditions should be allowed for during this procedure so that the machine can "grow" into alignment during operation. Also known as static alignment or primary alignment.

Complex Modes
The points on a structure have varying phase relationships between them at a natural frequency. This is unlike a real mode where the phase between points is either 0° or 180°.

Compliance
Frequency response function of displacement/force. Also known as Dynamic Compliance.

Coulomb Damping
Nonlinear damping that is a result of rubbing, looseness, etc.

Coupling
Mechanical fixture for joining two shafts.

Critical Damping
The smallest amount of damping required to return a system to its equilibrium condition without oscillating.

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.

Damped Natural Frequency
The damped natural frequency is the frequency at which a damped system will oscillate in a free vibration situation.

for a single-degree-of-freedom system.

Damping
Energy dissipation in an oscillating structure. For free vibration, that results in a decay in the amplitude of motion over time.

Damping Factor or Damping Ratio ( )
The ratio of actual damping in a system to its critical damping (  = C / C c )

Degrees of Freedom
The number of coordinates or independent variables it takes to completely describe the location of a structure.

Detector
An electronic circuit that determines the amplitude level of a signal in accordance with certain rules. The simplest type of detector consists of a resistor and a capacitor, and it measures the average value of a fluctuating DC signal. A more complex but much more useful type of detector is an RMS detector. RMS detectors are used because they are proportional to the power or energy present in the signal or a vibration.

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.

Dial Indicator
Instrument used to measure amounts of motion, or displacement in thousandths of an inch (mils) increments.

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, if performed on an analog signal, adding a significant amount of high frequency noise to the signal, and is generally not used very much in machinery vibration analysis. It is not inherently noisy if it is done digitally on the FFT spectrum. 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. It is characterized by several 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 signal representation may not be truly representative of the original signal.

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 that converts, or "transforms" a sampled and digitized waveform 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. See also Fast Fourier Transform.

Dodd Bars
A secondary alignment method. Consists of two bars that are similar in configuration to reverse dial indicator bars. However these bars are not mounted on the shaft, they are mounted to the machine. Each bar is fitted with a proximity probe and it corresponds to a block on the other bar. As the machines move to their on-line condition the gap between the proximity probe and the metal block changes, which changes the voltage. The analyzer converts the voltage to a distance and from these distances, the alignment corrections can be calculated.

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

Doweling
Permanently mounted pins in the baseplate, which are inserted into close tolerance holes in the machine's feet, used to bring machines back to the same aligned position.

Driving Point Measurement
A frequency response measurement where the excitation point and direction are the same as the response point and direction.

Dynamic Compliance
See compliance.

Dynamic Range
The ratio in dB between the highest signal level that can be tolerated without distortion and the broadband noise level measured in the absence of the signal.

Dynamic Stiffness
The frequency response function of force/displacement.

Eccentricity, Mechanical
The variation of the outer diameter of a shaft surface when referenced to the true geometric centerline of the shaft. Out-of- roundness. See also Runout.

Eccentricity Ratio
The vector difference between the bearing centerline and the average steady-state journal centerline. Applies to sleeve bearings not anti-friction bearings.

Eddy current probe
A non-contact electrical device that measures the displacement of one surface relative to the tip of the probe. Construction consists of an electrical coil of various lengths and diameters. This coil located in the tip of the probe is energized producing an electrical field around the tip of the probe. When a conductive surface is placed in the field and the distance from the probe is noted, variations in this gap can be determined by the variations in the voltage flow to the probe tip.

Effective Mass
The frequency response function of force/acceleration.

Eigenvalue
The roots of the characteristic equation.

Eigenvalue Problem
The mathematical formulation and solution of the characteristic equation is called the Eigenvalue problem.

Eigenvector
The mode shape vectors.

End Float
See axial float.

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 to which the data will be put. Modern instrumentation, such as FFT analyzers allow one to specify what the engineering units are and to apply conversion factors if needed.

EU
See Engineering Units.

Essinger Bars
A seconardy alignment method used to measure the difference between on-line and off-line running conditions. The method measures the change in distance and a change in angle between two tooling balls. One ball is fixed to the bearing and the other ball is fixed to a fixed reference point (usually the floor). The balls are connected by means of an inside micrometer with a resolution of at least 0.001." This should be set up for both sides of the bearing, so the readings can be taken simultaneously. And readings should be taken at every bearing. As the machine "grows" the distances betwen the balls and the angle between the inside micrometer and a fixed location (also usually the floor) will change. And these changes can be used to determine the changes in alignment.

Exponential (Response) Window
A special windowing function for minimizing leakage in lightly damped structures that is used in impact testing. In a lightly damped structure, oscillations may not die out within the sampled time data block, T, which results in leakage error. An exponential window adds damping to the time signal to force it to die out within the time T, thus minimizing leakage. The added damping is then removed mathematically after the signal is processed.

Vibration Terminology
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Parameter Estimation
The process of evaluating and curve fitting frequency response functions in order to estimate modal parameters.

Peak
The maximum positive or negative dynamic excursion from zero (for an AC coupled signal) or from the offset level (for a DC coupled) of any time waveform. Sometimes referred to as "true peak" or "waveform peak."

Peak-to-peak
The amplitude difference between the most positive and most negative value in the time waveform.

Peak Pick
A parameter estimation technique where the peak value of the imaginary part of the frequency response function is used to estimate the mode shape value at that point. The phase is given by its sense (positive or negative). This method is also known as quad picking since the value is being picked off the imaginary or quadrature part of the frequency response function.

Peak Scaling, Peak-to-Peak Scaling, RMS Scaling
Methods to display the amplitude axis of a spectrum.

Period
A signal that repeats the same pattern over time is called periodic, and the period is defined as 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 always contains a series of harmonics.

Perpendicular
At right angles (90°) to a given line or plane.
The difference in time between two events such as the zero crossing of two waveforms, or the time between a reference and the peak of a waveform.  The phase is expressed in degrees as the time between two events divided by the period (also a time), times 360 degrees.

Picket Fence Effect
The FFT spectrum is a discrete spectrum, containing information only at the specific frequencies that are decided upon by setting the FFT analyzer analysis parameters. The true spectrum of the signal being analyzed may have peaks at frequencies 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. The name arises because looking at an FFT spectrum is something like looking at a mountain range through a picket fence.
By a process of interpolation, it is possible to increase the apparent resolution and amplitude accuracy of the FFT spectrum by a factor of ten.
Pipe Strain
Casing and flange distortion caused by improper pipe flange fit up.

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

Primary Alignment
See Cold Alignment.

PSD
See Power Spectral Density.

Q (Sharpness of Resonance)
Another term for amplification factor.

Another name for the imaginary part of the frequency response function.

Quasi-Periodic
A quasi-periodic signal is a deterministic signal whose spectrum is not a harmonic series, but nevertheless exists at discrete frequencies. The vibration signal of a machine that has nonsynchronous components resembles a quasi-periodic signal. In most cases, a quasi-periodic signal actually is a signal containing two or more different periodic components.

Direction perpendicular to the shaft centerline.

The average location, relative to the radial bearing centerline, of the shaft's dynamic motion. Applies only to sleeve bearings.

Real Part
A plot of the real part of the frequency response function versus frequency. For a single degree of freedom, the magnitude is zero at the damped natural frequency.

Real or Normal Modes
In a real mode, all points on the structure reach a maximum or a minimum value at the same time and all pass through equilibrium at the same time.

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 used when the signal to be analyzed is a transient rather than a continuous signal. See also Hanning Window.

Repeatability
The consistency (or variation) of readings and results between consecutive sets of measurements. It has nothing to do with accuracy.

Residual Terms
Terms added to a curve fit algorithm to take into account the effects of modes outside the range being fitted. These terms consist of a mass term on the low frequency end and a stiffness term on the high.

Resolution
The smallest change or amount a measurement system can detect.

Resolution Bias Error
See Picket Fence Effect.

Resonance
When a forcing frequency is the same as a resonant frequency of the structure, the structure is said to be in resonance.

Resonant Frequency
The frequency of maximum amplification for a given damping ratio,  . Resonant frequency
.
Response Spectrum
The frequency response function, also called the response spectrum, 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.
Reverse Indicator Method
Method for taking shaft alignment readings with indicators mounted radially at opposite ends of a spanned section (on each machine).

Rim and Face Method
See Face-rim Method.

Rise/Run
For smaller angles, the ratio obtained when the change in offset between two center lines is divided by the distance along either centerline (between the points of offset measurement) . In effect, it is the slope of one line in a plane compared to another line in the same plane. Angularity is normally specified in mils/inch, or milliradians which is rise/run.

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

Roots
The roots of the characteristic equation are complex and have a real and imaginary part. The real part describes the damping (decay rate) of the system and the imaginary part describes the oscillations or damped natural frequency of the system.

Rotational Play
Looseness, usually in a coupling, where a rotor can rotate a given distance before the rotational play is out and the coupled shaft begins to rotate also.

Runout
A change in dial indicator position at the surface of the rotor during one rotation of the rotor, used to measure out-of-roundness or indicate a bent shaft. See also Eccentricity, Mechanical.

Sag
Deflection due to gravity acting on a cantilevered or otherwise supported object. Mechanical brackets that hold alignment tools always sag a certain amount. This sag must be corrected if the machine moves are to calculated correctly.

Secondary Alignment
The act of measuring off-line to on-line machinery movement.

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.

Sensor
Any device that translates the magnitude of one quantity into another quantity. Three of the most common transducers used in vibration measurements are accelerometer, velocity transducer, and eddy current probe.

Shim
A thin piece of material inserted between the machine feet and the baseplate used to produce precise vertical adjustments to the machine centerline. Shims are normally made of stainless steel, mild steel, or plastic. Shims come in various thicknesses from 1 mil to 125 mils.

Shim Machine
The machine whose position is changed during shaft alignment. Compare with Fixed Machine.

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 spaced apart at the gear rpm around the gearmesh frequency.

Signal
In vibration analysis, a signal is an electric voltage or current which is analog of the vibration being measured.

Single-Degree-of-Freedom System (SDOF)
A system whose position in space can be completely described by one coordinate.

Soft Foot
A term used to describe any condition where tightening or loosening the bolt(s) of the machine feet distorts the machine frame.

Spacers
A generic term for any coupling that has 2 flex planes separated by a connecting shaft without bearings or other supports (between the flex points). Sometimes called an insert or spider.

Spectra
Spectra is the plural of spectrum.

Spectrum
The spectrum is the result of transforming a time domain signal 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, but there are many other types.

Spool Piece
Any piece of pipe or shafting that can be removed from a line of piping or shafting without disturbing or disassembling any other components. The name spool piece comes from the physical appearance of the piece, often a short cylinder with flanges the ends, which resembles a spool of string or thread.

Standard Deviation
If the instantaneous distances from an equilibrium position of a vibrating body are squared and averaged, the result is called the variance of the vibration. The square root of the variance is the standard deviation. It is also equal to the rms (root mean square) value.

Static Alignment
See Cold Alignment

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

Structural Modification
Mathematically determining the effect of changing the mass, stiffness, or damping of a structure and determining its new modal parameters. A modal analysis provides, in essence, a mathematical model of the structure. This model can be manipulated to determine the effect of modifications to the structure. The modal model can be generated either experimentally or using a finite element program.

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 spectrum of a rotating machine, there will normally be a component at the turning speed along with several harmonics of 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.

Subsynchronous
Frequencies in a vibration spectrum that are lower than the fundamental frequency.

Sub synchronous
See Sub Harmonic.

Synchronous
Synchronous literally means "at the same time," but in spectrum analysis, synchronous components are defined as spectral components that 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 waveform 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 waveform 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.
Thermal Growth
Movement of the shaft center lines associated with (or due to) a change in machinery temperature between the static and operating conditions.

Thermal Profile
A secondary alignment method used to measure thermal growth. This method is only used for calculating the vertical thermal growth of the shaft centerline due to a change in temperature. The shim plane, under the machine feet, serves as a benchmark. This technique is usually used for machines under 500 HP. The technique uses the linear expansion equation where: Expansion in mils (E) is equal to the average change in temperature, F° (T) multiplied by the vertical distance from the shim plane to the shaft centerline, in inches mutiplied by the coefficient of thermal expansion, in mils/inch F°. E =3D T X L X C This is to be calculated for both sides of the bearing. The number of temperture readings is not critical, but at least 4 is recommended. The average change in temperature is between the offline and online temperatures.

TIR
Total Indicator Runout. The total movement in mils of a dial indicator after a given rotation of a rotor.

Tolerance
The maximum permissible deviation from the specified quantity.

Torsional Play
Misnomer for Rotational Play.

Transducer
Any device that translates the magnitude of one quantity into another quantity. Three of the most common transducers used in vibration measurements are accelerometer, velocity transducer, and eddy current probe.

Transfer Function
The output to input relationship of a structure. Mathematically it is the Laplace transform of the output divided by the Laplace transform of the input.

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

Transmissibility
The Fourier transform of the forced response of a structure measured at one location to the response at another location.

Tunable Filter
A filter whose cutoff frequencies are adjustable, either manually or under remote electrical control.

Uniform window
In the FFT analyzer, the uniform, or rectangular, window does not modify the signal amplitude 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.

Undamped Natural Frequency
The same as the natural frequency of a structure.

Velocity Transducer
An electrical/mechanical transducer whose output is directly proportional to the velocity of the measured unit. A velocity transducer consists of a magnet suspended on a coil, surrounded by a conductive coil. Movement of the transducer induces movement in the suspended magnet. This movement inside the conductive coil generates an electrical current proportional to the velocity of the movement. A time waveform or a Fourier transform of the current will result in a velocity measurement. The signal can also be integrated to produce a displacement measurement.

Viscous Damping
Damping that is proportional to velocity. Viscous damping is used largely for system modeling since it is linear.

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, spikes are usually caused by mechanical impacting, while random noise can be caused by the advanced stages of bearing degradation.

Wedge Shim
Technique where the use of several shims are used to fill the wedge-shaped gap of a bent foot. Each shim is inserted to a different depth so that the stair-stepped support is better built to support the entire foot.

Weighting
See Window.

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 a frequency domain spectrum. 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 are often multiplied by a weighting curve, such as a Hanning or Flattop weighting. These weighting curves are also called the Hanning window and the Flattop window respectively. See also Weighting.