Beginners guide vibration

Beginner's Guide to
Machine Vibration
Revision 28/06/06

ii
COPYRIGHT © 1999, 2006 Commtest Instruments Ltd.
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without the prior written permission of Commtest Instruments Ltd.
For information, contact:
Commtest Instruments Ltd
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New Zealand
E-mail help@commtest.com
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Information in this document is subject to change without notice.
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vbSeries® and Ascent® are registered trademarks of Commtest
Instruments Ltd. Other trademarks and registered trademarks belong
to their respective owners.

iii
Contents
Foreword....................................................................... 1
Section 1: Why is Monitoring Vibration Important?.. 2
What is Machine Vibration? ..................................................... 3
What Causes Machine Vibration?............................................ 5
(a) Repeating Forces ...................................................................5
(b) Looseness ..............................................................................7
(c) Resonance..............................................................................8
Why Monitor Machine Vibration?........................................... 10
(a) Severe Machine Damage.....................................................11
(b) High Power Consumption.....................................................12
(c) Machine Unavailability..........................................................12
(d) Delayed Shipments ..............................................................13
(e) Accumulation of Unfinished Goods ......................................13
(f) Unnecessary Maintenance....................................................14
(g) Quality Problems ..................................................................14
(h) Bad Company Image............................................................15
(i) Occupational Hazards ...........................................................15
Summary ................................................................................ 16
Section 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

iv
Section 3: How is Machine Vibration Measured?.... 27
Which Machines Need Monitoring? ....................................... 28
How Does the Instrument Work?........................................... 29
How is the Accelerometer Mounted?..................................... 30
(a) Mount as Close as Possible to the Bearing .........................31
(b) Make Sure the Accelerometer is Firmly Attached ................32
(c) Make Sure the Accelerometer is Oriented Correctly............34
(d) Mount the Same Accelerometer in the Same Location........35
(e) Mount the Accelerometer on Something Substantial...........35
(f) Take Care of the Accelerometer ...........................................36
(g) Take Care of Personal Safety ..............................................37
How are Parameters Set?...................................................... 38
(a) How Data is Collected ..........................................................39
(b) How Much or How Fast Data is Collected............................40
What Fmax Value Should be Used? ...................................41
How Many Spectral Lines Should be Used? .......................42
How Much Overlap Should I use? .......................................42
(c) How Data is Processed ........................................................43
(d) How Data is Displayed .........................................................45
How is Data Collected?.......................................................... 48
Summary ................................................................................ 54
Appendix: List of Symbols........................................ 55
Glossary Abbreviations Guide.................................. 57
Glossary of Terms...................................................... 58

Foreword 1
Foreword
At Commtest we know that vibration monitoring can be an easy and
painless task – not a mysterious art. We have written Beginner’s
Guide to Machine Vibration to give you the key information you need
to increase your profits using a vb vibration monitoring instrument.
Engineers, technicians, machine operators, and accountants will be
able to quickly grasp the concepts presented in this book. We have
avoided complicated mathematics and physics formulae, focussing
on just the principle concepts necessary for performing basic
vibration monitoring. The text is interspersed with simple diagrams,
and care has been taken to use everyday language wherever
possible.
We are confident that once you are armed with a vb vibration
monitoring instrument and after a few readings of Beginner’s Guide
to Machine Vibration, you will be able to perform basic vibration
monitoring. We welcome any comments you may have.
The symbols, units, and abbreviations used in this book are
explained in the Appendix (page 55).

Section 1: Why is Monitoring Vibration Important?2
Section 1: Why is Monitoring
Vibration Important?
Monitoring machine vibration and using the information you obtain
saves money!
How is this possible?
We will answer this question in the following pages.
After reading this section you will:
• Understand the term 'machine vibration'
• Cite some common causes of machine vibration
• Explain the reasons for monitoring machine vibration
• Understand how monitoring machine vibration saves money

Section 1: Why is Monitoring Vibration Important? 3
What is Machine Vibration?
Most of us are familiar with vibration; a vibrating object moves to and
fro, back and forth. A vibrating object oscillates.
We experience many examples of vibration in our daily lives. A
pendulum set in motion vibrates. A plucked guitar string vibrates.
Vehicles driven on rough terrain vibrate, and geological activity can
cause massive vibrations in the form of earthquakes.
There are various ways we can tell that something is vibrating. We
can touch a vibrating object and feel the vibration. We may also see
the back-and-forth movement of a vibrating object. Sometimes
vibration creates sounds that we can hear or heat that we can
sense
1
.
In industrial plants there is the kind of vibration we are concerned
about: machine vibration.
1
To observe how vibration can create sound and heat, rub your feet
back and forth on a carpet.

What is machine vibration? Machine vibration is simply the back-
and-forth movement of machines or machine components. Any
component that moves back and forth or oscillates is vibrating.
Machine vibration can take various forms. A machine component
may vibrate over large or small distances, quickly or slowly, and with
or without perceptible sound or heat. Machine vibration can often be
intentionally designed and so have a functional purpose
2
. At other
times machine vibration can be unintended and lead to machine
damage.
Most times machine vibration is unintended and undesirable. This
book is about the monitoring of undesirable machine vibration.
Shown below are some examples of undesirable machine vibration.
2
Not all kinds of machine vibration are undesirable. For example,
vibratory feeders, conveyors, hoppers, sieves, surface finishers and
compactors are often used in industry.

What Causes Machine Vibration?
Almost all machine vibration is due to one or more of these causes:
(a) Repeating forces
(b) Looseness
(c) Resonance
(a) Repeating Forces
Imagine a boat anchored in a bay. Waves are slapping the sides of
the boat, and as long as the waves continue to act on the boat we
would expect the boat to rock.
The boat would be rocking because the waves would be exerting a
repeating force on the boat - a force of a pattern repeated over
and over again.
Most machine vibration is due to repeating forces similar to those
causing the boat to rock. Repeating forces such as these act on
machine components and cause the machine to vibrate.
Where do the repeating forces that cause machine vibration come
from?

Repeating forces in machines are mostly due to the rotation of
imbalanced, misaligned, worn, or improperly driven machine
components. Examples of these four types of repeating forces are
shown below.

(b) Looseness
Looseness of machine parts causes a machine to vibrate. If parts
become loose, vibration that is normally of tolerable levels may
become unrestrained and excessive.

(c) Resonance
Imagine a child swinging freely on a swing, that is, without the child
propelling himself or anyone pushing him. If we observe the motion
closely we will see the child swinging at a particular rate. For
example, we may see that it consistently takes him three seconds to
complete one cycle of swinging.
The rate of the child’s free-swinging is in fact a physical property of
the child-swing system - much as the weight of the child is a physical
property of the child. It is the rate at which the child will tend to swing
while seated on that particular swing. It is the child’s most natural
swinging rate on the swing, and the only way he can change it is to
interfere with the natural swinging by propelling himself with his feet,
changing his posture, rubbing his feet on the ground and so on.
Machines also tend to vibrate at certain oscillation rates. The
oscillation rate at which a machine tends to vibrate is called its
natural oscillation rate. The natural oscillation rate of a machine is
the vibration rate most natural to the machine, that is, the rate at
which the machine 'prefers' to vibrate. A machine left to vibrate freely
will tend to vibrate at its natural oscillation rate.
Most machines have more than one natural oscillation rate. For
example, a machine comprising two substructures of different natural
oscillation rates will exhibit at least two natural oscillation rates. In
general, the more complex the machine, the more natural oscillation
rates it has.

Now consider again the child on the swing. If we aided the swinging
motion by repeatedly pushing the child, we would expect the child to
swing higher and higher over time.
We would however only cause the child to swing higher and higher if
we pushed with the right rhythm. If our pushing rhythm is such that
he is sometimes pushed down while he is ascending, we would not
expect him to swing properly. To make him swing higher and higher,
our pushing rhythm would in fact need to be in harmony with his
natural oscillation rate. For example, we could push him every time
- or every alternate time - he reaches his highest point. Only by
pushing the child at a rate which is in harmony with his natural or
preferred oscillation rate can we cause him to quickly swing higher
and higher.
What happens if a machine is 'pushed' by a repeating force with a
rhythm matching the natural oscillation rate of the machine?
A similar situation will arise – the machine will vibrate more and more
strongly due to the repeating force encouraging the machine to
vibrate at a rate it is most natural with. The machine will vibrate
vigorously and excessively, not only because it is doing so at a rate it
'prefers' but also because it is receiving external aid to do so. A
machine vibrating in such a manner is said to be experiencing
resonance.
A repeating force causing resonance may be small and may
originate from the motion of a good machine component. Such a mild
repeating force would not be a problem until it begins to cause
resonance. Resonance, however, should always be avoided as it
causes rapid and severe damage. For example, whole bridges
have collapsed due to their natural oscillation rates being excited by
the mere rhythm of soldiers marching in unison across the bridges.

Why Monitor Machine Vibration?
To do a good job of monitoring machine vibration and to fully reap
the benefits, we must understand the answers to the above question.
Monitoring the vibration characteristics of a machine gives us an
understanding of the 'health' condition of the machine. We can use
this information to detect problems that might be developing.
Why be concerned about the condition of a machine? Why not just
continue to run the machine until it breaks down and then repair it?
Operating a machine until it breaks down might be acceptable if the
machine were a 'disposable' one. Most machines, however, are not
'disposable' due to their cost.
If we regularly monitor the conditions of machines we will find any
problems that might be developing, therefore we can correct the
problems even as they arise.
In contrast, if we do not monitor machines to detect unwanted
vibration the machines are more likely to be operated until they break
down.
Because machine vibration monitoring finds potentially damaging
vibration, we can prevent problems arising and this saves a lot of
time, money, and frustration. How?
Below we discuss some common problems that can be avoided by
monitoring machine vibration. These problems are worth avoiding as
the costs of dealing with them are large and far exceed the cost of
reasonably priced machine vibration monitoring programs.

(a) Severe Machine Damage
Machine vibration that is not detected early enough will often lead to
severe machine damage requiring costly repairs or even total
machine replacement. However, if the condition of a machine is
monitored regularly, potential problems can be detected - and
corrected - at an early stage when the repair required is simpler,
faster, and cheaper. This is similar to our own health. Regular visits
to a doctor help us to detect problems early and so avoid the large
costs of remedying severe health damage.

(b) High Power Consumption
A machine that is vibrating consumes more power. As well as the
power required for the machine to perform its intended function,
additional power is also required to sustain the vibration. We can
minimize this problem by regularly monitoring and maintaining the
machine.
(c) Machine Unavailability
Because an unmonitored machine is more likely to break down, it is
more often out of action. However, the cost of procuring and
operating a machine is normally justified by its availability to process
goods efficiently, or by its availability to convert raw material into
cash. A machine should be consistently available to generate the
money to justify its investment. Regular monitoring helps ensure that
a machine is always available to generate money.

(d) Delayed Shipments
Because an unmonitored machine is more likely to break down, it is
also more likely to cause delays in the shipping of goods. Customers
have to wait and their payment is delayed. Customers could also
cancel their order and stop doing business with us.
(e) Accumulation of Unfinished Goods
Because an unmonitored machine is prone to breaking down it is
often unavailable. Goods still in the making tend to get stuck at the
input point of the machine. This leads to unnecessary wastage – the
waiting goods run the risk of spoiling, occupy floor space, and tie
up money.

(f) Unnecessary Maintenance
To constantly ensure proper machine condition, some companies
stop running machines according to predetermined schedules to
adjust and replace parts regardless of whether or not the machines
are malfunctioning. As a result, machines are often stopped
unnecessarily to replace parts that are still good and to correct
problems that do not exist. We can avoid such waste if the
machines are regularly monitored and repaired only when
necessary.
(g) Quality Problems
Sometimes a machine can be running into trouble even though it
appears to be functioning normally. This is a dangerous situation. If
not caught early, the problem could lead to poor quality products
being made, large yield losses, rework costs, or worse still,
warranty returns by irate customers. A machine that is regularly
monitored is less likely to lead to such problems.

(h) Bad Company Image
We noted above that machines that are not regularly monitored can
lead to shipment delays and produce goods of poor quality. Just one
incident of shipment delinquency or product defect is often enough to
seriously strain or even end relationships with customers. A bad
company image associated with shipment delays and poor quality is
something to be avoided. For a relatively small cost, machine
vibration monitoring can protect customer relations and thus
profitability.
(i) Occupational Hazards
Due to the noise and shaking they create, vibrating machines can
cause occupational hazards and human discomfort. Human
discomfort results in a loss to the company as workers who feel
unwell will not be fully productive. Also, unexpected machine
breakdowns leave workers with no work, and production planners
with frustration.

Summary
In this section we described machine vibration and discussed the
benefits of monitoring machines on a regular basis.
Machine vibration is simply the back-and-forth movement of any
machine or machine component, and is generally caused by
repeating forces acting on the machine, loose machine parts, or
resonance (a repeating force with a rhythm matching the natural
oscillation rate of the machine).
We identified the reasons for monitoring machine vibration regularly,
as well as the consequences of not doing so. By regularly monitoring
the vibration characteristics of a machine we can detect and correct
machine problems as they arise. By correcting machine problems
early we avoid many unpleasant and costly problems, some of which
involve customers. The cost of failing to monitor machine vibration
far exceeds the cost of implementing a vibration monitoring program.
To find out how to set up your own machine vibration monitoring
program, contact Commtest Instruments Ltd or one of our resellers
for a demonstration of a vbSeries vibration monitoring system. For
the address of your nearest reseller please visit our website at
www.commtest.com.

Section 2: How is Machine Vibration Described? 17
Section 2: How is Machine
Vibration Described?
To analyze the condition of a machine you first need to accurately
describe the behavior or symptoms of the machine.
How can vibration symptoms be described accurately?
How do vibration analysts describe the condition of a machine?
In this section we present the basic methods of describing machine
vibration.
After reading this section you will:
• Know the two most important methods of describing machine
vibration
• Understand the term 'amplitude'
• Understand the term 'frequency'
• Understand what a spectrum or waveform is

Section 2: How is Machine Vibration Described?18
How is Vibration Described?
By watching, feeling, and listening to machine vibration, we can
sometimes roughly determine the severity of the vibration. We may
observe that certain kinds of machine vibration appear 'rough', others
'noticeable', and yet others 'negligible'. We can also touch a vibrating
bearing and feel that it is 'hot', or hear that it is 'noisy', and so
conclude that something is wrong.
Describing machine vibration with these general terms is, however,
imprecise and depends on the person making the assessment. What
appears 'rough' to one person may appear acceptable to another.
Verbal description is usually unreliable.
To accurately analyze a vibration problem it is necessary to describe
the vibration in a consistent and reliable manner. Vibration analysts
rely primarily on numerical descriptions, rather than on verbal
descriptions, to analyze vibration accurately, and to communicate
effectively.
The two most important numerical descriptors of machine vibration
are amplitude and frequency.
Amplitude describes the severity of vibration, and frequency
describes the oscillation rate of vibration (how frequently an object
vibrates). Together, amplitude and frequency of vibration provide a
basis for identifying the root cause of vibration.

What is Amplitude?
The amplitude of vibration is the magnitude of vibration.
A machine with large vibration amplitude is one that experiences
large, fast, or forceful vibratory movements. The larger the
amplitude, the more movement or stress is experienced by the
machine, and the more prone the machine is to damage.
Vibration amplitude is thus an indication of the severity of vibration.
In general, the severity or amplitude of vibration relates to:
(a) the size of the vibratory movement
(b) the speed of the movement
(c) the force associated with the movement
In most situations it is the speed or velocity amplitude of a machine
that gives the most useful information about the condition of the
machine.
What is velocity? Velocity is simply speed measured in a particular
direction, as shown over the page.

Velocity amplitude can be expressed in terms of its peak value, or
what is known as its root-mean-square value.
The peak velocity amplitude of a vibrating machine is simply the
maximum (peak) vibration speed attained by the machine in a
given time period, as shown below.

In contrast to the peak velocity amplitude, the root-mean-square
velocity amplitude of a vibrating machine tells us the vibration
energy in the machine. The higher the vibration energy, the higher
the root-mean-square velocity amplitude.
The term 'root-mean-square' is often shortened to 'rms'. It is useful to
remember that the rms amplitude is always lower than the peak
amplitude.
How do we decide whether the peak amplitude or the rms amplitude
is to be used? It is really a matter of personal choice. However, it is
essential to always use the same amplitude type when making
comparisons.
Velocity amplitude, whether peak or rms, is always expressed with a
unit. Listed below are two commonly used velocity amplitude units
3
.
3
Some vibration analysts prefer the logarithmic amplitude unit adB.
However, discussion on logarithmic scales and units is beyond the
scope of this book.

What is Frequency?
A vibrating machine component oscillates, that is, it goes through
repeated cycles of movement. Depending on the force causing the
vibration, a machine component may oscillate rapidly or slowly.
The rate at which a machine component oscillates is called its
oscillation or vibration frequency. The higher the vibration
frequency, the faster the oscillation.
You can determine the frequency of a vibrating component by
counting the number of oscillation cycles that are completed every
second. For example, a component going through 5 vibration cycles
every second is said to be vibrating at a frequency of 5 cycles per
second. As shown below, one cycle of a signal is simply one
complete sequence of the shortest pattern that characterizes the
signal.
Just as a person’s pulse rate or frequency indicates the person’s
state of excitement or general health condition, the vibration rate or
frequency of a machine component is often a useful indicator of the
condition of the machine.
Frequency, as with amplitude, is always expressed with a unit.
Commonly used frequency units are cps (cycles per second), Hz
(Hertz), and cpm (cycles per minute). Hertz is a unit equivalent to
'cycles per second'. One Hz is equal to one cps (one cycle per
second), or 60 cpm (60 cycles per minute).

What is A Waveform?
The graphical display of electrical signals from a person’s heart
(electrocardiogram or ECG) is useful for analyzing the medical
condition of the person’s heart. In a similar way, graphical displays of
vibratory motion are useful tools for analyzing the nature of vibration.
We can often find clues to the cause and severity of vibration in the
graphical display of vibratory motion.
One display commonly used by vibration analysts is the waveform. A
waveform is a graphical representation of how the vibration level
changes with time. Shown below is an example of a velocity
waveform. A velocity waveform is simply a chart that shows how the
velocity of a vibrating component changes with time.
The amount of information a waveform contains depends on the
duration and resolution of the waveform. The duration of a
waveform is the total time period over which information may be
obtained from the waveform. In most cases, a few seconds are
sufficient. The resolution of a waveform is a measure of the level of
detail in the waveform and is determined by the number of data
points or samples characterizing the shape of the waveform. The
more samples there are, the more detailed the waveform is.

What is A Spectrum?
Another kind of display commonly used by vibration analysts is the
spectrum. A spectrum is a graphical display of the frequencies at
which a machine component is vibrating, together with the
amplitudes of the component at these frequencies. Shown below is
an example of a velocity spectrum.
But how can a single machine component be simultaneously
vibrating at more than one frequency?
The answer lies in the fact that machine vibration, as opposed to the
simple oscillatory motion of a pendulum, does not usually consist of
just one simple vibratory motion. Usually, it consists of many
vibratory motions taking place simultaneously.
For example, the velocity spectrum of a vibrating bearing usually
shows that the bearing is vibrating at not just one frequency but at
various frequencies. Vibration at some frequencies may be due to
the movement of bearing elements, at other frequencies due to the
interaction of gear teeth, and at yet other frequencies due to the
rotation of motor windings.

Because a spectrum shows the frequencies at which vibration
occurs, it is a very useful analytical tool. By studying the individual
frequencies at which a machine component vibrates, as well as the
amplitudes corresponding to those frequencies, we can infer a great
deal about the cause of the vibration and the condition of the
machine.
In contrast, a waveform does not clearly display the individual
frequencies at which vibration occurs. A waveform instead displays
only the overall effect. It is thus not as easy to diagnose machine
problems using waveforms. With the exception of a few specialized
cases, spectra
4
(and not waveforms) are usually the primary tool for
analyzing machine vibration.
The information a spectrum contains depends on the Fmax and
resolution of the spectrum. The Fmax of a spectrum is the frequency
range over which information may be obtained from the spectrum.
How high Fmax needs to be is dependent on the operating speed of
the machine. The higher the operating speed, the higher Fmax
needs to be. The resolution of a spectrum is a measure of the level
of detail in the spectrum, and is determined by the number of
spectral lines characterizing the shape of the spectrum. The more
spectral lines, the more detailed the spectrum.
4
Spectra is the plural of spectrum.

Summary
In this section we described machine vibration using methods that
are useful for analysis purposes.
We defined the terms 'amplitude' and 'frequency', and described the
physical significance of these terms. Amplitude is a measure of
vibration severity while frequency is a measure of oscillation rate.
Together, the amplitude and frequency of a vibrating machine
component provide us with an understanding of the condition of the
machine as well as the cause of the vibration.
We noted that machine vibration is much easier to analyze when it is
graphically displayed, and we presented the two most common
displays: waveforms and spectra. Usually, spectra are more useful
for analysis purposes.

Section 3: How is Machine Vibration Measured? 27
Section 3: How is Machine
Vibration Measured?
In the last section we identified the most important vibration analysis
tool as the spectrum. When we measure machine vibration we
usually measure vibration spectra, since the spectrum of a vibrating
component tells us a great deal about the condition of the
component as well as about the cause of vibration. Naturally it is vital
that the spectrum, which gives such valuable information, be
obtained accurately.
What guidelines must be observed to ensure measurements are
accurate?
How should measurements be taken and for which machines should
they be taken?
In this section we will answer these questions.
After reading this section you will be able to:
• Recognize which machines should be monitored
• Understand how vibration sensors should be mounted
• Determine how measurement parameters should be set
• Take measurements in a systematic way

Section 3: How is Machine Vibration Measured?28
Which Machines Need Monitoring?
When deciding which machines to monitor, critical machines
should be given priority over other machines. This is much the same
as monitoring the health of people. It is inappropriate to closely
monitor the health of perfectly healthy people, and then to forsake
the monitoring of others who genuinely need it. The same applies
when monitoring the condition of machines.
In general, the following critical types of machines should be
monitored on a regular basis in order to avoid unexpected and costly
problems:
(a) Machines that require expensive, lengthy, or difficult
repairs if broken down
(b) Machines that are critical to production or general
plant operations
(c) Machines that are known to frequently suffer damage
(d) Machines that are being evaluated for their reliability
(e) Machines that affect human or environmental safety

How Does the Instrument Work?
Before taking a vibration measurement, you need to attach a sensor
that can detect vibration behavior to the machine that is being
measured. Various types of vibration sensors are available, but a
type called accelerometer is normally used as it offers advantages
over other sensors. An accelerometer is a sensor that produces an
electrical signal that is proportional to the acceleration of the
vibrating component to which the accelerometer is attached.
What is the acceleration of a vibrating component? It is a measure of
how quickly the velocity of the component is changing.
The acceleration signal produced by the accelerometer is passed on
to the instrument that in turn converts the signal to a velocity signal.
Depending on the user’s choice, the signal can be displayed as
either a velocity waveform or a velocity spectrum. A velocity
spectrum is derived from a velocity waveform by means of a
mathematical calculation known as the Fast Fourier Transform or
FFT.
The diagram below is a very simplistic explanation of how vibration
data is acquired. You may wish to consult other literature such as the
vbSeries Instrument Reference Guide for further information.

How is the Accelerometer Mounted?
Most machines involve rotary mechanisms. Motors, pumps,
compressors, fans, belt conveyors, gearboxes, all involve rotary
mechanisms and are frequently used in machines.
Most rotary mechanisms in turn have bearings that support the
weight of rotating parts and bear the forces associated with rotary
motion and vibration. In general, large amounts of force are borne by
bearings. It is not surprising that bearings are often the place where
damage occurs and where symptoms first develop.
Vibration measurements are thus usually taken at the bearings of
machines, with accelerometers mounted at or near the bearings.
Since conclusions regarding machine condition - and hence whether
or not money and human safety are risked - depend on the
accuracy of measurements, we must be very careful how
measurements are taken. It is important to always remember that
the way in which we mount the accelerometer very much
determines the accuracy of measurements.
How should accelerometers be mounted to ensure measurements
are accurate and how can we do so safely? Here are some
guidelines:

(a) Mount as Close as Possible to the Bearing
Imagine a doctor who listened to your heart through thick clothing
and placed the stethoscope closer to your kidney than to your heart.
You would likely doubt his diagnosis as he would be basing it on
sounds distorted by undue obstruction and noise from other
organs.
When measuring vibration we must always attach the accelerometer
as close as possible to the bearing. More specifically, we must
attach it as close as possible to the centerline of the bearing to
avoid picking up distorted signals.

(b) Make Sure the Accelerometer is Firmly
Attached
For the accelerometer to detect true vibration behavior, it needs to
undergo exactly the same vibratory movement as the vibrating
component. An accelerometer must therefore be attached firmly to
the vibrating component so that it does not rock or move
independently of the component. A loosely mounted accelerometer
produces signals distorted by its own independent movements and
therefore gives the wrong message.
Various mounting methods exist, but mounting by means of a
magnet is the most popular as it offers a balance between
measurement reliability and convenience to the user. The
magnetic mounting supplied in the Commtest vb kit can be attached
very firmly
5
, while allowing the user to measure multiple machines
using the same accelerometer, with minimum time spent on
attaching and detaching the accelerometer.
To ensure that the accelerometer is firmly attached, it must be stuck
to a magnetic mounting surface this is even. The magnetic mount
must sit securely on the surface with the accelerometer positioned in
the prescribed orientation.
5
When pulled perpendicularly away from the mounting surface, the
vb accelerometer's magnetic mounting resists with a force of 22 kgf
(48.4 lbf).

For the surface to be even, it must be free of debris, rust, and flaking
paint.
The mounting surface must be truly magnetic (iron, nickel, or cobalt
alloys). The magnetic mounting must not, for example, be attached
to an aluminum surface by virtue of iron beneath the aluminum
surface.
To avoid loss of magnetism, the magnetic mounting must not be
dropped or heated. Care must also be taken not to strip the screw
thread on the accelerometer and magnetic mounting.

(c) Make Sure the Accelerometer is Oriented
Correctly
Different situations require the accelerometer to be oriented
differently. For example, to detect parallel misalignment the
accelerometer is usually mounted in the radial direction of the
bearings, but to detect angular misalignment the accelerometer
needs to be mounted in the axial direction.
The signal produced by the accelerometer is dependent on the
orientation in which the accelerometer is mounted, since the
amplitude (amount) of vibration varies in different directions.

(d) Mount the Same Accelerometer in the Same
Location
For a particular measurement point it is important to always mount
the accelerometer at the same location to minimize measurement
inconsistencies that may lead to wrong conclusions. Where possible,
always use the same accelerometer for a particular measurement
point.
(e) Mount the Accelerometer on Something
Substantial
The accelerometer must never be mounted on a very flexible part of
the machine as the spectrum will be distorted by the flapping of the
flexible part.
The accelerometer must never be used on structures that are very
light as the weight of the accelerometer and magnetic mounting will
distort the vibration behavior of the structure. In general, the
combined weight of the accelerometer and magnetic mounting
should be less than 10% of the weight of the vibrating structure.

(f) Take Care of the Accelerometer
If the accelerometer is treated roughly it may produce unreliable
signals. Because of the strength of the magnetic mount, you must
take care when attaching the accelerometer to a mounting surface.
You can achieve this by approaching the mounting surface with the
magnetic mounting tilted at an angle. When detaching the magnetic
mounting, you must not use the accelerometer as a lever for
breaking contact. Instead, the magnetic mounting should be gripped
tightly and then tilted sideways to break the contact.
The accelerometer cable should never be twisted acutely, but must
be anchored in a manner that prevents it from being damaged.
Twisted or freely swinging cables can distort the measured
spectrum.

(g) Take Care of Personal Safety
You must manage hazards at all times. When taking vibration
measurements, three kinds of hazards stand out in likelihood or
severity: injury by moving parts, electrical shock, and magnet-
induced damage.
Firstly, when mounting the accelerometer, you must take care to
prevent the cable from becoming entangled with moving
machinery. While the quick-release connector minimizes this danger
it should not be relied on as a substitute for correct installation.
Other things that could tangle with moving machinery include loose
clothing, long hair, data transfer cables and straps.
Secondly, you must never attach the accelerometer to any high
voltage surface as this may cause electrical shock.
Thirdly, you must never bring the magnetic mounting near any
magnet-sensitive objects such as pacemakers, credit cards, floppy
disks, video tapes, cassette tapes and watches since these items
can be damaged by magnetic fields.
There are other possible hazards. You should read and thoroughly
understand the vbSeries Instrument Reference Guide before using
the instrument or its accompanying accessories.

How are Parameters Set?
What are measurement parameters?
Measurement parameters are the details that specify how a
measurement is to be taken. By specifying measurement
parameters, we specify how data is to be collected and processed
before it is presented to us. Before taking a vibration measurement
we need to specify what parameters will be used.
The parameters for vibration measurement may be likened to the
'what and how' details that a doctor must specify before a medical
test is performed.
We will now look at how measurement parameters are set when we
measure a spectrum. For the rest of this section, we will use the
Commtest vb instrument as an example vibration monitoring
instrument for our discussions, as it is a particularly simple
instrument to use. For example, the default measurement parameter
values (except for the default Fmax value) are suitable for taking
most vibration measurements, so that in most situations few or none
of the default parameter values requires adjusting. These
parameters are those displayed in the Set Parameters screen of the
vb instrument, with 'domain' set to 'frequency'.
What are some of these measurement parameter values and what
do they mean?

The parameters used for measuring vibration spectra may be divided
into four classes; namely, parameters that determine:
(a) How data is collected
(b) How much or how fast data is collected
(c) How data is processed
(d) How data is displayed
(a) How Data is Collected
The parameters that determine how data is collected are 'Trigger
type' and the parameters listed under 'Sensor setup'.
'Trigger type' is the parameter that tells the instrument how to begin
measuring. If set to 'Free run', the instrument will take measurements
continuously. If set to 'Single', only one measurement cycle will take
place. In most cases the instrument can be set to 'Free run'.
The parameters under 'Sensor setup' inform the instrument what
type of accelerometer is being used to take measurements. If the
ICP®-type accelerometer supplied in the vb kit is used, the 'Drive
current' needs to be turned 'ON', and the 'Sensitivity' of the
accelerometer needs to match that specified on the vb Quality
Assurance Card. 'Settling time' is the time required for the
accelerometer and instrument to settle before measurements can be
taken accurately. You should use the default 'Settling time' value
(which varies with the Fmax value) to ensure measurement
accuracy.

(b) How Much or How Fast Data is Collected
The parameters that determine how much or how fast data is
collected are the parameters 'Fmax', 'Spectral lines', and 'Overlap
percentage'.
In Section 2, we noted that the higher the Fmax, the larger the
frequency range over which information
6
may be obtained from the
spectrum.
Thus, if the Fmax value is high, data is displayed up to high vibration
frequencies. To acquire information regarding high vibration
frequencies, the measurement frequency - or rate of sampling data -
needs to be high as well. As a result, the higher the Fmax, the faster
the measurement will be.
The more spectral lines a spectrum has, the more information can
be obtained from it. This means that the more spectral lines there
are, the more data needs to be collected to generate the additional
information, and therefore the longer the measurement will take.
6
A higher Fmax does not cause more data to be collected but
causes the data to span across a wider range of frequencies.

What Fmax Value Should be Used?
The higher the operating speed of the machine, the higher its
frequencies of vibration will be, and the higher the Fmax will need to
be in order to capture vibration behavior at those high frequencies.
For vibration that does not involve rotary fingers such as gear teeth,
fan blades, pump vanes, and bearing elements, an Fmax value
equal to 10 times the operating speed is usually sufficient to capture
all crucial information.
For example, if the operating speed is 10 000 rpm, then an Fmax
value of 100 000 cpm (100 kcpm) is most likely sufficient.
For vibration that does involve fingered elements such as gears,
fans, pumps, and roller bearings, an Fmax value equal to 3 times
the number of fingers multiplied by the operating speed is usually
sufficient to capture all crucial information.
For example, for a gear driven by a 12-toothed pinion rotating at 10
000 rpm, an Fmax value of 360 000 cpm (360 kcpm) is most likely
sufficient.
If the Fmax value required is very large the resolution of the
spectrum will be low, and information pertaining to low vibration
frequencies may be lost. It may be necessary to take some low
Fmax measurements in addition to the high Fmax measurement.

How Many Spectral Lines Should be Used?
In most cases 400 lines of resolution are sufficient. However, if a
large Fmax value is used, the lines will be spread out over a large
frequency range, leaving wide gaps between lines. Thus, for large
Fmax values, more spectral lines may be needed to avoid loss of
detail.
It should, however, be noted that the more spectral lines are used
the longer the measurement will take and the more instrument
memory space will be occupied. A high Fmax value or a high number
of spectral lines should therefore be used only where necessary.
How Much Overlap Should I use?
Overlapping data is a means of reusing a percentage of a
previously measured waveform to calculate a new spectrum. The
higher the 'Overlap percentage', the less newly acquired data is
needed to generate a spectrum, and thus the faster the spectrum
can be displayed. 50% overlap is ideal for most cases.

(c) How Data is Processed
The parameters that determine how data is processed are the
parameters 'Average type', 'Number of averages', and 'Window type'.
Imagine you had to accurately measure the width of the pages in this
book. Because the width may vary slightly from page to page, you
would probably measure not just the width of one page but rather
that of a few pages and then take the average.
Similarly, when vibration is measured several spectra are usually
measured and then averaged to produce an average spectrum. The
average spectrum better represents vibration behavior as the
averaging process minimizes the effect of random variations or noise
spikes that are inherent in machine vibration.
The parameter 'Average type' determines how spectra are
averaged. 'Linear' averaging is recommended for most cases.
'Exponential' averaging is usually used only if vibration behavior
varies significantly over time. 'Peak hold' does not really involve
averaging but causes the worst-case (largest) amplitude for each
spectral line to be displayed.

The parameter 'Number of averages' determines the number of
consecutive spectra used for averaging. The larger the number of
spectra used for averaging, the more noise spikes are smoothed out
and the more accurately true spectral peaks are represented.
However, the larger the number of averages, the more data needs to
be collected, and therefore the longer it takes to obtain the 'average
spectrum'. A 'Number of averages' of 4 is sufficient for most cases.
The collected data is usually not directly used to generate a
spectrum, but is often modified beforehand to cater for certain
limitations of the FFT process (the process that transforms the data
into a spectrum). Data is usually modified by multiplication with a
correction window. This prevents spectral lines from 'smearing' or
'leaking' into one another.
'Window type' is the parameter that determines the kind of window
that is used. The 'Hanning' window is usually used. If the
'rectangular' window is used, the data will effectively not be modified.

(d) How Data is Displayed
The parameters that determine how the spectrum is to be displayed
are listed under 'Display units'.
To specify how the spectrum is to be displayed, the scale of the
spectrum needs to be specified. The scale of the spectrum
determines how easily spectral details can be seen, and is defined
by the parameters 'Amplitude scale', 'vdB reference', 'Log range', and
'Velocity max.
In most cases, the 'Amplitude scale' can be 'Linear'. If a linear
amplitude scale is used, then the parameters 'vdB reference' and
'Log range' are of no consequence (and therefore need not be set).
In general, you should set 'Velocity max' to 'Automatic' to allow the
instrument to automatically select an ideal amplitude scale that
allows spectral peaks to be clearly seen.

To specify how the spectrum is to be displayed, the 'amplitude type'
to be used also needs to be specified. In Section 2 (page 18), we
defined two amplitude types - peak amplitude and rms amplitude.
If the 'Ø-peak' (or 'peak') amplitude is used, the spectrum will display
the maximum speed achieved by the vibrating component at the
various vibration frequencies.
On the other hand, if the 'rms' amplitude is used, a quantity
indicative of vibration energy at the various frequencies will be
displayed instead.
For vibration spectra, the peak amplitude at a particular frequency is
exactly √2 times (roughly 1.4 times) the rms amplitude at that
frequency. Thus which amplitude type is used is not really important
since amplitude conversions
7
may be readily done.
We recommend that you always use the same amplitude type for a
particular measurement point to avoid misinterpretations. A
switchover from the rms amplitude to the peak amplitude causes an
apparent rise in vibration amplitude that might be mistakenly
interpreted as machine deterioration. On the other hand, a
switchover from the peak amplitude to the rms amplitude might hide
a genuine rise in vibration amplitude.
7
For a spectrum, the peak amplitude is times the rms amplitude.
This relationship is generally not valid for waveforms.

Finally, the amplitude and frequency units to be used in the
spectrum also need to be specified. Which units should be used is
really a matter of personal choice, or more often, geographic
location.
In North America, the velocity unit usually used (for linear velocity
scales8
) is in/s, and a commonly used frequency unit is kcpm
(kilocycles per minute).
In other parts of the world, the velocity unit and frequency unit
usually used are mm/s and Hz respectively. Shown below are the
relationships between the units
9
:
8
Many vibration analysts prefer the logarithmic velocity unit vdB.
However, discussion on logarithmic scales and units is beyond the
scope of this book.
9
We have rounded the in/s ø-peak, mm/s rms conversion to 18. The
correct ratio is 17.96.

How is Data Collected?
As machine surroundings are often hazardous and uncomfortable,
vibration analysis is normally performed away from the machine.
To do this, measurements are usually recorded with the instrument
then transported to an office where the recorded data can be
analyzed in a quiet and safe environment. In the office, the data can
be transferred to a computer for more detailed analysis.
In most factories there are usually numerous critical machines that
need to be monitored. Furthermore, to enable thorough analysis,
each machine usually needs to be monitored at various points. Each
point in turn often requires monitoring using different accelerometer
orientations, and occasionally, using different measurement
parameters as well. Thus, on every round of data collection a large
number of recordings usually need to be taken.

To avoid having to repeatedly travel between the office and
machines, recordings are usually taken of all machines before the
recordings are brought to the office for analysis.
It is important that recordings be taken both accurately and
systematically. When you have an organized method of taking
recordings there is less chance of confusing the spectra of different
machines. If recorded spectra get mixed up they would most likely
lead to wrong conclusions and perhaps to very costly
consequences as well.
In view of the large matrix of recordings that need to be taken, how
do we ensure that recordings are always taken of the locations
intended, that the recordings that are taken are not confused with
one another, and that no recordings are left out? A recording list is
used.

A recording list shows all the recordings that need to be taken on a
given round of data collection. It is like a detailed shopping list that
shows us exactly what to buy during a shopping mission. From a
recording list, we can see which recordings need to be taken on
which machines, at which points on the machines, in which
orientations, and using which measurement parameters.
Although a recording list in the vb instrument does not appear
exactly like that shown in the last page, it has the same information
structure.

In the example shown, 'Motor A1', 'Gearbox B2', 'Rotor B2' are
machines for which data is to be collected. 'Front end', 'back end',
'input end', and so forth are the measurement points on the various
machines. 'horizontal', 'vertical', 'axial', and 'radial' are the
orientations in which measurements are to be taken, and in
brackets are the measurement parameters that are to be used. Note
that for 'Gearbox B2', two recordings are to be taken, each using a
different set of parameters. More information regarding recording
lists may be found in the vbSeries Instrument Reference Guide.
To avoid confusion, you must give machines and measurement
points unique and meaningful names in the recording list. To rule
out misidentifications, you must clearly label machines and
measurement points with names that match those adopted in the
recording list. When taking recordings, you must take care to ensure
that the mounting orientation of the accelerometer matches that
described in the recording list.
Not all machines on the recording list may be equally critical. Less
critical machines can be monitored less frequently. If only certain
machines or measurement points from the recording list need to be
monitored during a particular round of data collection, you can tag
those machines that need to be monitored so that recordings are
only taken for items that are tagged. The tagging of items in a
recording list is further explained in the vbSeries Instrument
Reference Guide.

To help ensure data collection is done regularly, you should create a
schedule showing when data collection will be carried out.
For most machines, data should be collected every month. For
critical machines, data may need to be collected every week, and for
less important machines, every alternate month. We advise you to
begin with a rigorous schedule then adjust it later as more
experience is gained.
Imagine going shopping with a shopping list but without enough
money to buy what is needed, and without the means to transport
things bought back home. We would expect such a shopping mission
to fail.
Similarly, with machine vibration monitoring, we need sufficient
battery and memory capacity in the vb instrument to complete a
round of data collection. Before beginning to collect data, you must
ensure that there is sufficient battery and memory capacity in the
instrument (see the vbSeries Instrument Reference Guide for further
details).

Most kinds of vibration problems are detected while the machine is
running steadily and exhibiting a steady vibration pattern.
If a machine has just started up, or if its operating speed has just
been changed, you need to ensure that the machine is given time to
settle into a steady state before taking spectrum recordings,
otherwise, the recorded spectra will not reflect the true steady-state
behavior of the vibrating machine.
When a round of data collection is complete, you should transfer the
recorded data to a computer with Ascent™ software for analysis and
archiving. Once the recorded data has been archived, you can erase
the data from the vb instrument, thus freeing up memory space on
the instrument for another round of data collection.

Summary
In this section we studied how machine vibration is measured.
We discussed methods for deciding which machines to monitor, and
what factors determine which machines are critical. We also
examined how the measuring instrument works, and described the
function of accelerometers. We emphasized the importance of
mounting the accelerometer carefully, since the accuracy of a
measurement is largely dependent on accelerometer mounting.
We provided guidance on how to set measurement parameters;
setting the parameters for a measurement simply means specifying
the details on how the measurement is to be carried out. This
includes specifying how, how much and how fast data is to be
collected, as well as how the collected data is to be processed and
displayed.
We also emphasized the importance of collecting and storing data in
a systematic way. For a given round of data collection, data is
usually recorded for each machine with the aid of a recording list
before the data is transferred to a computer for detailed analysis and
archiving. To help ensure data collection is done regularly, you
should have a clear schedule detailing when data collection is to be
carried out.

Appendix: List of Symbols 55
Appendix: List of Symbols
Symbol Meaning
adj. adjective
Ascent™ software Commtest’s vibration analysis software
cos x the cosine of x
cpm cycles per minute
cps cycles per second
dB decibel(s)
FFT fast Fourier transform
Fmax 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
Ibf/in pound force per inch
log x the logarithm of x

Appendix: List of Symbols56
Symbol Meaning
log10 x the base-10 logarithm of x
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 instrument Commtest vibration analyzer
vdB decibel unit for velocity
w.r.t. with reference to
the average value of x
x² the square of x (x times x)
1X fundamental frequency
° degree(s)
the square root of x
angle
phase angle
the constant pi (roughly equal to 3.14)
the sum of x values
angular frequency (expressed in rad/s)

Glossary Abbreviations Guide 57
Glossary Abbreviations Guide

Glossary of Terms58
Glossary of Terms
A
A/D converter
The electronic hardware that converts analog signals to digital values
by way of data sampling.
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/s
2
(metric),
m/s
2
(SI), in/s
2
(imperial), ft/s
2
(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 component is
usually measured using an accelerometer. See also Triaxial
accelerometer.
Alarm envelope
A chart 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.

Glossary of Terms 59
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 Fmax (by way of a 'low pass' or 'anti-aliasing'
filter) and sampling the filtered signal at a rate at least twice the
Fmax.
Alignment
The process where the axes of machine components are positioned
and oriented 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-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,
amplitude-modulated 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.

Glossary of Terms60
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 Ascent™ software.
Angular contact bearing
A bearing that supports both radial and axial shaft loads. The rolling
elements in an angular contact bearing are usually oriented 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 2 radians per
second (since one cycle, or an angle of 2 radians, is traversed
every second). Angular frequency is usually denoted by the symbol
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 Fmax. See also Aliasing.
Ascent software
A Windows®-based analysis software developed by Commtest that
facilitates the archiving and analysis of vb data on a PC. The Ascent
software allows vibration data to be charted, analyzed, and printed.
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 time-
synchronized 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.

Glossary of Terms62
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 movement 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. charts)
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.
Balance weights
See Correction weights.
Balanced
The condition where the axis of rotation and mass centerline of a
rotating part are coincident. See also Imbalance.
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 Imbalance.
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.

Glossary of Terms64
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.
Baseline spectrum
See Reference spectrum.
Baud rate
The rate at which data is transferred between a computer and the vb
instrument. Baud rate is measured in 'bits per second' or 'kilobits per
second'.
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
Abbreviation for ball pass frequency inner. See Ball pass frequency.
BPFO
Abbreviation for ball pass frequency outer. See Ball pass frequency.

Glossary of Terms66
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.
BSF
Abbreviation for ball spin frequency. See Ball spin frequency.
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
Imbalance.
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.

Glossary of Terms68
Cepstrum
A chart 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
Imbalance.

Cosine wave
The sine wave phase-shifted by 90° i.e.
cos = sin ( + 90°)
where 'cos' and 'sin' denotes 'cosine' and 'sine' respectively, and 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
imbalance.
Couple imbalance
An imbalance 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 imbalance can be
corrected by adding two correction weights to the appropriate
locations on the rotor. See also Dynamic imbalance and Static
imbalance.

Glossary of Terms70
cpm
A measurement unit for the frequency of periodic motion. cpm stands
for 'cycles per minute'. One cpm is equal to one 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 imbalanced rotor is roughly the same as a
sinusoidal waveform and has a crest factor roughly equal to
(approximately 1.4). If the dominant cause of vibration is
misalignment, the crest factor will usually be less than and if there
is impacting in gear teeth or bearing rolling elements, the crest factor
will generally be higher than .
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.
cyc/sec
See cps.
Cycle
One complete sequence of the shortest signal pattern that
characterizes a periodic waveform or motion.
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.

Glossary of Terms72
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 structure
The hierarchical structure of data storage in a vibration measurement
instruments. In the vb instrument, there are six levels in the
hierarchy: Folder, 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 well-
defined 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.

Glossary of Terms74
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 chart 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 imbalance
An imbalance condition involving both static and couple imbalance.
The mass centerline is both offset from and not parallel to the axis of
rotation. Most cases of imbalance in machines are dynamic
imbalance.
Dynamic range
The difference between the highest and the lowest amplitude an
instrument can measure, with the amplitudes expressed in dB.
E
Eccentricity
The distance between the center of mass and the center of rotation.
The larger the eccentricity, the larger the imbalance force.
Elastic
That which can be easily distorted, and which 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.
Engineering units
See Unit.

Glossary of Terms76
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.
EU
Abbreviation for Engineering units. See Unit.
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 imbalanced, 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)
n = number of spectra used for averaging

F
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 the 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.

Glossary of Terms78
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 newer 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.
Fmax
The maximum frequency displayed on a vibration spectrum i.e. the
frequency range over which amplitudes are displayed. Increasing the
Fmax (while keeping other parameters the same) reduces the
measurement duration required, but also reduces the resolution of
the spectrum.
Folder
An Ascent software file that contains the data transferred to it from
the vb instrument.

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.

Glossary of Terms80
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 chart 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 Fmax.
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.

Glossary of Terms82
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/s
2
or
32.1740 ft/s
2
. The acceleration of a vibrating body is sometimes
measured in terms of gs.
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 for 0 ≤ ≤ 2
The Hamming window is used to reduce signal leakage but because
it is not as effective as some other windows, it is rarely used. See
also Windowing.

Hanning Window
A mathematical function named after its inventor and defined as
follows:
Hanning window = ½ (1 - cos ) for 0 ≤ ≤ 2
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.

Glossary of Terms84
Harmonic force
An excitation force that is sinusoidal in nature i.e. of the form:
F(t) = Fo sin (t - )
where F(t) = the instantaneous force magnitude
= angular frequency
t = time
= 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.

Glossary of Terms86
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 mA 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
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. Imbalance is
one of the most common causes of vibration in machines. See also
Couple imbalance, Dynamic imbalance, and Static imbalance.
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.
In-phase signals
See Phase.
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.

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 chart. 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.

Glossary of Terms88
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 (pref.)
1000 times. The prefix 'k' stands for 'kilo'. 1 kHz (kiloHertz) is
equivalent to 1000 Hz, 1 kg (kilogram) to 1000 grams, 1 kcpm
(kilocycles per minute) to 1000 cpm.
k (w.r.t. springs)
See Spring constant.
kcpm
A frequency unit equivalent to 1000 times the frequency unit, cpm
i.e. 1 kcpm (kilocycles per minute) is equal to 1000 cpm (cycles per
minute).
kgf
A measurement unit for force. 'kgf' is short for 'kilogram force'. 1 kgf
is equivalent to the weight of a 1 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'. 1 lbf is
equivalent to the weight of a one pound (1lb) 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:
where i = spectral line number
j = spectrum number
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.

Glossary of Terms90
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 = 10
2
). 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 chart).
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 imbalanced 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.

Glossary of Terms92
Mask
See Alarm envelope.
Measurement parameters
The details about a measurement that must be specified before the
measurement is taken e.g. before a spectrum is taken, the Fmax,
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'. 1
micrometer (µm) equals one millionth of a meter i.e. 10
-6
meter.
Micron
See Micrometer.
mil
A measurement unit for small distances. 1 mil is equal to 0.001 inch.

Misalignment
The condition where the axes of machine components are not
positioned or oriented 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
which corresponds 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.

Glossary of Terms94
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-of-freedom 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 n
th
natural frequency is called the n
th
natural mode shape. See also Mode shape and Nodal points.
Natural vibration
See Free vibration.
Navigator
The navigator is a display area in the Ascent software that allows
you to navigate through the data in a machine database.
The top half of the navigator (the navigator tree) shows the structure
of your machines i.e. their points and axes.
The bottom half of the navigator (the navigator list) lists any items
that belong to whichever item is currently selected in the navigator
tree e.g. if a point is selected the navigator list will display all the
axes around that point.
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 n
th
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.

Glossary of Terms96
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 Fmax, thus
ensuring that the Nyquist frequency is greater than the Fmax.
Nyquist plot
A complex numbers chart 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.

Glossary of Terms98
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.
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.
Overall level
See Root-mean-square.
Overall rms level

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.
P
Parallel misalignment
See Misalignment.
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.
Parameters
See Measurement parameters.
Peak (w.r.t. a spectrum)
The highest amplitude value in a spectrum.

Glossary of Terms100
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' (Ø-peak) 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-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
steady-state 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 imbalance, 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 imbalanced 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
imbalanced 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
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
'root-mean-square' is often abbreviated as 'rms'. For a discrete
waveform with n instantaneous values, the overall rms amplitude is
given by:
where xi = the i
th
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:
where xi = the amplitude of the i
th
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.
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
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.
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 Fmax 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 second to 3 seconds. The
settling time required for the vb instrument is dependent on the
frequency range (Fmax) or duration of the measurement, and ranges
from 4 to 13 seconds. The lower the Fmax 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
Abbreviation for simple harmonic motion. 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.
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 to 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 shown below is equal to b/h. The symbol for 'sine' is
'sin'. See also Cosine wave.
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 imbalanced 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.
Sine waveform
A time domain signal described by the function:
f(t) = sin ( t - )
where f(t) = the instantaneous value at time t
= angular frequency
t = time
= phase angle
See also Sine.

Sinusoid
A mathematical function of the form:
(t) = A sin ( t - )
where x(t) = the instantaneous value of x at time t
A = maximum x value (zero-to-peak amplitude of x)
= angular frequency
t = time
= 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 imbalance 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
Spectral peak
See Peak (w.r.t. spectrum).
Spectrum
An amplitude (e.g. of velocity) versus frequency chart 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:
where xi = the ith instantaneous signal value during the time
period
= the average signal value during the time period
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:
Thus the standard deviation is simply equal to the rms amplitude.
The larger the standard deviation, the larger the vibration amplitude.

Static imbalance
An imbalance 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 imbalance can be corrected
by adding one correction weight to the appropriate location on the
rotating part. See also Couple imbalance and Dynamic imbalance.
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 chart 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.
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
cross-sectional view depicts the 'trend' of vibration pattern at that
point for the particular frequency or time value. See also Trending
and Waterfall chart.

Trending
The analyzing, usually by way of waterfall and trend charts, of
vibration data taken on 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.
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 are started on the vb
instrument. Measurements can be triggered 'manually' one-by-one,
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
See Imbalance.

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.
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.
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.
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 on 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
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 chart 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 times 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.

Beginners guide vibration

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