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|موضوع: كتاب Beginner’s Guide to Machine Vibration الجمعة 28 مايو 2021, 1:40 am|| |
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Beginner’s Guide to Machine Vibration
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Why Is Monitoring Vibration Important? . 1
What is machine vibration? . 2
What causes machine vibration? 4
Why monitor machine vibration? 9
Summary . 15
How Is Machine Vibration Described? . 17
How is vibration described? 18
What is amplitude? . 19
What is frequency? . 22
What is a waveform? 23
What is a spectrum? . 24
Summary . 26
How Is Machine Vibration Measured? 27
Which machines need monitoring? 28
How does the instrument work? . 29
How is the accelerometer mounted? 30
How are parameters set? . 38
How is data collected? 48
Summary . 54
List Of Symbols . 55
Common Vibration Terms
cos x the cosine of x
cpm cycles per minute
cps cycles per second
FFT fast Fourier transform
f max the maximum frequency value on a spectrum
ft foot (or feet)
ft/s feet per second
ft/s² feet per second per second
g acceleration due to gravity (9.80665 m/s²)
in/s inches per second
kcpm kilocycles per minute (1000 cpm)
kgf kilogram force
kHz kiloHertz (1000 Hz)
lbf pound force
The following are
the symbols, units,
used in this bookSymbol Meaning
Ibf/in pound force per inch
log x the logarithm of x
log10 x the base-10 logarithm of x
MAS Measurement Analysis Software
mil 0.001 inch
mm/s millimeters per second
m/s meters per second
m/s² meters per second per second
mV/g milliVolts per g
rad/s radians per second
rpm revolutions per minute
sin x the sine of x
vb COMMTEST INSTRUMENTS vibration analyzer
vdB decibel unit for velocity
w.r.t. with reference to
x the average value of x
x² the square of x (x times x)
1X fundamental frequency
√x the square root of x
∅ phase angle
π the constant pi (roughly equal to 3.14)
Σx the sum of x values
ω angular frequency (expressed in rad/s)APPENDIX B
w.r.t. = with
adj. = adjective
n. = noun
pref. = prefixA
The rate of change of velocity. The acceleration of an object is the rate
at which it is gaining or losing speed in a particular direction. The
acceleration of an object is proportional to the force causing it to
accelerate. Commonly used acceleration units are mm/s2 (metric),
m/s2 (SI), in/s2 (imperial), ft/s2 (imperial), and g. See also
Accelerometer and Triaxial accelerometer.
Acceleration due to gravity
A transducer with an electrical output directly proportional to the
acceleration of the vibrating point in the direction in which the
transducer is attached. The acceleration of a vibrating body is usually
measured using an accelerometer. See also Triaxial accelerometer.
The electronic hardware that converts analog signals to digital values
by way of data sampling.
A graph that specifies the maximum allowable amplitude for each
frequency value in a spectrum or group of spectra. An alarm envelope
is usually based on a reference spectrum that is “ideal” or “normal” for
the measurement point.Algorithm
The procedure for performing a task e.g. the procedure for calculating
a spectrum from a waveform - the Fast Fourier transform - is an
The illusion of high frequency signals appearing as low frequency
signals due to the sampling frequency being less than twice the highest
frequency component in the signal. Vibration measurement
instruments avoid aliasing by filtering out frequency components above
the specified f max (by way of a “low pass” or “anti-aliasing” filter) and
sampling the filtered signal at a rate at least twice the f max.
The process where the axes of machine components are positioned
and orientated correctly and accurately with respect to one another.
See also Misalignment.
The magnitude of a signal or periodic motion e.g. the magnitude of the
velocity of a vibrating body. Amplitude can be expressed in a variety of
ways, the most common amplitude types being “peak”, “peak-to-peak”,
and “root-mean-square” (rms).
The fluctuation in the amplitude of a signal due to the influence of
another signal that is of a different frequency. In rotating machinery,
high frequency signals, such as bearing inner race defect signals, are
often amplitude-modulated by the lower frequency signal of the rotating
shaft, due to the defect passing in and out of the load zone once every
revolution. The spectrum corresponding to a sinusoid amplitudemodulated by another is characterized by a peak located at the
frequency of the sinusoid, and a sideband on either side of the peak,
each sideband distanced from the peak by the frequency of the
modulating sinusoid. The term “amplitude modulation” is sometimes
abbreviated as “AM”. See also Frequency modulation.Analog (w.r.t. signals)
Having a continuous relationship with the physical quantity being
measured e.g. an accelerometer outputs an analog signal that bears
continuous similarity to the vibration being measured. Due to the
continuity with which an analog signal describes the physical quantity
being measured, information regarding the physical quantity can be
obtained from the analog signal at any instant in time. See also A/D
converter and Digital.
See A/D converter.
See Measurement parameters.
Analysis software (w.r.t. vibration monitoring)
Computer software for the detailed analysis of collected data. See also
Measurement Analysis Software.
Angular contact bearing
A bearing that supports both radial and axial shaft loads. The rolling
elements in an angular contact bearing are usually orientated at an
angle to the shaft axis. See also Thrust bearing.
The oscillation rate of a signal or periodic motion expressed as the
angular distance traversed per unit time e.g. an object vibrating at one
cycle per second has an angular frequency of 2π radians per second
(since one cycle, or an angle of 2π radians, is traversed every second).
Angular frequency is usually denoted by the symbol, ω and measured
in rad/s (radians per second). See also Frequency and Radian.Angular misalignment
A low pass filter that removes all signal components of frequencies
higher than the specified f max. See also Aliasing.
See Non-synchronous peak.
Reduction in the level of a signal. As a vibration signal travels through
a mechanical structure, its level decreases. In general, high frequency
components decrease in level more than low frequency components.
The level of similarity between two “snapshots” of the same waveform.
Two snapshots that are identical have an auto-correlation of one, and if
they are entirely different, the auto-correlation is zero.
A mathematical operation aimed at reducing spectral or waveform
distortions arising from random noise signals. An “average” spectrum
or waveform is derived from a series of individual spectra or timesynchronized waveforms. The amplitude at each frequency or time
value of an average spectrum or waveform, is the average of
amplitudes of the individual spectra or waveforms at that frequency or
time value. The two most common methods of amplitude averaging
are linear averaging and exponential averaging. See also Peak hold.Axes
Plural of Axis.
The direction of the centerline of a shaft or rotor.
A force acting in the direction of the centerline of a shaft or rotor. Axial
force is sometimes called “thrust”. An overhung rotor vibrates in the
axial direction because the moment caused by the weight of the rotor
causes an axial excitation force.
Vibration in the direction of the centerline of a shaft or rotor. Axial
vibration is seen in overhung rotors. See also Radial vibration.
Axis (w.r.t. graphs)
See x-axis and y-axis.
Axis (w.r.t. motion)
An imaginary line around or along which motion takes place e.g. the
lengthwise centerline of a shaft is the axis of rotation of the shaft.
Axis (w.r.t. the vb instrument)
A data group in the vb instrument data structure, namely, a data group
for grouping recordings taken in the same orientation at a particular
measurement point. See also Data structure.Axis (w.r.t. vibration measurements)
The orientation or direction in which the accelerometer is mounted
when a vibration measurement is taken. The accelerometer is usually
mounted in the axial, radial, horizontal, vertical, or tangential direction
of a rotating part.B
A condition where a machine part can move independently of the part
driving it e.g. a gear that can rotate freely a slight distance without
being obstructed by the pinion, or a pulley that can rotate slightly to
take up slackness in a belt. Backlash is caused by looseness in a drive
train and leads to motion inaccuracy.
The condition where the axis of rotation and mass centerline of a
rotating part are coincident. See also Unbalance.
The adjustment of the mass distribution in a rotating part so that the
axis of rotation and mass centerline of the rotating part are coincident.
See also Correction weights and Unbalance.
See Correction weights.
Ball pass frequency
The speed at which bearing rolling elements pass a certain point on the
inner or outer race of the bearing. The ball pass frequencies for the
inner and outer races are often abbreviated as “BPFI” and “BPFO”
respectively. The vibration spectrum of a defective bearing often has
peaks at the BPFI and BPFO frequencies. The BPFI is usually about
0.6 times the operating speed multiplied by the number of rolling
elements, and the BPFO is usually about 0.4 times the same quantity.Ball spin frequency
The speed at which a rolling element revolves around its own axis in a
bearing. The term “ball spin frequency” is often abbreviated as “BSF”.
The vibration spectrum of a defective bearing often has a peak at the
ball spin frequency. The ball spin frequency is usually not a whole
number multiple of the fundamental frequency.
Band pass filter
A filter that allows only signal components of frequencies between two
cut-off frequency values to pass through. Band pass filters are used
when only a certain frequency range is of interest.
The difference between the upper and the lower cut-off frequency
values of a band pass filter, or the range of frequencies over which an
instrument will measure.
The rate at which data is transferred between the computer and the vb
instrument. Baud rate is measured in “bits per second” or “kilobits per
See Reference spectrum.
The frequencies of rotation of the elements of a rolling element
bearing. The bearing tones of a rolling element bearing include the
frequency of rotation of the cage (FTF), the frequency of rolling
elements making contact with a certain point on the inner race (BPFI),
the frequency of rolling elements making contact with a certain point on
the outer race (BPFO), and the frequency of rolling elements spinning
around their own axes (BSF). See also Ball pass frequency, Ball
spin frequency, and Fundamental train frequency.Beating
A phenomenon where a signal pulsates periodically because the signal
comprises two signals of nearly the same frequency. The frequency of
pulsation or beating is equal to the difference between the frequencies
of the two signals. Beating can occur when there are identical
machines operating at about the same speed, or when the frequency of
the excitation force is close to the natural frequency.
The cause of bending and shear stress. A force applied
perpendicularly to the tip of a cantilever causes a bending moment at
every position of the cantilever. The higher the bending moment, the
higher the shear stress, and the more the bending.
See Spectral line.
Binary digit. The binary number system uses only two digits, “0” and
“1” (as opposed to the decimal number system which uses ten digits,
“0” to “9”). Each “0” or “1” appearing in a binary number is a “bit”.
Blade pass frequency
The speed at which fan blades rotate past a fixed reference point. This
is equal to the operating speed of the fan multiplied by the number of
fan blades. The vibration spectrum of a fan shows a peak at the blade
pass frequency. The term “blade pass frequency” is often abbreviated
A set of two graphs, one showing how amplitude varies with frequency
and the other showing how phase varies with frequency. A Bode plot
is used to show the frequency response of a system. See also
See Ball pass frequency.
See Ball pass frequency.
See Ball spin frequency.
Indentation of the races of a bearing by its rolling elements. The
indentation is usually caused by vibration of the shaft while the shaft is
not rotating. The indentation could also be due to large static forces
being applied to the shaft while it is not rotating. Brinneling causes
spectral peaks at the ball pass frequencies.
Broad band analysis
See Broad band measurement.
Broad band measurement
The measurement of the overall vibration level over a large frequency
range. A broad band measurement indicates any change to the overall
vibration energy of the system but cannot indicate specifically at what
frequencies energy change is taking place. See also Narrow band
A test for determining the natural frequencies of a system. The system
is struck with an impulsive force, e.g. by a hammer, and allowed to
vibrate freely. The frequencies corresponding to spectral peaks in the
free vibration spectrum of the system are the natural frequencies of the
Cage defect frequency
See Fundamental train frequency.
The verification and/or correction of the accuracy of an instrument,
using a known standard as the reference.
The frequency of a signal that is being modulated by another signal
e.g. the rotor bar pass frequency of a motor is often a carrier frequency
that is modulated by the shaft rotation frequency. See also Amplitude
modulation, Frequency modulation, and Modulation.
See Waterfall chart.
A condition where the inlet pressure of a pump or water turbine is too
low and therefore causes a mixed flow of fluid and vapor. Cavitation
causes random high frequency vibration.
Center of mass
The center point of mass concentration in a body. The weight of the
body acts through the center of mass of the body. The imaginary line
connecting the center of mass at every cross-section of a rotor is the
mass centerline of the rotor. See also Principal inertia axis and
The force that keeps a rotating object in a circular path. The centrifugal
force acts through the center of mass of the object and towards the
center of rotation. The magnitude of the centrifugal force is
proportional to the mass and the square of the speed of the rotating
object, and inversely proportional to the radius of rotation.
A graph that shows the Fourier transform of a spectrum i.e. the
spectrum of a spectrum. A cepstrum extracts periodic patterns from a
spectrum in the same way a spectrum extracts periodic patterns from a
waveform. A cepstrum is useful for analyzing spectra containing many
harmonics and sidebands just as a spectrum is useful for analyzing
waveforms made up of many sinusoids. Cepstrum analysis is
particularly useful for gearboxes and rolling element bearings as the
vibration spectra often contain many harmonics and sidebands. A
series of equally spaced harmonics or sidebands on a spectrum
appears as a single peak on a cepstrum.
A measure of the level of proportionality between two signals. For
example, there is coherence between the response and the excitation
force in a linear system. On the other hand, there is no coherence
between an excitation force and random noise. Coherence is rated on
a scale ranging from zero to one. A directly proportional relationship is
given a coherence of one, and where there is no relationship
whatsoever between the two signals, the coherence is zero. See also
Communications port of a computer, which allows data transfer to or
from the computer.Continuous (w.r.t. signals)
Having data corresponding to all time values, all frequency values, or
all values on the x-axis. The analog signal output by an accelerometer
is a continuous signal. See also Discrete.
Weights that are attached to a rotating part in order to adjust the mass
distribution of the rotating part such that the axis of rotation and mass
centerline of the rotating part are coincident. See also Unbalance.
The sine wave phase-shifted by 90° i.e.
cos θ = sin (θ + 90°)
where “cos” and “sin” denotes “cosine” and “sine” respectively, and θ
is the angle.
The dissipation of vibration energy due to friction between dry surfaces.
Friction in movable joints and hinges is a common source of Coulomb
damping. The quantity of energy dissipated is dependent on the texture
of the sliding surfaces, the force pressing the sliding surfaces together,
and the distance over which friction occurs. The French physicist,
Charles A. de Coulomb first expounded the proportionality of friction to
applied pressure. See also Hysteretic damping and Viscous
A pair of forces distanced apart and acting in opposite directions. A
couple acting on a body causes the body to rotate. See also Couple
An unbalance condition where the mass centerline of a rotor is not
parallel to the axis of rotation but intersects it. This is caused by two
heavy spots one located at each end of the rotor and which are on
opposite sides of the rotor surface. When rotated, the centripetal
forces associated with the oppositely positioned heavy spots give rise
to a couple that rotates at the rotational speed of the rotor. The
rotating couple in turn causes out-of-phase repeating forces to act on
the support bearings i.e. the force acting on one bearing is always
pointing in a direction opposite to that acting on the other bearing. As a
result, the rotor rocks from side to side. Couple unbalance can be
corrected by adding two correction weights to the appropriate locations
on the rotor. See also Dynamic unbalance and Static unbalance.
A measurement unit for the frequency of periodic motion. cpm stands
for “cycles per minute”. One cpm is equal to a sixtieth of a Hertz (1/60
Hz). See also cps.
A frequency unit equivalent to 60 times the frequency unit, cpm i.e. one
cps (cycles per second) is equal to 60 cpm (cycles per minute). See
The ratio of the peak amplitude of a waveform to the rms amplitude of
the waveform. The crest factor of a vibration waveform provides
information regarding the nature of the vibration. For example, the
waveform from an unbalanced rotor is roughly the same as a
sinusoidal waveform and has a crest factor roughly equal to √2
(approximately 1.4). If the dominant cause of vibration is misalignment,
the crest factor will usually be less than √2 and if there is impacting in
gear teeth or bearing rolling elements, the crest factor will generally be
higher than √2.Critical damping
The quantity of damping just enough to stop a system from vibrating. A
critically damped system that is momentarily excited will complete only
part of an oscillation before returning to and remaining at its equilibrium
position. If the damping is more than the critical amount, the system
will return to its equilibrium position more slowly, though without
vibrating. Large guns are usually critically damped to ensure they
return to their original position after recoil in the minimum time without
vibrating. Over-damping a gun would cause delays between firings.
See also Over-damped system and Under-damped system.
See Critical speed.
A machine operating speed that matches one of the natural
frequencies of the machine. A machine operated at any of its critical
speeds will vibrate excessively due to resonance. To avoid machine
damage, the operating speed of the machine should be increased or
decreased rapidly past its critical speeds.
A measure of how similar a waveform is to another waveform. The
cross-correlation of two identical waveforms is one, and of two
completely dissimilar waveforms is zero. See also Coherence.
One complete sequence of the shortest signal pattern that
characterizes a periodic waveform or motion.
Damped natural frequency
The natural frequency of a damped system. In practice, all machines
are damped to a certain extent. When a machine is undergoing free
vibration, it will vibrate at its damped natural frequencies. If all
damping were removed from the machine (something impossible in
practice), the free vibration of the machine would occur at its
undamped natural frequencies or resonant frequencies. Damped
natural frequencies are always slightly lower than their corresponding
The dissipation of vibration energy as heat and/or sound. The gradual
decrease in amplitude of a freely vibrating object is evidence of the
presence of damping. See also Coulomb damping, Hysteretic
damping, and Viscous damping.
A collection of instantaneous amplitude values derived from sampling a
continuous time domain signal (using an A/D converter). FFT
calculations are performed on time domain data blocks to produce
frequency domain spectra.
A MAS file that contains the data transferred to it from the vb
The hierarchical structure of data storage in an instrument. In the vb
instrument, there are five levels in the hierarchy: machine, point, axis,
parameter set, and recording.dB
A dimensionless logarithmic unit for amplitude often abbreviated as
“dB”, and defined as follows:
Amplitude dB = 20 log10 (Amplitude / Reference Amplitude)
dB units can be used for displacement, velocity, or acceleration
amplitude. Due to the use of the logarithm function, dB units are useful
for displaying signals with both very large and very small amplitudes. A
6 dB increase, for instance, represents a 100% increase in amplitude
on the linear scale. See also vdB.
A measurement unit for angle, often denoted by the symbol, °. One
complete rotation is equal to 360°, half a rotation is equal to 180°, a
quarter rotation is equal to 90°, etc. See also Radian.
Degrees of freedom
The minimum number of independent coordinates required to
determine completely the positions of all parts of a system at any
instant of time. The motion of a simple pendulum can be described by
one coordinate: its angle around the axis of rotation. It is thus a single
degree-of-freedom system. In comparison, a shaft has an infinite
number of mass points and an infinite number of coordinates is
required to specify its deflected configuration. Thus, it has an infinite
number of degrees of freedom. The larger the number of degrees of
freedom, the more complex the system. See also Natural frequency
and Natural mode shape.Demodulation
The process of extracting the modulating signal from a modulated
signal. Shaft rotation signals sometimes modulate higher frequency
signals such as rotor bar pass frequencies and gear mesh frequencies.
A demodulator can be used to recover the shaft rotation signals. See
also Amplitude modulation, Frequency modulation, and
Not random and the value of which can be determined at any given
time. Deterministic signals can be non-periodic. As most machine
vibration is deterministic as well as periodic, their spectra show welldefined harmonics.
See Discrete Fourier transform.
A mathematical operation which yields the rate at which a variable is
changing with respect to another variable. For example, acceleration is
the rate at which velocity is changing with respect to time, and may be
derived from velocity by way of differentiation (with respect to time). In
vibration analyzers, differentiation can be performed on analog signals
by means of hardware or it can be calculated from a discrete signal by
means of software. Differentiation however amplifies noise signals and
is seldom performed in vibration analyzers. See also Integration.
Digital (w.r.t. signals)
That which has quantized signal values. Digital signals are obtained
from analog signals and may or may not be continuous. Digital signals
are easier to manipulate than analog signals. Most vibration
measurement instruments display digital rather than analog signals.
See also A/D converter and Quantization.Discrete
Finite, discontinuous, that can be counted. A discrete waveform does
not have data corresponding to all time values, but has data
corresponding to certain time values only. Similarly, a discrete
spectrum does not have amplitude data corresponding to all frequency
values, but to certain frequency values only. See also Continuous.
Discrete Fourier transform
A mathematical operation which calculates a discrete spectrum from a
discrete waveform. The term “discrete Fourier transform” is often
abbreviated as “DFT”. The FFT algorithm is a method of performing
the DFT operation in an efficient manner typically on a computer.
The position of an object relative to a fixed reference point, measured
in a particular direction. Two objects positioned at equal distance but
in opposite directions from the reference point have displacements of
equal magnitude but of opposite signs. Displacement units commonly
used in the field of vibration analysis are mm (metric) and mil
A transducer with an electrical output directly proportional to the
displacement of the vibrating point to which the transducer is attached.
An example of a displacement transducer is the proximity probe.
A set of values to which is mapped another set of values. The x-axis of
a graph is often the domain. See also Frequency domain and Time
The constant electric current supplied to an accelerometer. ICP
accelerometers require this constant current. When using an ICP
accelerometer with the vb instrument, the drive current should be
The difference between the highest and the lowest amplitude an
instrument can measure, with the amplitudes expressed in dB.
An unbalance condition involving both static and couple unbalance.
The mass centerline is both offset from and not parallel to the axis of
rotation. Most cases of unbalance in machines are dynamic
The distance between the center of mass and the center of rotation.
The larger the eccentricity, the larger the unbalance force.
That can be easily distorted, and that tends to revert to an original
shape after being distorted e.g. a guitar string is elastic. In an
engineering sense, an “elastic” material is one that exhibits linear
proportionality between mechanical stress and strain e.g. a steel rod is
elastic when deflected slightly i.e. the amount by which the steel rod
deflects is linearly proportional to the force applied to it.
The state of a body where either no force is acting on the body or the
resultant force acting on the body is zero (i.e. the forces acting on the
body cancel out one another).
The position of lowest potential energy or the position a freely
oscillating object will come to rest.Excitation force
A force that initiates free vibration or sustains forced vibration.
Excitation forces may be periodic, non-periodic, or random in nature.
Machine vibration is usually caused by excitation forces originating
from unbalanced, misaligned, loose, or defective parts. See also
See Excitation force.
A method of spectra or waveform averaging where more weighting is
given to the most recent spectrum or waveform than to preceding ones.
This allows the average to better reflect time-varying vibration patterns
while maintaining a measure of noise suppression. Exponential
averaging is a continuously running average and for a spectrum, is
Average i,k = Average i,k-1 + (Amplitude i,k – Average i,k-1) / n
where i = spectral line number;
k = average number (in the sequence of averages done for
spectral line i); and
n = number of spectra used for averaging.F
The maximum frequency displayed on a vibration spectrum i.e. the
frequency range (starting from zero Hz) over which amplitudes are
displayed. Increasing the f max (while keeping other parameters the
same) reduces the measurement duration required, but also reduces
the resolution of the spectrum.
Fast Fourier transform
An algorithm for performing the DFT operation efficiently i.e. an
algorithm for calculating a discrete spectrum from a discrete waveform.
The term “fast Fourier transform” is often abbreviated as “FFT”. The
FFT algorithm determines the frequencies and the amplitudes
corresponding to the frequencies that are present in the waveform.
Jean B. J. Fourier was a French mathematician who developed a
means of expanding periodic functions in terms of harmonic functions,
thereby contributing much to the fields of heat flow and vibration
analysis. See also Fourier transform.
The progressive development of the size of cracks in a material due to
the action of cyclic forces. Vibration is a cause of fatigue. The rate of
growth of a fatigue crack is proportional to the size of the crack.
Fatigue can be minimized by grinding surfaces to remove surface
imperfections and by minimizing stress spots in the design.
The frequency of repeating forces caused by faulty machine
components. Usually, the vibration spectrum shows spectral peaks at
the fault frequencies and their harmonics. Some examples of fault
frequencies are blade pass frequencies, rotor bar pass frequencies,
ball pass frequencies, gear mesh frequencies, and the operating speed
of the machine.FFT
See Fast Fourier transform.
A spectrum analyzer that uses the FFT algorithm to calculate spectra
from waveforms. Most spectrum analyzers are FFT analyzers.
A collection of data in a computer.
A device that allows certain frequency components of a signal to pass
through, but blocks other frequency components. See also Band pass
filter, High pass filter, and Low pass filter.
The operating system of an electronic instrument e.g. that of the vb
instrument. The firmware of the vb instrument can be upgraded with a
later version by means of PROFLASHing.
See Fundamental frequency.
First natural frequency
See Fundamental natural frequency.
Flat top window
The window that gives the best amplitude accuracy at spectral peaks,
at the expense of more signal leakage. The flat top window does not
separate closely spaced spectral peaks as well as the Hanning
window. See also Windowing.Fluid-film bearing
See Journal bearing.
The cause of acceleration or mechanical stress. The higher the force
applied to an object, the higher the acceleration of the object, or the
higher the stress in the object.
Response of a system to an excitation force. See also Free response.
The vibration of an object due to an excitation force acting on the
object. Most kinds of machine vibration are due to periodic excitation
forces. Forced vibration due to a periodic excitation force typically
occurs at the frequency of the excitation force, but can also occur at
other frequencies, especially at integral multiples of the frequency of
the excitation force. See also Free vibration.
The frequency of an excitation force. Several forcing frequencies may
be simultaneously present in a vibrating system.
See Excitation force.
A mathematical operation that transforms a time domain function into
an equivalent frequency domain function. The fast Fourier transform, a
computational version of the Fourier transform, is used to calculate
discrete frequency domain spectra from discrete time domain
waveforms. See also Discrete Fourier transform.Free response
Response of a system that is left to vibrate by itself without the
influence of an excitation force. See also Forced response.
The measurement mode of an instrument where measurements are
taken continually until manually stopped by the user.
The natural vibration of an object i.e. vibration without the influence of
an excitation force. The free vibration of an object can be initiated by
exciting the object with a force and then leaving it to vibrate freely by
itself. In practice, a freely vibrating object will eventually stop due to
damping. See also Forced vibration, Natural frequency, and
Natural mode shape.
The number of periodic cycles or oscillations completed per unit time.
Frequency is the reciprocal of period, and is usually expressed in Hz
(which is equivalent to cps or cycles per second), cpm (cycles per
minute), rad/s (radians per second), or derivatives of these units. See
also Angular frequency.
A portion of the frequency range of a spectrum.
That which has a frequency axis as its x-axis, or a set of frequency
values to which are mapped a set of other values e.g. amplitude. A
spectrum is a frequency domain graph i.e. a spectrum has a frequency
axis as its x-axis (and an amplitude axis as its y-axis).Frequency modulation
The fluctuation in the frequency of a signal due to the influence of
another signal, often of lower frequency. In rotating machinery, gear
mesh signals are often frequency-modulated by the lower frequency
signals of rotating shafts. The spectrum corresponding to a sinusoid
frequency-modulated by another is characterized by a peak located at
the frequency of the sinusoid, and many sidebands located
symmetrically on either side of the peak, with the spacing between the
sidebands equal to the frequency of the modulating sinusoid. The term
“frequency modulation” is often abbreviated as “FM”.
See f max.
The vibration amplitude and phase of a system at various vibration
frequencies in response to a particular force. The frequency response
of a system can be plotted on a Bode plot or on a Nyquist plot. The
response amplitude is usually normalized through division by the
amplitude of the input force, and expressed as a dimensionless
See Fundamental train frequency.
The rotational speed of the shaft or rotor, known also as the “1X” or
“first harmonic”. A machine usually vibrates at more than one
frequency, but the dominant frequency is often the fundamental
frequency, or a multiple of it. See also Harmonic (n.).Fundamental natural frequency
The first or lowest natural frequency of a system. When a system
vibrates freely, it vibrates at all its natural frequencies, but the first
natural frequency will be the dominant vibration frequency.
Fundamental train frequency
The frequency of rotation of the cage of a rolling element bearing. The
term “fundamental train frequency” is often abbreviated as “FTF”. A
spectral peak at the FTF is rare as the inertia of the cage is relatively
small. The FTF usually modulates other bearing tones so that
sidebands appear at those bearing tones. If a spectral peak appears at
the FTF, damage to one of the rolling elements should be suspected.G
The acceleration due to gravity i.e. the acceleration of an object
towards the center of the earth when the object is allowed to fall freely
in vacuum at sea level. One g is taken to be 9.80665 m/s² or 32.1740
ft/s². The acceleration of a vibrating body is sometimes measured in
terms of g’s.
Gear mesh frequency
The rate at which gear teeth contact. This is equal to the number of
teeth on the gear multiplied by the rotation speed of the gear. A
machine with gears will potentially vibrate at the gear mesh frequency.
A gearbox vibration frequency which does not relate to the geometry of
the gearbox. “Ghost” frequencies are caused by irregularities in gears
and usually disappear as the gears wear.H
A mathematical function named after its inventor and defined as
Hamming window = 0.54 - 0.46 cos θ for 0 ≤ θ ≤ 2π
The Hamming window is used to reduce signal leakage but because it
is not as effective as some other windows, it is now not popularly used.
See also Windowing.
A mathematical function named after its inventor and defined as
Hanning window = ½ (1 - cos θ) for 0 ≤ θ ≤ 2π
When multiplied with a data block, the Hanning window suppresses
amplitude values at the beginning and end of the data block while
preserving those in the middle. Multiplying a data block by the Hanning
window makes the data block appear like a complete wave, thereby
reducing signal leakage associated with limitations of the FFT
algorithm. See also Windowing.
Sinusoidal. See also Harmonic function and Harmonic motion.Harmonic (n.)
A spectral peak at a frequency that is a whole number multiple of the
fundamental frequency or of the frequency of any excitation force
present. A harmonic of a frequency n times that of the fundamental
frequency is called "nX". The frequency at which a harmonic occurs
may or may not be a whole number multiple of the fundamental
frequency e.g. the frequencies of harmonics of the ball pass and ball
spin frequencies are not whole number multiples of the fundamental
frequency. Most kinds of machine vibration are periodic and can be
described as the sum of a series of sinusoids. The harmonics in a
spectrum correspond to these sinusoids. See also Synchronous
Excitation by a harmonic force.
An excitation force that is sinusoidal in nature i.e. of the form:
F(t) = Fo sin (ωt - ∅)
where F(t) = the instantaneous force magnitude;
Fo = amplitude of the excitation force;
ω = angular frequency;
t = time; and
∅ = phase angle.
Sinusoidal function. See also Sinusoid.Harmonic motion
Sinusoidal motion i.e. motion that can be described by a sinusoid. The
free vibration of an undamped single degree-of-freedom system is
harmonic motion e.g. the swinging of a simple pendulum, in the
absence of friction, is harmonic motion. Harmonic motion is often
called simple harmonic motion or SHM.
The response of a system to harmonic excitation. The response is
dependent on the number of degrees of freedom and the damping in
A frequency unit equivalent to cps (cycles per second) and often
abbreviated as “Hz”. One Hz is equal to one cps or 60 cpm. Heinrich
R. Hertz was a German physicist famous for his works on radio waves.
High pass filter
A filter that allows only signal components of frequencies higher than a
particular cut-off frequency value to pass through. A high pass filter
may be used to remove low frequency noise and to reduce ski slope
See Hunting tooth frequency.Hunting tooth frequency
The frequency at which a particular tooth on a gear makes contact with
a particular tooth on a mating gear. The hunting tooth frequency is
equal to the gear mesh frequency divided by the least common multiple
of the numbers of teeth on the gears. For example, if a 24-toothed
gear is driven by a 12-toothed pinion rotating at 1000 rpm, then the
hunting tooth frequency is equal to 500 cpm. The term “hunting tooth
frequency” is often abbreviated as “HTF”. Spectral peaks will appear at
the HTF and multiples of the HTF if both the gear and pinion have
The dissipation of vibration energy by materials that convert energy to
heat when deformed. Hysteretic behavior is exhibited by most
materials but is most prevalent in viscoelastic materials such as
rubbers and plastics. A car tire that feels hot following a long journey is
in part due to hysteretic damping. The quantity of energy dissipated is
dependent on the volume of the material undergoing deformation, the
amount of deformation, the hardness of the material, and the ability of
the material to dissipate energy. See also Coulomb damping and
A piezoelectric accelerometer with a built-in charge amplifier (an
integrated circuit) which performs signal conditioning. When supplied
with a constant current of typically 2 to 6 mA, the voltage across the
accelerometer varies with acceleration with a sensitivity of typically 100
mV/g. ICP stands for “integrated circuit piezoelectric” and is a
registered trademark of PCB Piezotronics, Inc. See also Piezoelectric
See Bump test.
A system of measurement units based on measurement units used in
England in the past. Imperial units are sometimes called English units.
Common imperial units include “foot”, “inch”, “pound”, and “ounce”.
Unlike metric units, imperial units are not decimally related, and are no
longer commonly used in most parts of the world except in North
America. See also Metric units and S.I
Resistance to motion change. Mass is a measure of inertia. The
larger the inertia of an object, the more force it takes to move or stop
That which pertains to an infinitesimal moment e.g. the instantaneous
velocity of a vibrating object is the velocity of the object at a particular
instant in time.
A mathematical operation that yields the area under a graph. For
example, velocity is derived from acceleration by calculating the area
under the acceleration waveform. Integration is the inverse operation
A piece of electronic hardware that integrates an analog signal over
time. An integrator is often used to integrate accelerometer signals
over time to produce velocity signals.
The mathematical process of estimating or inserting values between
known or measured values. Various interpolation methods exist, the
simplest being linear interpolation. For example, if a discrete spectrum
contains amplitude information at 1000 Hz and 1002 Hz but not at 1001
Hz, then linear interpolation can be used to estimate the amplitude at
1001 Hz by taking the average of the amplitudes at 1000 Hz and 1002
A method of reducing machine vibration by means of placing a flexible
member between the machine and its supporting structure. The
flexible member, known as the “isolator”, is made of materials such as
rubber, cork, felt, or metallic springs. The isolator reduces the
magnitude of the force transmitted from the machine to its supporting
structure, and from the supporting structure to the machine.J
The rate of change of acceleration. A rapid change in acceleration is
apparent as “jerking”. Jerk can be derived by differentiating the
acceleration signal with respect to time.
The part of a shaft that spins within a bearing. The load is imparted to
the bearing by the journal.
A bearing without rolling elements but which depends on a fluid film to
enable the smooth spinning of the journal. See also Oil whirl and Oil
k (w.r.t. springs)
See Spring constant.
1000 times. The prefix “k” stands for “kilo”. One kHz (kiloHertz) is
equivalent to 1000 Hz, one kg (kilogram) to 1000 grams, one kcpm
(kilocycles per minute) to 1000 cpm.
A frequency unit equivalent to 1000 times the frequency unit, cpm i.e.
one kcpm (kilocycles per minute) is equal to 1000 cpm (cycles per
A measurement unit for force. “kgf” is short for “kilogram force”. One
kgf is equivalent to the weight of a one-kg mass.
The energy associated with motion. The vibratory motion of an object
involves a continual interchange of kinetic energy and potential energy.
When the object is moving, it possesses kinetic energy, and when it
attains maximum displacement (during which time it is momentarily
stationary), it possesses potential energy but zero kinetic energy.L
A measurement unit for force. “lbf” is short for “pound force”. One lbf
is equivalent to the weight of a one-lb mass.
See Signal leakage.
A commonly used method of averaging spectra or time-synchronized
waveforms. The amplitude at each frequency or time value of the
“average” spectrum or waveform is the arithmetic mean of amplitudes
of the individual spectra or waveforms at that frequency or time value
i.e. for an average spectrum:
Average i = E (Amplitude i,j) / n
where i = spectral line number;
j = spectrum number; and
n = number of spectra used for averaging.
Motion along an axis i.e. motion along a straight line.
A relationship governed by direct proportionality. See also
Proportional, directly.Linear scale
A scale with uniformly spaced marks, the distance between adjacent
marks representing a fixed quantity. See also Logarithmic scale.
A system which, when excited by a composite excitation force, outputs
a response that is the sum of its responses to the individual
components of the excitation force i.e. if the response to excitation
force F1 is x1 and to F2 is x2, then the response to the composite
excitation force F1 + F2 is x1 + x2 if the system is linear. At small
vibration amplitudes, most mechanical systems are linear systems.
See Spectral lines.
Load zone (w.r.t. bearings)
The part of a bearing that is subject to the greatest load e.g. load
associated with the weight of the rotor it is supporting.
Logarithm function, base-10
A mathematical function that yields the base-10 exponent of a number
e.g. the base-10 logarithm of the number 100 is equal to 2 (since 100 =
10²). The logarithm function is a useful tool for working with numbers
that vary greatly in magnitude e.g. the base-10 logarithm of a thousand
is 3 and of a million is 6 (which is not much bigger than 3 and therefore
easily displayed together on a graph). The symbol for “base-10
logarithm” is “log10”.
A scale with marks representing the logarithm of a value rather than
the actual value. Logarithmic scales are useful for displaying values of
greatly varying magnitudes. See also Linear scale.Looseness
The condition where there are undesired gaps between mating parts.
Looseness is usually caused by excessive bearing clearances, loose
mounting bolts, mismatched parts, and cracked structures. Depending
on the type of looseness, the vibration spectrum can appear different.
Bearing looseness is the most common form of looseness and
produces a vibration spectrum that contains many harmonics.
Low pass filter
A filter that allows only signal components of frequencies lower than a
particular cut-off frequency value to pass through. See also Aliasing.M
Machine (w.r.t. the vb instrument)
A data group of the vb data structure, for grouping recordings taken of
the same physical machine. See also Data structure.
The reciprocating or back-and-forth movement of a machine or
machine component involving a continual interchange of kinetic energy
and potential energy. The most common cause of machine vibration is
the rotation of unbalanced or misaligned parts. See also Free
vibration and Forced vibration.
The distortion of magnetic materials in the presence of magnetic fields.
Magnetostriction worsens the vibration caused by the reciprocation of
motor magnetic poles (which occurs at twice the line frequency).
Main unit (w.r.t. the vb instrument)
The part of the vb instrument which houses the LCD, keypad, RS232
COM port, battery pack and charger circuitry.
See Measurement Analysis Software.
See Alarm envelope.Measurement Analysis Software
A Windows-based analysis software developed by COMMTEST
INSTRUMENTS, that facilitates the archiving and analysis of vb data on
a PC. The software is also known as MAS, the abbreviation of
“Measurement Analysis Software”. MAS allows vibration data to be
graphed, analyzed, and printed.
The details about a measurement or recording, that must be specified
before the measurement or recording is taken e.g. before a spectrum is
taken, the f max, number of spectral lines to be used, averaging type,
windowing type, etc. need to be specified. The way in which
parameters are set can and often does affect measurement results.
A decimal system of measurement units based on S.I. units. For
example, the metric units for length, “kilometer”, “centimeter”,
“millimeter”, “micrometer”, etc. are related by factors of 10, 100, 1000,
etc., and are based on the S.I. unit for length, “meter”. See also
Imperial units and S.I.
A measurement unit for small distances, known also as “micron”. One
micrometer (µm) equals one millionth of a meter i.e. 10-6 meter.Micron
A measurement unit for small distances. One mil is equal to 0.001
The condition where the axes of machine components are not
positioned or orientated accurately with respect to one another.
Angular misalignment is the situation where the axes of mating parts
are tilted with respect to one another, and parallel misalignment is
where the axes are parallel but do not coincide. Usually, both kinds of
misalignment are involved. Misalignment is one of the most common
causes of vibration in machines.
The process of developing a mathematical model for the vibration of a
system so that the mode shapes of the system can be determined for
different excitation forces.
Mode of vibration
See Mode shape.
The collection of vibration amplitudes at all points of a system, or the
"shape" of a system, when it is subjected to a particular excitation
force. The mode shape of a vibrating system is a mixture of all the
natural mode shapes of the system, the dominant mode being that
corresponding to the natural frequency closest to the frequency of
The varying or fluctuation of a signal due to the influence of another
signal. The signal that is being modulated is called the “carrier” and
the signal causing the modulation of the carrier is called the
“modulating signal”. See also Amplitude modulation and Frequency
A hardware unit within the vb instrument, that performs most of the
calculations and stores most of the data associated with recordings.
The module has the accelerometer port attached to it.
The cause of rotation or bending. The moment about a point on a body
is caused by a force being applied on the body at a distance away from
the point. The greater the force, or the greater the distance, the
greater the moment about the point. If motion of the body is
unobstructed, the body will rotate because of the moment, but if the
body is restrained, the moment will cause the body to bend. See also
The product of mass and velocity. Momentum is a measure of the
tendency of a moving object to continue moving.N
Narrow band analysis
See Narrow band measurement.
Narrow band measurement
The measurement of the vibration spectrum of a system i.e. the
measurement of the vibration amplitude at individual frequency values
or for small frequency bands. See also Broad band measurement.
The frequency at which a system will vibrate when it is vibrating freely
by itself without the influence of an excitation force. An n degrees-offreedom system has n natural frequencies. A shaft (which has an
infinite number of degrees of freedom) has an infinite number of natural
frequencies. See also Fundamental natural frequency and Natural
Natural mode shape
The collection of vibration amplitudes at all points of a system, or the
"shape" of a system, when the system is vibrating at a particular
natural frequency. Each natural frequency has a corresponding natural
mode shape e.g. a simply-supported shaft vibrating at its first natural
frequency will have the shape of a bow, but when vibrated at its second
natural frequency will have an "s" shape. The natural mode shape
corresponding to the nth natural frequency is called the nth natural mode
shape. See also Mode shape and Nodal points.
See Free vibration.Navigator
A MAS tool that allows the locating and display of vibration data
archived on the PC. The navigator is displayed on the left side of the
MAS Main window and consists of two windows. The top window, the
Outline window, shows a “tree” of all machines, points, and axes in the
current data folder, and the bottom window, the List window, lists the
contents of the item highlighted in the Outline window. Any number of
items in the List window can be selected to be viewed, annotated,
printed, exported, plotted and/or deleted.
The points in a mode shape where there is no motion e.g. the second
natural mode shape of a simply-supported shaft is an "s" shape that
has a nodal point at the center of the shaft and one at each end of the
shaft. The nth natural mode shape of a shaft has n+1 nodal points.
Unwanted signal, often of a random nature, caused by electrical and/or
The amplitude level below which amplitude peaks cannot be
distinguished from noise.
A spectral peak occurring at a frequency that is not a whole number
multiple of the fundamental frequency. See also Harmonic (n.).
Normal mode shape
See Natural mode shape.Normalization
The dividing of all values by the largest value e.g. amplitude
normalization involves dividing all amplitude values by the largest
amplitude, so that all amplitude values are expressed as a fraction of
the largest amplitude. See also Order normalization.
The maximum frequency that can be sampled correctly i.e. without
aliasing occurring. The Nyquist frequency is half the sampling rate.
The vb instrument uses a sampling rate 2.56 times the f max, thus
ensuring that the Nyquist frequency is greater than the f max.
A complex numbers graph used to show the frequency response of a
system. The amplitude and phase of a system vibrating at a particular
frequency can be represented by a complex number (i.e. a number
consisting of a real part and an imaginary part). By plotting the
imaginary part against the real part for a range of frequencies, the
Nyquist plot is obtained.O
A frequency interval over which the frequency value is doubled. For
example, the 2X frequency is one octave above the fundamental
frequency. Vibration frequency is seldom expressed in octaves. It is a
term used in the fields of music and sound measurement.
An oil whirl condition where the journal orbits around the bearing at one
of the resonant frequencies of the shaft. Oil whip causes the shaft to
vibrate at large amplitudes.
A condition in a journal bearing where the oil film whirls and orbits the
journal around the bearing at about 40 to 49% of the shaft rotation
speed. Oil whirl is undesirable and is caused by excessive clearance
in the journal bearing or insufficient radial loading on the bearing. See
also Oil whip.
The shaft speed of the motor or engine in a rotating machine.
Orbit (w.r.t. journal bearings)
The circular path of the journal within the bearing. A large orbit
indicates the presence of oil whirl.
The frequency of a spectral peak expressed as a proportion or multiple
of the fundamental frequency e.g. a spectral peak at twice the
fundamental frequency has an order of 2X.Order analysis
See Order normalization.
The division of all frequency values on the frequency axis of a
spectrum by the fundamental frequency. Spectral peak frequencies
are thus expressed as multiples or fractions of the fundamental
frequency. This helps the analyst to identify the root cause of vibration.
See Order normalization.
To-and-fro, back-and-forth, or reciprocating motion. Vibration is
mechanical oscillation. “One oscillation” means one cycle of
Overall rms level
A system with a quantity of damping that is more than necessary to
prevent the system from vibrating. An over-damped system does not
vibrate but has a slow response. See also Critical damping and
Under-damped system.Overlap processing
The combining or overlapping of data from adjacent time domain data
blocks for FFT calculations. A percentage of data from the most
recently collected data block is combined with a portion of data of the
preceding data block, and the resultant data block is fed to the FFT
algorithm to obtain a spectrum more quickly than if no overlapping is
done. 50% overlap processing, as shown below, is ideal in most
FFT 1 FFT 3 FFT 5 FFT 7
FFT 2 FFT 4 FFT 6
Data block 1 Data block 2 Data block 3 Data block 4
See Measurement parameters.
Parameter set (w.r.t. the vb instrument)
A data group of the vb instrument data structure, for grouping
recordings taken at a particular location using the same measurement
parameter values. See also Data structure.
Peak (w.r.t. a spectrum)
The highest amplitude value in a spectrum.
Peak (w.r.t. a wave)
The highest point in a wave. See also Trough.
The maximum amplitude attained by a vibrating object in a given time
period e.g. the peak velocity amplitude of a vibrating object during a
given time period is the maximum velocity achieved by the object
during that time period. The terms “peak amplitude” and “zero-to-peak
amplitude” are synonymous.Peak hold
A mathematical operation resulting in the “largest-so-far” amplitude of
each line of a spectrum to be always displayed. This is done by
comparing each line of the most recent spectrum with the
corresponding line in the preceding spectrum and displaying the larger
of the two amplitudes. Although sometimes regarded as a form of
averaging, “peak hold” does not involve averaging.
The difference between the highest positive value and the lowest
negative value in a waveform. Displacement amplitudes are usually
expressed in terms of the peak-to-peak amplitude.
The time taken to complete one oscillation or one cycle. Period is
usually expressed in s (seconds) or ms (milliseconds). See also
Having a pattern that is repeated over and over again, each cycle
taking a fixed amount of time. See also Period and Repeating force.
See Repeating force.
Motion of a pattern repeated over and over again, each cycle or
oscillation taking a fixed amount of time. Examples of periodic motion
are circular motion, simple harmonic motion, and most kinds of steadystate vibration. Periodic motion can be mathematically described by
the arithmetic sum of a series of sinusoids. See also Period and
The time relation of a signal to another signal of the same frequency, or
the time relation of a vibrating object to another object vibrating at the
same frequency. The vibratory motion of an object is “in phase” with
that of another object if they oscillate at the same frequency in a
synchronized manner e.g. the two objects attain maximum positive
displacement simultaneously and zero displacement simultaneously. If
the motions of the objects are not synchronized e.g. if one object
attains maximum displacement when the other attains the minimum,
and vice versa, the vibratory motions are said to be “out of phase”.
A quantity that indicates the phase of a waveform or vibratory motion in
relation to another waveform or vibratory motion. Phase angle can be
expressed in degrees or radians. For example, a waveform that leads
a reference waveform by half a cycle, is ascribed a phase angle of
The difference between the phase of a vibratory motion and that of
another vibratory motion occurring at the same frequency. Phase
difference is measured in terms of cycles, degrees, or radians. The
phase difference between two objects vibrating in phase is zero cycles
or zero degrees. If an object attains maximum positive displacement
when another object (vibrating at the same frequency) attains minimum
negative displacement, the phase difference between the two vibratory
motions is 180°. A phase difference of 360° i.e. a phase difference of
one complete cycle, is equivalent to no phase difference or zero
degrees phase difference.
The number of cycles, degrees, or radians a waveform or vibratory
motion leads or lags another waveform or vibratory motion of the same
frequency. A sine waveform phase-shifted forward a quarter cycle
(90°) is equivalent to a cosine waveform.Pi
A constant value roughly equal to 3.14 and often denoted by the
symbol, π. The circumference-to-radius ratio of a circle is equal to 2π.
See also Radian.
Picket fence effect
A lack of accurate representation of peaks and troughs by a discrete
spectrum. Since amplitude data is not available for frequencies
between spectral lines, peaks generally appear too low and troughs,
too high. This effect may be reduced by increasing the sampling
duration (thereby increasing the number of spectral lines) and/or by
interpolating between spectral values.
A transducer in which a crystal converts mechanical force to electricity.
Most accelerometers are piezoelectric transducers and often have an
in-built mass – called the seismic mass – which exerts a force on the
piezoelectric crystal when vibrated. Due to the force exerted on it, the
piezoelectric crystal, typically a quartz crystal, generates an electrical
signal that is proportional to the force. See also ICP accelerometer.
Noise of which the level decreases with increasing frequency at the
rate 3 dB per octave. It is a term used in the field of sound
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