Beginner’s Guide to Machine Vibration
CONTENTS
Page
Foreword .vii
Chapter 1
Why Is Monitoring Vibration Important? . 1
What is machine vibration? . 2
What causes machine vibration? 4
Why monitor machine vibration? 9
Summary . 15
Chapter 2
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
Chapter 3
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
Appendix A
List Of Symbols . 55
Appendix B
Common Vibration Terms
APPENDIX A
LIST
OF
SYMBOLS
Symbol Meaning
adj. adjective
cos x the cosine of x
cpm cycles per minute
cps cycles per second
dB decibel(s)
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)
Hz Hertz
in inch(es)
in/s inches per second
kcpm kilocycles per minute (1000 cpm)
kg kilogram
kgf kilogram force
kHz kiloHertz (1000 Hz)
lb pound(s)
lbf pound force
The following are
the symbols, units,
and abbreviations
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
m meter(s)
mil 0.001 inch
mm millimeter(s)
mm/s millimeters per second
m/s meters per second
m/s² meters per second per second
mV/g milliVolts per g
n. noun
pref. prefix
rad radian(s)
rad/s radians per second
rms root-mean-square
rpm revolutions per minute
s second(s)
sec second(s)
sin x the sine of x
t time
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
° degree(s)
√x the square root of x
θ angle
∅ 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
COMMON
VIBRATION
TERMS
w.r.t. = with
reference
to
adj. = adjective
n. = noun
pref. = prefixA
Acceleration
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
See g.
Accelerometer
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.
A/D converter
The electronic hardware that converts analog signals to digital values
by way of data sampling.
Alarm envelope
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
algorithm.
Aliasing
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.
Alignment
The process where the axes of machine components are positioned
and orientated correctly and accurately with respect to one another.
See also Misalignment.
Amplitude
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).
Amplitude modulation
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.
Analog-to-digital converter
See A/D converter.
Analysis parameters
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.
Angular frequency
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
See Misalignment.
Anti-aliasing filter
A low pass filter that removes all signal components of frequencies
higher than the specified f max. See also Aliasing.
Asynchronous peak
See Non-synchronous peak.
Attenuation
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.
Auto-correlation
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.
Averaging
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.
Axial direction
The direction of the centerline of a shaft or rotor.
Axial force
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.
Axial vibration
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
Background noise
See Noise.
Backlash
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.
Balanced
The condition where the axis of rotation and mass centerline of a
rotating part are coincident. See also Unbalance.
Balancing
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.
Balance weights
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.
Bandwidth
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.
Baud rate
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
second”.
Baseline spectrum
See Reference spectrum.
Bearing tones
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.
Bending moment
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.
Bin
See Spectral line.
Bit
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
as “BPF”.
Bode plot
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
Nyquist plot.BPFI
See Ball pass frequency.
BPFO
See Ball pass frequency.
BSF
See Ball spin frequency.
Brinneling
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
measurement.
Bump test
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
system.C
Cage defect frequency
See Fundamental train frequency.
Calibration
The verification and/or correction of the accuracy of an instrument,
using a known standard as the reference.
Carrier frequency
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.
Cascade plot
See Waterfall chart.
Cavitation
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
Unbalance.Centrifugal force
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.
Cepstrum
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.
Coherence
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
Cross-correlation.
COM port
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.
Correction weights
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.
Cosine wave
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.
Coulomb damping
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
damping.
Couple
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
unbalance.Couple unbalance
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.
cpm
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.
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
also Hertz.
Crest factor
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.
Critical frequency
See Critical speed.
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.
Cross-correlation
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.
Cycle
One complete sequence of the shortest signal pattern that
characterizes a periodic waveform or motion.
cyc/sec
See cps.D
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
resonant frequencies.
Damping
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.
Data block
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.
Data folder
A MAS file that contains the data transferred to it from the vb
instrument.
Data structure
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
See decibel.
decibel
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.
Degree
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
Modulation.
Deterministic
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.
DFT
See Discrete Fourier transform.
Differentiation
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.
Displacement
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
(imperial).
Displacement transducer
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.
Domain
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
domain.Drive current
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
turned on.
Dynamic range
The difference between the highest and the lowest amplitude an
instrument can measure, with the amplitudes expressed in dB.
Dynamic unbalance
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
unbalance.E
Eccentricity
The distance between the center of mass and the center of rotation.
The larger the eccentricity, the larger the unbalance force.
Engineering units
See Unit.
EU
See Unit.
Elastic
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.
Equilibrium
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).
Equilibrium position
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
Repeating force.
Excitation function
See Excitation force.
Exponential averaging
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
given by:
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
f max
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.
Fatigue
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.
Fault frequency
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.
FFT analyzer
A spectrum analyzer that uses the FFT algorithm to calculate spectra
from waveforms. Most spectrum analyzers are FFT analyzers.
File
A collection of data in a computer.
Filter
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.
Firmware
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.
First harmonic
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.
Force
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.
Forced response
Response of a system to an excitation force. See also Free response.
Forced vibration
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.
Forcing frequency
The frequency of an excitation force. Several forcing frequencies may
be simultaneously present in a vibrating system.
Forcing function
See Excitation force.
Fourier transform
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.
Free run
The measurement mode of an instrument where measurements are
taken continually until manually stopped by the user.
Free vibration
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.
Frequency
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.
Frequency band
A portion of the frequency range of a spectrum.
Frequency domain
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”.
Frequency range
See f max.
Frequency response
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
quantity.
FTF
See Fundamental train frequency.
Fundamental 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
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.
Ghost 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
Hamming window
A mathematical function named after its inventor and defined as
follows:
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.
Hanning window
A mathematical function named after its inventor and defined as
follows:
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.
Harmonic (adj.)
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
peak.
Harmonic excitation
Excitation by a harmonic force.
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.
Harmonic function
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.
Harmonic response
The response of a system to harmonic excitation. The response is
dependent on the number of degrees of freedom and the damping in
the system.
Hertz
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
distortions.
HTF
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
defective teeth.
Hysteretic damping
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
Viscous damping.
Hz
See Hertz.I
ICP accelerometer
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
transducer.
Imbalance
See Unbalance.
Impact test
See Bump test.
Imperial units
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
Inertia
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
the object.
In-phase signals
See Phase.Instantaneous
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.
Integration
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
of differentiation.
Integrator
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.
Interpolation
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
Hz.
Isolation
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
Jerk
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.
Journal
The part of a shaft that spins within a bearing. The load is imparted to
the bearing by the journal.
Journal bearing
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
whip.K
k (w.r.t. springs)
See Spring constant.
k (pref.)
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.
kcpm
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
minute).
kgf
A measurement unit for force. “kgf” is short for “kilogram force”. One
kgf is equivalent to the weight of a one-kg mass.
Kinetic energy
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
lbf
A measurement unit for force. “lbf” is short for “pound force”. One lbf
is equivalent to the weight of a one-lb mass.
Leakage
See Signal leakage.
Linear averaging
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:
n
Average i = E (Amplitude i,j) / n
j=1
where i = spectral line number;
j = spectrum number; and
n = number of spectra used for averaging.
Linear motion
Motion along an axis i.e. motion along a straight line.
Linear relationship
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.
Linear system
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.
Lines
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”.
Logarithmic scale
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.
Machine vibration
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.
Magnetostriction
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.
MAS
See Measurement Analysis Software.
Mask
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.
Measurement parameters
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.
Measurement unit
See Unit.
Mechanical looseness
See Looseness.
Mechanical runout
See Runout.
Metric units
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.
Micrometer
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
See Micrometer.
mil
A measurement unit for small distances. One mil is equal to 0.001
inch.
Misalignment
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.
Modal analysis
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.
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
vibration.Modulation
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
modulation.
Module
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.
Moment
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
Bending moment.
Momentum
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.
Natural frequency
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
mode shape.
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.
Natural vibration
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.
Nodal points
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.
Noise
Unwanted signal, often of a random nature, caused by electrical and/or
mechanical effects.
Noise floor
The amplitude level below which amplitude peaks cannot be
distinguished from noise.
Non-synchronous peak
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.
Nyquist frequency
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.
Nyquist plot
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
Octave
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.
Oil whip
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.
Oil whirl
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.
Operating speed
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.
Order
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.
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.
Order tracking
See Order normalization.
Oscillation
To-and-fro, back-and-forth, or reciprocating motion. Vibration is
mechanical oscillation. “One oscillation” means one cycle of
reciprocating motion.
Out-of-phase signals
See Phase.
Overall level
See Root-mean-square.
Overall rms level
See Root-mean-square.
Over-damped system
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
situations.
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
Time
50% of
a data
blockP
Parallel misalignment
See Misalignment.
Parameters
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.
Peak amplitude
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.
Peak-to-peak amplitude
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.
Period
The time taken to complete one oscillation or one cycle. Period is
usually expressed in s (seconds) or ms (milliseconds). See also
Frequency.
Periodic
Having a pattern that is repeated over and over again, each cycle
taking a fixed amount of time. See also Period and Repeating force.
Periodic force
See Repeating force.
Periodic motion
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
Repeating force.Phase
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”.
Phase angle
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
180°.
Phase difference
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.
Phase shift
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.
Piezoelectric transducer
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.
Pink noise
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
measurement.
Point (w.r.t. the vb instrument)
A data group of the vb instrument data structure, for grouping
recordings taken of the same physical location on a particular machine.
See also Data structure.Potential energy
The energy associated with the state of an object e.g. a pendulum at its
highest point possesses gravitational potential energy (that will cause it
to continue swinging), and a compressed spring possesses strain
potential energy (that will cause it to return to its equilibrium state).
Preload
Static force applied to a bearing to ensure that the rolling elements roll
(and not slide) within the bearing and that the shaft makes proper
contact with the bearing. Too little or too much preload can cause
bearing damage.
Principal inertia axis (w.r.t. rotors)
The mass centerline of a rotor, constructed by joining the centers of
mass at every cross-section of the rotor. To avoid unbalance, the axis
of rotation must coincide with the principal inertia axis.
PROFLASH
A way by which the firmware in the vb instrument can be upgraded to
later versions without hardware changes.
Proportional
See Proportional, directly.
Proportional, directly
Increases or decreases along with another value, in a linear way e.g.
the acceleration of an object (with a constant mass) is directly
proportional to the force causing it to accelerate i.e. if the force
increases by 10%, then the acceleration will also increase by 10%.Proportional, inversely
Increases or decreases linearly in an opposite way in relation to
another value e.g. for a given applied force, the acceleration of an
object is inversely proportional to the mass of the object i.e. if the mass
increases by 10%, then the acceleration will decrease by 10%.
Proportional, linearly
See Proportional, directly.
Proximity probe
A transducer that measures displacement e.g. the displacement of a
shaft. Proximity probes are normally used to measure low frequency
signals only.Q
Quantization (w.r.t. signals)
The process of assigning values from a discrete and finite range to
represent the signal values of an analog signal. Quantization is
inherent in the sampling and digitization of analog signals using an A/D
converter. See also Digital.
Quasi-periodic waveform
A waveform with a period that varies over time but which has sufficient
periodicity to have a corresponding spectrum that shows clear peaks.
Spectral peaks corresponding to quasi-periodic motion occur at
frequencies that are not whole number multiples of the fundamental
frequency. Loose or worn rotating belts often cause quasi-periodic
vibration.R
Radial direction
A direction perpendicular to the centerline of a shaft or rotor.
Radial vibration
Vibration in a direction perpendicular to the centerline of a shaft or
rotor. Radial vibration is seen in unbalanced rotors. See also Axial
vibration.
Radian
A measurement unit for angle. 2π radians (2π being the
circumference-to-radius ratio of a circle) is equivalent to a full circle of
rotation, or 360°. Thus one radian is roughly equal to 57°.
Mathematical calculations are often more conveniently done in radians
than in degrees. See also Angular frequency.
Random
Non-deterministic or not having a specific pattern. Random signals can
only be described in terms of statistical quantities. Vibration caused by
turbulent fluid flow is usually random in nature. The spectrum of
random vibration shows no clear peaks but shows energy spread over
a range of frequencies.
Recording (w.r.t. the vb instrument)
The data collected for a particular location during a single recording
session. See also Data structure.Rectangular window
A mathematical function with a constant value of one throughout. All
values of a data block multiplied by a rectangular window, are
multiplied by one i.e. the values are preserved. This is equivalent to
not using a window. See also Signal leakage and Windowing.
Reference spectrum
A spectrum that is the basis for an alarm envelope. A reference
spectrum should be “ideal” or “normal” for the measurement point and
axis for which it is used as a reference. See also Alarm envelope.
Repeating force
A periodic force i.e. a force with a pattern repeated over and over
again, each cycle taking a fixed amount of time. Machine vibration is
most often due to repeating forces originating from the rotation of
unbalanced or misaligned parts. A repeating force may or may not be
harmonic, and can be mathematically described by the arithmetic sum
of a series of sinusoids. See also Excitation force.
Resolution (w.r.t. waveforms and spectra)
The finest frequency or time “step” possible on the horizontal axis of a
discrete spectrum or waveform. The resolution of a spectrum improves
with the number of spectral lines used i.e. the more spectral lines used,
the better the spectrum represents the true spectrum. However, the
more spectral lines used, the more instrument memory is used up to
store the spectrum, and the longer the data collection time. Likewise,
for waveforms, the larger the number of samples used (for a given
measurement duration), the better the resolution of the waveform is,
but the more instrument memory space is used to store the waveform.
Resolution bias error
See Picket fence effect.Resonance
The situation where the vibration amplitude increases rapidly due to the
natural frequency of the system being excited by a periodic force that
has a frequency similar to the natural frequency. A machine should
never be operated continuously at its natural frequency. If it is
necessary for a machine to operate at a frequency higher than its first
natural frequency, the speed of the machine should be increased past
the natural frequency as quickly as possible.
Resonant frequency
The natural frequency of a system when there is no damping in the
system. An n degree-of-freedom system has n resonant frequencies.
See also Damped natural frequency.
Response spectrum
See Frequency response.
Rest position
See Equilibrium position.
Rigid
Infinitely stiff and does not deform. There are no truly “rigid” objects in
the real world. The concept of “rigid” objects is invented by engineers
for the purpose of simplifying mathematical modeling. In practice, a
rotor is considered “rigid” if it does not bend significantly at its rotating
speed.
Rigid body motion
Movement of a body as a unit with no relative movement or
deformation within the body.rms
See Root-mean-square.
Rolling element bearing
A bearing with rolling elements to enable smooth shaft rotation. The
shape of a rolling element is usually cylindrical, conical, or spherical.
See also Angular contact bearing and Thrust bearing.
Root-mean-square
An amplitude expression defined as the square root of the arithmetic
mean of a set of squared instantaneous signal values. The term “rootmean-square” is often abbreviated as “rms”. For a discrete waveform
with n instantaneous values, the overall rms amplitude is given by:
n
Overall rms amplitude = E xi² / n
i = 1
where xi = the ith instantaneous signal value in the set of n
instantaneous signal values.
For a discrete spectrum with n spectral lines, the overall rms amplitude
(with no windowing) is given by:
n
Overall rms amplitude = E xi²
i = 1
where xi = the amplitude of the ith spectral line in the set of n
spectral lines.
For true sinusoidal waves (only), the rms amplitude is times (i.e.
approximately 0.7 times) the peak amplitude.
Rotary motion
Motion around an axis i.e. circular motion.
√
1
√2
√Rotor
A machine part that rotates. See also Rigid.
Rotor bar pass frequency
The speed at which the rotor bars of an AC induction motor rotate past
a fixed reference point. This is equal to the operating speed of the
motor multiplied by the number of rotor bars. The vibration spectrum of
an induction motor usually shows a peak at the rotor bar pass
frequency.
Running speed
See Operating speed.
Runout
The error that is indicated by a displacement probe when it is used to
measure the position of the centerline of a shaft. Runout can be
caused by the axis of rotation not coinciding with the shaft centerline,
or a lack of roundness. Runout is sometimes called “TIR” or “total
indicator reading”. The larger the runout, the larger the excitation force
generated when the shaft is rotated.S
Sampling
The extracting of discrete, instantaneous data, usually at regular
intervals, from a continuous signal e.g. from the output signal of an
accelerometer. In a sampled time domain signal, data is not available
for all time values, but only for time values corresponding to when data
was sampled. See also Aliasing.
Sampling duration
The total time period data is sampled from a continuous signal.
Increasing the number of spectral lines or the number of averages for a
spectrum increases the sampling duration. On the contrary, increasing
the f max or the overlap percentage reduces the sampling duration.
Sampling frequency
See Sampling rate.
Sampling rate
The rate at which data is sampled from a continuous signal e.g. from
the output signal of an accelerometer. See also Aliasing.
Scalar
A quantity that denotes magnitude but not direction e.g. speed is a
scalar quantity: it is the magnitude of velocity. See also Vector.
Seismic
Caused by the movement of a mass. The output of a seismic
transducer are signals originating from the movement of a mass within
the transducer.Sensitivity (w.r.t. accelerometers)
The change in the magnitude of the output signal per unit change in the
acceleration sensed. The sensitivity of an accelerometer is usually
expressed in mV/g (where “mV” stands for “milliVolts”, and “g” is
“acceleration due to gravity”).
Settling time (w.r.t. the vb instrument)
The period of time that must be allowed for the electrical hardware in
the vb instrument and accelerometer to stabilize before accurate
measurements can be taken. The settling time required for the
accelerometer is a value specified by the manufacturer of the
accelerometer and typically ranges from 1 to 3 seconds. The settling
time required for the vb instrument is dependent on the frequency
range (f max) or duration of the measurement, and ranges from 4 to 13
seconds. The lower the f max or the longer the duration of the
measurement, the longer the settling time required for the vb
instrument. The total settling time i.e. the sum of the settling time
required for the accelerometer and that for the vb instrument is
automatically calculated by the instrument.
SHM
See Harmonic motion.
Shock
A suddenly applied force that results in the transient response of a
system. The force experienced by a system struck with a hammer is
an example of shock. The severity of the shock can be measured in
terms of the maximum value of the response of the system.
S.I.
Abbreviation of “Systeme Internationale”, the international system of
measurement units. The primary S.I. units, from which all other units
can be derived, are “meter”, “kilogram”, “second”, “Kelvin”, “Ampere”,
“mol”, and “candela”. S.I. units are widely used throughout the world
except in North America. See also Imperial units and Metric units.
Sidebands
Minor peaks, caused by amplitude or frequency modulation, located
symmetrically on either side of spectral peaks. The distance between
adjacent sidebands is equal to the frequency of the modulating signal.
Sidebands are often seen in the spectra of faulty gearboxes and
electrical motors with faulty rotor bars.
Signal
An electrical voltage or current that is proportional to the magnitude of
a physical quantity. The output signal of an accelerometer is a
continuous voltage that is proportional the acceleration of the point
being measured. A signal may be analog or digital, and continuous or
discrete.
Signal conditioning
The modification of a signal by devices such as attenuators, filters, and
amplifiers, before the signal is processed or displayed. The main
purposes of signal conditioning are to alter signal amplitude to a
suitable level for sampling, and to remove noise and other errors from
the signal.
Signal leakage
A spectral distortion where the amplitude of a spectral line affects or
“leaks” to adjacent spectral lines. If FFT calculations are performed on
a data block not consisting of an integral number of waves, signal
leakage will be evident in the resulting spectrum. Signal leakage can
be minimized by multiplying data blocks with a suitable “window” prior
to performing FFT calculations on the data blocks. See also
Windowing.
Signature
The vibration spectrum of a system, from which much can be inferred
regarding the vibration behavior of the system.Simple harmonic motion
See Harmonic motion.
Sine
The ratio of the length of the side opposite an angle, to the length of
the longest side (hypotenuse) in a right-angled triangle i.e. the sine of
the angle θ shown below is equal to b/h. The symbol for “sine” is “sin”.
See also Cosine wave.
sin θ = b/h
cos θ = a/h
Sine function
See Sine.
Sine wave
The signal or graph generated by plotting the sine of angles. A sine
wave oscillates between maximum and minimum values of 1 and -1.
A sine wave may be considered to represent the vertical projection of
the position of a point on a shaft rotating at a constant speed, as shown
above. On an unbalanced rotor, the vertical projection of the rotational
motion of the heavy spot is a sine wave. This causes an excitation
force with a sine wave pattern that in turn causes a vibration response
that resembles a sine wave. See also Cosine wave.
Sin θ
θ
1
-1
θ1 0
θ2
θ1 θ2
θ
b h
aSine waveform
A time domain signal described by the function:
f(t) = sin (ωt – ∅)
where f(t) = the instantaneous value at time t;
ω = angular frequency;
t = time; and
∅ = phase angle.
See also Sine.
Sinusoid
A mathematical function of the form:
x(t) = A sin (ωt – ∅)
where x(t) = the instantaneous value of x at time t;
A = maximum x value (zero-to-peak amplitude of x);
ω = angular frequency;
t = time; and
∅ = phase angle.
See also Sine.
Sinusoidal
That can be described by a sinusoid. The free vibration of an
undamped single degree-of-freedom system is sinusoidal e.g. the
undamped free vibration of a mass suspended on a spring is
sinusoidal. In practice, true sinusoidal behavior is not observed – the
amplitude will decay exponentially due to damping present in the
system.Ski slope
An amplitude distortion that resembles the shape of a “ski slope” at the
low frequency end of a spectrum. The distortion is due to the
integration of a signal containing low frequency noise. Because
integrating sinusoids (of which periodic signals comprise) causes their
amplitudes to be multiplied by the inverse of their frequencies, low
frequency noise is accentuated. Hence the increased amplitude values
at the low frequency end of the spectrum. The distortion will become
worse if the settling time allowed for the accelerometer is not long
enough.
Slip
The difference between the rotation speed of an induction motor and
the synchronous speed e.g. if the rotation speed is 2900 rpm and the
synchronous speed is 3000 rpm, then the slip is 100 rpm and the slip
percentage is 3.3% (100 rpm / 3000 rpm). The greater the load on the
motor, the higher the slip will be.
Slow roll speed
Low operating speed that makes excitation forces negligible. The
amplitude of excitation forces associated with unbalance is proportional
to the square of the operating speed. At low operating speeds, the
amplitude of the excitation force becomes very small.
Soft foot
A condition where the feet of a machine do not lie on a level plane, and
structural distortion occurs when the hold-down bolts are tightened.
Soft foot can also be caused by some bolts being fastened more tightly
or more loosely than other bolts. The resulting structural distortion
causes misalignment in machine parts, thereby causing vibration.
Spectra
Plural of Spectrum.Spectral lines
Vertical lines that make up a discrete spectrum. The height of a
spectral line represents the amplitude of vibration at the frequency
indicated by the spectral line. The more spectral lines used for a
spectrum, the better the resolution of the spectrum (but the more
instrument memory used and the longer the sampling duration
required). See also Resolution and Spectrum.
Spectral map
See Waterfall chart.
Spectral peak
See Peak (w.r.t. spectrum).
Spectrum
An amplitude (e.g. of velocity) versus frequency graph e.g. of
measured vibration. A discrete vibration spectrum consists of a series
of “spectral lines”, the height of each spectral line representing the
amplitude at the frequency indicated by the spectral line. See also
Waveform.
Spectrum analyzer
An instrument capable of calculating a spectrum from a waveform. See
also Fast Fourier transform.
Spring constant
The ratio of applied force to the amount of distortion e.g. a spring that
is compressed by 0.2 inch by a 2 lb force has a spring constant of 10
lbf/in. “k” is the symbol for spring constant. See also Stiffness.Standard deviation
A statistical value that indicates the variation in signal level in a given time period. For a discrete waveform,
the standard deviation over a given time period is defined as follows:
n
Standard deviation = E (xi – x)² / n
i = 1
where xi = the ith instantaneous signal value during the time period;
x = the average signal value during the time period; and
n = total number of instantaneous signal values for the time
period.
Because the average vibration signal value is zero or close to zero, the
standard deviation may be written as:
n
Standard deviation = E xi² / n
i = 1
Thus the standard deviation is simply equal to the rms amplitude. The
larger the standard deviation, the larger the vibration amplitude.
Static unbalance
An unbalance condition where the mass centerline of a rotating part is
parallel to the axis of rotation but offset from it. This causes “in-phase”
repeating forces to act on the support bearings i.e. the force acting on
one bearing is always pointing in the same direction as that acting on
the other bearing. As a result, all points on the rotating part vibrate in a
synchronized manner. Static unbalance can be corrected by adding
one correction weight to the appropriate location on the rotating part.
See also Couple unbalance and Dynamic unbalance.
Steady-state response
See Steady-state vibration.
√ √Steady-state vibration
The vibration behavior of a system after it has stabilized. Most kinds of
machine vibration settle into a steady state. See also Transient
response.
Stiffness
Resistance against deformation. The stiffness of a spring is quantified
by the spring constant, k. The stiffness of a component is dependent
on the material it is made of and its physical dimensions.
Strain
The ratio of elongation to original length e.g. a shaft, of length L, that is
being elongated lengthwise by an amount x, is said to experience an
axial strain of x/L.
Strain gage
A transducer that measures strain. A strain gage is usually glued on
the surface being measured and outputs a voltage proportional to the
strain.
Stress
The force experienced per unit area e.g. a shaft, of cross-sectional
area A, that is being stretched lengthwise by a force, F, is said to
experience an axial stress of F/A.
Subharmonic
A spectral peak that occurs at a frequency that is a whole number
fraction of the fundamental frequency e.g. at 1/2, 1/3, 1/4, 1/5, or 1/6
times the fundamental frequency. The spectrum of shaft rubbing the
surface of a journal bearing exhibits a subharmonic at 1/2 the
fundamental frequency.Subsynchronous peak
A spectral peak that occurs at any frequency below the fundamental
frequency. A subsynchronous peak may or may not be a subharmonic.
The spectrum of a journal bearing subjected to an oil whirl condition
usually has a subsynchronous peak at roughly 0.45 times the
fundamental frequency.
Synchronous averaging
See Time-synchronous averaging.
Synchronous peak
A spectral peak at a frequency that is an integer multiple of the
fundamental frequency. The gear mesh frequency, blade pass
frequency, vane pass frequency, rotor bar pass frequency, and their
multiples, are synchronous with the fundamental frequency and have
synchronous peaks corresponding to them in the spectrum. In
contrast, spectral peaks corresponding to ball pass and ball spin
frequencies are not synchronous peaks. See also Harmonic (n.).
Synchronous speed
The speed at which the magnetic field in the stator of an AC motor is
rotated. The synchronous speed is usually the same as the AC line
frequency i.e. if the line frequency is 50 Hz, then the synchronous
speed is 50 cycles per second or 3000 rpm.
System (w.r.t. vibration)
A mechanism or machine which has a means of storing potential and
kinetic energy, and a means by which energy is dissipated. In most
vibratory systems, potential energy is stored in elastic members, kinetic
energy is stored in moving masses and energy is dissipated through
friction or other damping devices.T
Tagging (w.r.t. the vb instrument)
The identifying of data to be collected or transferred to a computer.
Tagging is a means of creating a “plan” for data collection, and a
means of mass-transferring data automatically to a computer.
Tangential direction
A direction perpendicular to the axial and radial directions. The
tangential direction of a shaft is a direction perpendicular to the
centerline of the shaft and at a tangent to the surface of the shaft.
Thrust
See Axial force.
Thrust bearing
A bearing that supports loads that act in the axial direction of the shaft.
Thrust bearings usually have rolling elements, and are used to support
vertical rotors. See also Angular contact bearing.
Time averaging
See Time-synchronous averaging.
Time domain
That which has a time axis as its x-axis, or a set of time values to which
are mapped a set of other values e.g. amplitude. A waveform is a time
domain graph i.e. a waveform has a time axis as its x-axis (and an
amplitude axis as its y-axis).Time-synchronous averaging
The averaging of waveforms to produce a relatively noise-free average
waveform. To obtain an accurate average spectrum, the phases of the
waveforms used in the averaging process must be the same. This is
achieved by taking the waveforms by means of a common reference
trigger e.g. by means of a tachometer sensing the key way on a shaft.
Since noise values are equally likely to be positive or negative, they
cancel one another when they are averaged. The average spectrum is
thus relatively free of noise. The higher the number of waveforms used
in the averaging process, the more accurately the average waveform
represents true vibration behavior.
TIR
See Runout.
Tolerance
The maximum allowable variation from a specified quantity e.g. if a
dimension is specified as “20.0 ± 0.2 inches”, then the tolerance for the
dimension is “± 0.2 inch”, and the maximum and minimum allowable
dimensions are 20.2 inches and 19.8 inches.
Tone
A sharp distinct peak at a specific frequency. Bearing tones are
spectral peaks that correspond to the motion of moving elements in the
bearing.
Torque
The rotational force that causes rotational acceleration or stress. The
higher the torque applied to an object, the higher the rotational
acceleration of the object, or the higher the stress in the object.
Torsion
Twisting of a body about an axis. The quantity of torsion is measured
by the angle of twist.Torsional vibration
Oscillation of a body about an axis. The displacement of the body is
measured by an angular coordinate. An example of torsional vibration
is the oscillation of a heavy rotor about its axis when the rotor is
suddenly stopped.
Total indicator reading
See Runout.
Transducer
A device that translates the magnitude of one quantity into another
quantity e.g. an accelerometer is a transducer that translates
acceleration into voltage.
Transient
See Transient response.
Transient response
The temporary behavior of a system immediately after a change in the
excitation to the system e.g. the transient response of a machine can
be observed while it is being powered up, or just after it has been
struck by a hammer. When analyzing a transient response, windowing
and averaging are not normally used. See also Steady-state
vibration.
Trending
The analyzing, usually by way of waterfall and trend charts, of vibration
data taken of a particular physical point and collected regularly over a
period of time so that changes in spectrum or time-synchronized
waveform characteristics can be detected, physical explanations
assigned, and corrective actions taken accordingly. See also Trend
chart and Waterfall chart.Trend chart
A cross-sectional view of a waterfall chart at a particular frequency or
time value. If the recordings plotted in the waterfall chart are arranged
chronologically and pertain to the same physical point, the crosssectional view depicts the “trend” of vibration pattern at that point for
the particular frequency or time value. See also Trending and
Waterfall chart.
Trial weight
A weight that is used during the process of balancing a rotor. By noting
the change in vibration amplitude and phase after a trial weight (of
known mass) is attached to the rotor, the size and location of the
correction weight required to balance the rotor can be determined.
Triaxial accelerometer
An accelerometer that is capable of measuring vibration in three
orthogonal directions simultaneously at a particular point.
Trigger
A signal that is used as a timing reference or to initiate a process e.g. a
tachometer signal can be used to derive phase angles and/or to start a
measurement.
Triggering Mode
The method by which measurements or recordings are started on the
vb instrument. Measurements can be triggered “manually” one-byone, or using the “free run” mode whereby measurements are
continuously taken and displayed (until manually stopped).
Trough (w.r.t. a wave)
The lowest point in a wave. See also Peak.U
Unbalance
The condition where the axis of rotation and mass centerline of a
rotating part do not coincide. This condition causes a centripetal force
to act on the bearings on every cycle of rotation. With the presence of
such a “repeating force”, vibration occurs. Unbalance is one of the
most common causes of vibration in machines. See also Couple
unbalance, Dynamic unbalance, and Static unbalance.
Undamped
Not having any means of dissipating energy. In practice, no vibrating
system is truly undamped. See also Damping.
Under-damped system
A system with a quantity of damping that is insufficient to prevent the
system from vibrating. A machine that vibrates is an under-damped
system. See also Critical damping and Over-damped system.
Uniform window
See Rectangular window.
Unit
A standard quantity used as a measure e.g. “inch” is a unit for
quantifying length. In the engineering field, there are two generally
accepted systems of units: S.I. units and imperial units. See also
Metric units.V
Vane pass frequency
The speed at which pump vanes rotate past a fixed reference point.
This is equal to the operating speed of the pump multiplied by the
number of pump vanes. The vibration spectrum of a pump usually
shows a peak at the vane pass frequency.
Vector
A quantity that denotes magnitude as well as direction e.g. velocity is a
vector quantity. Although two objects may be moving at the same
speed, their velocities, depending on the direction of movement of the
objects, may not be the same. See also Scalar.
vdB
A dimensionless logarithmic unit for velocity amplitude, defined as 20
times the logarithm (base-10) of the ratio of velocity amplitude to a
reference amplitude of 10-6 mm/s rms (or 10-5 mm/s rms as used by
some US government departments) i.e.
Amplitude vdB = 20 log10 (Amplitude / 10-6 mm/s rms)
or for some US government departments,
Amplitude vdB = 20 log10 (Amplitude / 10-5 mm/s rms)
Due to the use of the logarithmic function, the vdB unit is useful for
displaying signals with both very large and very small amplitudes. See
also decibel and Logarithm function, base-10.Velocity
The rate of change of displacement, or the speed of an object in a
particular direction e.g. if an object is moving Northward, the velocity of
the object in the North direction is its speed, but its velocity in the East
or West direction is zero, and its velocity in the South direction is the
negative of its speed. Velocity units commonly used in the field of
vibration analysis are mm/s (metric), in/s (imperial), and vdB
(logarithmic).
Velocity transducer
A transducer that measures velocity. Compared to accelerometers,
velocity transducers have many drawbacks e.g. they are subject to
wear and require frequent calibration.
Vibration
A reciprocating or back-and-forth movement involving a continual
interchange of kinetic energy and potential energy. The vibration of a
mass supported by a spring is an up-and-down motion that involves
continual interchange of kinetic energy associated with motion of the
mass and potential energy associated with distortion of the spring.
Vibration signature
See Signature.
Vibratory system
See System.
Viscous damping
The dissipation of vibration energy due to viscous fluid flowing through
constricted gaps e.g. oil flowing around a piston in a cylinder (as in car
shock absorbers) and lubricant circulating in a journal bearing. The
quantity of energy dissipated is dependent on the viscosity of the fluid
and the velocity of vibration. See also Coulomb damping and
Hysteretic damping.W
Waterfall chart
A three-dimensional graphical view of recordings laid out in succession
on the third axis. Waterfall charts are useful for “trending” vibration
patterns i.e. recordings taken of the same physical point and collected
over a period of time can all be displayed chronologically on a waterfall
chart so that changes in spectrum or waveform characteristics can be
detected. See also Trending and Trend chart.
Waterfall plot
See Waterfall chart.
Wave
A disturbance traveling through a medium. Throwing a stone into
water causes ripples or waves to travel through the water. Vibrating a
metal sheet causes waves to travel through it. As a result, each point
of the metal sheet oscillates. See also Peak, Trough, and
Wavelength.
Waveform
A signal level (e.g. of velocity) versus time graph e.g. of measured
vibration.
Wavelength
The distance between two adjacent peaks or troughs in a wave. The
wavelength is equal to the speed of the wave divided by its frequency.
The stiffer the material, the faster waves travel through it, and the
longer the wavelength (for a given vibration frequency).
Weighting
See Windowing.White noise
Noise that has the same magnitude for all frequency values.
Window
See Windowing.
Windowing
The multiplying of time domain data block values by a mathematical
function (the window) before FFT calculations are performed on the
data block. The purpose of windowing is to compensate for certain
FFT algorithm limitations that cause signal leakage. “Windowing” or
multiplying data block values by a suitable mathematical function to
ensure that the data block begins and ends with zero amplitude,
thereby making the data block appear like a complete wave, is a way of
reducing signal leakage. The Hanning window is commonly used. See
also Flat top window, Hamming window, and Rectangular window.X
X
Operating speed. 1X, or one time the operating speed, is the
Fundamental frequency. 2X is twice the fundamental frequency, 3X is
three times the fundamental frequency, etc.
x-axis (w.r.t. graphs)
The horizontal line on which the horizontal scale of a graph is marked.
The x-axis of a vibration waveform represents the time elapsed since
the beginning of the measurement, and that of a vibration spectrum
represents the frequency of vibration.Y
y-axis (w.r.t. graphs)
The vertical line on which the vertical scale of a graph is marked. The
y-axis of a vibration waveform represents the instantaneous vibration
level, and that of a vibration spectrum represents the amplitude of
vibration.Z
Zero-to-peak amplitude
See Peak amplitude
Zooming
Image enlargement, or scale enlargement. Zooming into a particular
part of a spectrum enlarges the view of that part of the spectrum.
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