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
Face-Rim Method (or Rim-face method)
- A method of shaft alignment where the indicators are mounted both radially and axially on one machine or the other, not both.
- The FFT is an algorithm, or digital calculation routine, that efficiently calculates the discrete Fourier transform from the sampled time waveform. In other words it converts, or "transforms" a signal from the time domain into the frequency domain. See also DFT.
The illustration shows the relation between the time record length, the time between samples, the frequency span f and the frequency resolution. The most important relation here is that the frequency resolution is inversely proportional to time record length. Therefore, high-resolution spectrum analysis of necessity takes a long time to collect the time record.
- See Fast Fourier Transform.
- 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. See also Fast Fourier Transform.
- A filter is an electrical circuit that allows signals in certain frequency ranges to pass through, and attenuates or 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 frequency band pass filters were used in the past to perform spectrum analysis, but they have been largely supplanted by the FFT analyzer.
- A computer-aided design technique for mathematically modeling a structure. Finite element modeling is used for structural analysis, heat transfer analysis, and modal analysis.
- The machine whose position is not changed during shaft alignment. Compare with Shim Machine.
- 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 amplitude 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.
- A special windowing function for minimizing noise in impact testing. Since the duration of the actual impact is usually very short relative to the overall digitized time sample, the frequency response function of the force signal can have a low signal to noise ratio. The force window does not alter the actual force pulse but minimizes the noise in the rest of the data block giving a much improved signal to noise ratio.
- Mathematically calculating the system response to an arbitrary forcing function using modal analysis data as the system model.
- The oscillation of a system under the action of a forcing function.
- The surface to which the machine baseplate is mounted.
- The famous many-talented French engineer, mathematician, and one time president of Egypt, who devised the Fourier series and Fourier Transform for the conversion of time functions into frequency functions and vice versa.
- The mathematically rigorous operation which transforms from the time domain to the frequency domain and vice versa. See also Fast Fourier Transform.
- Fourier analysis is another term for spectrum analysis, although it generally refers to analysis using an FFT analyzer, q.v.
- The repetition rate of a periodic vibration, per unit of time, determined by taking the reciprocal of the period (T). Frequency is expressed in three ways: Hz (how many cycles per second); cpm (how many cycles per minute); and orders (how many cycles per shaft turning speed [TS]). Frequency is also the x-axis of the vibration spectrum; it identifies the source of the vibration.
- 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 it is sometimes more convenient to express frequency in cycles per minute (cpm), which corresponds to rpm. Frequency in cpm 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 cpm 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 spectra from the same machine 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 vibration monitoring analyzers.
- 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 one 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.
- The frequency response function, also called the FRF, is a characteristic of a system which 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 it 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.
- The output to input relationship of a structure. Mathematically, it is the Fourier transform of the output divided by the Fourier transform of the input. It is also the transfer function measured along the j
axis in the s-plane.
- For an N degree of freedom system, it is an N x N symmetrical matrix whose elements are the frequency response functions between the various points on the structure. Rows correspond to response points and columns to excitation points. For example, H23 is the frequency response with excitation at point 3 and response at point 2. The matrix is redundant, that is, by knowing any row or column, the other elements of the matrix can be computed.
- The spectrum of a periodic signal will consist of a fundamental component at the reciprocal of the period and possibly a series of harmonics of this frequency. The frequency is directly related to the phase-locked, rotational speed being measured and its amplitude may be low enough that it is difficult to see in the spectrum.
- The spectrum of a periodic signal will consist of a fundamental component at the reciprocal of its 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.
- The rotation frequency or rate of the cage supporting the rolling elements in an anti-friction bearing. The FTF is always less than one-half shaft TS
- The minimum number of independent coordinates necessary to completely describe a systems position constitutes a set of generalized coordinates. For an N degree of freedom system, N generalized coordinates are required.
- 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 sidelobes 42 dB down, whereas the Hanning window's first sidelobes 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 sidelobes 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.
- The Hanning window, also called "Hanning weighting," is a digital manipulation of the sampled signal in an FFT analyzer which forces the beginning and ending samples of the time record to zero amplitude. This compensates for an inherent error in the FFT algorithm which 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 wave form used by the analyzer to calculate the spectrum, and this results 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.
- A frequency that is an integer multiple of a given (subsynchronous, synchronous or nonsynchronous) frequency.
- Harmonics, also called a harmonic series, are components of a spectrum which are integral multiples of the fundamental frequency. A harmonic series in a spectrum is the result of a periodic signal in the waveform. Harmonic series are very common in spectra of machinery vibration.
- 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.
- A filter that passes signal frequencies above a specific, or cut off, frequency is called a high pass filter. They are used in instrumentation to eliminate low-frequency noise, and to separate alternating components from direct (DC) components in a signal.
- Non-uniqueness in the relationship between two variables as a parameter increases or decreases. Also called deadband, or the portion of the system's response where a change in input does not produce a change in output.
- Energy losses within a structure that are caused by internal friction within the structure. These losses are independent of speed or frequency of oscillation but are proportional to the vibration amplitude squared.
- A plot of the imaginary part of the frequency response function versus frequency. For a single-degree-of-freedom system, the magnitude is a maximum or minimum at the damped natural frequency.
- A method of measuring the frequency response function of a structure by hitting it with a calibrated hammer and measuring the system's response. The impact hammer is instumented with a load cell to measure the input force pulse while the response is typically measured using an accelerometer. The impact imparts a force pulse to the structure which excites it over a broad frequency range.
- 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.
- The response of a system to a unit impulse or Dirac's delta function. The Fourier transform of the impulse response is the frequency response function.
- A gravity device that measures angular position in degrees.
- A type of soft foot that is caused by external forces (coupling, pipe strain, etc.) acting on a machine independent of the foot to baseplate connection.
- The frequency response function of acceleration/force. Also known as accelerance.
- Integration is the mathematical operation which 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. For this reason an accelerometer is the transducer of choice because velocity and displacement can be so easily derived from its output. An analog integrator is actually a low pass filter with 6 dB of attenuation per octave. This is true of an analog integrator only above its low cutoff. And since the low cutoff cannot be zero, analog integrators have low-frequency limits, usually either 1 or 10 Hz.
- A bolt or screw attached to the baseplate or foundation that is used to move or position the machine that is being moved.
- A long shaft that is used as a spacer between two machines. Also, a long turning shaft with several sheaves.
- The physical location of a rotor relative to the fixed, or non- rotating parts of the machine.
- In an FFT analyzer, the input signal is recorded in time blocks, called time records, and individual spectra are computed from each block of data. Because the input signal period is not synchronized with the duration of the time block, the signal will be truncated at the beginning and end of the block. This truncation causes an error in the calculation which 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. See also Hanning.
- In common usage the level of a signal is its amplitude, but strictly speaking the term should be reserved for the amplitude expressed on a decibel scale relative to a reference value.
- In an FFT spectrum, the frequency difference between two adjacent bin centers or lines.
- 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 these two types.
- A filter that passes signals with less than 3 dB attenuation up to its cutoff frequency, and attenuates the signal above that frequency. The attenuation slope is called the roll off, q.v. An anti-aliasing filter is an example of a low pass filter.
- Three or more machines that must be aligned to one another.
- The frequency response function of force/velocity.
- See Impedance, Mechanical.
- Tool used to measure thickness.
- This is one thousanth of a radian. A radian is an angle whose subtended arc is equal to the radius at which the arc is measured. It amounts to about 57.3 degrees. There are 2
radians in a circle. A unit (normally metric) used to describe the angle of one machine centerline to the other. It is the equivalent to 1 mils/inch. It can also be expressed as rise/run. (1 unit = 17.45 milliradians)
- A unit of measure for displacement (thousandths of an inch). Usually measured in mils peak to peak, which represents total displacement.
- A unit (normally English) used to describe the angle of one shaft centerline to the other. It is equivalent to milliradians. It can also be expressed as rise/run (1 unit = 17.45 mils/inch), as long as the rise is measured in mils and the run is measured in inches.
- The frequency response function of velocity/force.
- Mobility is the inverse of mechanical impedance. It is a measure of the ease with which a structure is able to move in response to an applied force, and varies it with frequency.
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 equal to the magnitude of the force times the mobility of the structure. From this it follows that the amplitude of the destructive forces acting on a machine are not determined directly by measuring its vibration if the mobility of the machine 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.
- The process of determining a set of generalized coordinates for a system such that the equations of motion are both inertially and elastically uncoupled. More commonly, it is a process of determining the natural frequencies, damping factors, and mode shapes for a structure. This is usually done either experimentally through frequency response testing or mathematically using finite element analysis.
- The relative position of all points on a structure at a given natural frequency.
- An N-degree-of-freedom system is a system whose position in space can be completely described by N coordinates or independent variables.
- Narrow band analysis is technobabble for FFT analysis.
- The frequency of oscillation of the free vibration of a system if no damping were present. For a single-degree-of-freedom system, the natural frequency
where k is the spring constant and m is the mass.- A point or line on a vibrating structure that remains stationary.
- Any unwanted signal. Can be random or periodic.
Asynchronous- Frequencies in a vibration spectrum that exceed shaft turning speed (TS), but are not integer or harmonic multiples of TS. See asynchronous.
- Digital signal processing requires analog to digital (A to D) conversion of the input signal. The first step in A to D conversion is sampling of the instantaneous amplitudes of signal at specific times determined by the sampling rate. 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. This is called aliasing. The theoretical maximum frequency that can be correctly sampled is equal to one-half the sampling rate, and is called the Nyquist frequency.
In all digital signal processing systems, including FFT analyzers, the sampling rate is made to be significantly greater than twice the highest frequency present in the signal in order to be certain the aliasing will not occur.
- A plot of the real part versus the imaginary part of the frequency response function. For a single-degree-of-freedom system, the Nyquist plot is a circle.
- 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.
- 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, but the US Navy has used 1/3 octave band analysis for vibration measurements on submarines for a long time.
- Movement of the shaft center lines associated with (or due to) a change in pressures, temperatures and other forces between the static and operating condition.
- Distance between rotational center lines at any given normal plane, usually measured at the coupling midpoint. Usually measured in mils in the US, and mm or microns in the rest of the world.
- A secondary alignment method for determining on-line and off-line changes in alignment conditions. This method involves a scale of some type affixed to a machine such that a transit can be used to measure movement of the machine as it grows to its on-line position.
- An expression of frequency which relates a frequency (subsynchronous, synchronous or nonsynchronous) to shaft TS. It is calculated using the simple formula: Order=f/TS. In order analysis, the frequency axis of the spectrum is expressed in orders of shaft TS (i.e. peaks may be refered to as 1xTS, 2xTS or .43xTS or 6.77xTS ).
- Order analysis is simply frequency analysis where the frequency axis of the spectrum is expressed in orders of rpm rather than in Hz or rpm.
- Order tracking is a special case of FFT analysis applied to variable-speed rotating machines where the sampling frequency of the analyzer is varied to be an exact multiple of the running speed of the machine while a series of spectra are recorded. The spectra are usually shown on top of one another on the page, and this is sometimes called a waterfall plot. In this way, the running speed and its harmonics will always occur at the same frequencies, or orders, in the spectrum regardless of the machine speed. Other vibration components not related to running speed, such as line frequency effects will not be synchronous with running speed, and will show up as curves on the waterfall plot. A tachometer pulse from the machine is needed to determine the FFT analyzer's sampling frequency. Some analyzers have the order tracking function built in, but others need an external frequency multiplier to derive the sampling frequency from the tachometer signal.
- A measure of the total RMS magnitude within a specified frequency range.
- In the FFT analyzer, the time signal is stored in a buffer before being processed to form the spectrum. The FFT algorithm only processes the data when the time buffer is full, and after the widowing function, i.e. Hanning, is applied to it. This windowing causes data at the beginning and end of the time records to be represented at the wrong amplitude values, creating errors in the spectral amplitude levels. If two time buffers are used, and if the FFT algorithm is allowed to process the signal alternately from each buffer at a rate faster than the time it takes to fill the buffers, overlap processing is said to be 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. An overlap of 66.7% will completely correct for amplitude errors caused by the Hanning window.
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