Vibration Analysis.pdf

Vibration Analysis
Dr./ Ahmed Nagib
November 9, 2015

Vibration Analysis Lectures
Chapter I Vibration Sources and Uses
Chapter II Basic Machinery Vibrations
Chapter III Data Collection and Analysis
Chapter IV Machine Characteristics
Chapter V Vibration Instruments
Chapter VI Vibration Testing
Chapter VII Basic Analysis
Chapter VIII Vibration Severity

Vibration
Q: Will structure fail before the human body in
a factory or vice versa?

Sources of Vibration
Table
1.1.

Sources
of
Vibration.
Function
Inadequate
Design
Manufacturing
Processes
Installation
Wear
and
Abuse
Faulty
Maintenance

Sources of Vibration - Function
Vibration by imposed motion

Sources of Vibration - Function
The two causes of vibration are imposed
motions and forces. Imposed motions usually
relate to the function of the machine. Cams,
slider cranks (reciprocating compressors and
engines), chain and sprocket cogging, and
misalignment are examples of devices and
conditions that generate vibrations by imposed
motions. The imposed motion creates internal
forces in the machine. In reality all vibration is
essentially caused by forces that are generated
internally or applied externally.

Sources of Vibration - Inadequate
machine design
can be responsible for excessive vibration
because the machine enhances or is the cause
of unnecessary pulsating or vibratory forces.
For example, if a motor stator flexes as a result
of electromagnetic forces, unnecessary
vibration results.

Sources of Vibration – Manufacturing
Process and Assembly
poor quality machining and manufacturing or
assembly errors. These conditions enhance
background noise and, in some cases, will
produce unacceptable vibration.
• Gears cut with a poor hobbing tool will
produce a high-frequency gear-mesh like
vibration.
• Motors assembled with rotors that are not
centered in the stator will cause unbalanced
electromagnetic forces that excite vibration.
• Inadequate balancing causes excessive
forces and vibration

Sources of Vibration – Manufacturing
Process
Table
1.3.

Vibrating
Forces.
Poor
Quality
Machining

Assembly
Errors

Installation

• misalignment

• distortion

• looseness

Structural
and
Material
Defects

Thermal
Distortion

Lack
of
Lubrication

Unbalance

Sources of Vibration – Installation Erroes
Misalignment,
distortion
(soft
foot),
and
looseness

(bolts
not
tight)
are
examples
of
conditions
that
cause

excessive
vibration;
Figure
1.4.
Normal
wear,

structural
damage,
and
abuse
can
modify
the
function

of
a
machine
and
so
cause
vibration.

Sources of Vibration – Installation Erroes

Sources of Vibration – Lack or Faulty
maintinance
Machines become unbalanced, need
lubrication, and require changing of worn parts.
Some parts, such as vibration isolators,
deteriorate over time, depending on the
environment. Lack of or excessive lubrication is
detrimental to the life of rolling element
bearings as well as gears. Bolts must be tight,
and properly torqued. Fits and clearances are
important in assembly. Above all it is important
to keep good records. Lack of good
professional maintenance is an open invitation
to machine vibration.

Harmonic Mass Unbalance
Periodic Misalignment
Impulsive Rolling Element
Bearing, Gears tooth
Pulsating
Random Cavitation in
Pumps
Types Vibration

Vibration Effect
Table
1.4.

Vibration
Effects.
Catastrophic
Failure
Fatigue
Failure
Loss
of
Product
Quality
Human
Annoyance
The
weakest
link
in
a
machine
exterior,
its
piping,
ductwork,

or
supporting
structure,
can
fail
as
a
result
of
excessive

vibration.
Coupling,
shaft
and
bearing
failures
occur
in
the

rotating
elements.
Cracks,
prior
to
failure,
can
occur
in

ductwork
and
foundations;
piping
can
become
overstressed

and
fail.

Uses of Vibration
Table
1.5.

Uses
of
Vibration.
Acceptance
Testing
Predictive
Maintenance
Manufacturing

Predictive Maintinance Procedure
Table
1.6.

Predictive
Maintenance.
Monitoring
Fault
Diagnosis
Severity
Evaluation

Measurement and Analysis
Schematic
of
Data
Collection
Instrument.

Data
Acquisition

Data
Acquisition
with
two
sensors

Vibration
Monthly Trend Plot of a Pump Motor for
Peak Velocity.

Periodic Monitoring
data are acquired sequentially in a route from
bearing to bearing and machine to machine.
The data collector is preprogrammed and
routes are uploaded in the computer to accept
and store the data acquired from the machines
in the route. After acquisition, the data are
downloaded to the computer for trending and
analysis.

Review
Sources of vibration include function, inadequate
design, manufacturing processes, installation,
wear, abuse and bad maintenance
Forces cause vibration
Types of vibration include harmonic, periodic,
impulsive, pulsating, and random
Effects of vibration are component failures, loss of
product quality, and human annoyance
Uses of vibration include acceptance testing,
predictive maintenance, and manufacturing
Sensors are used to detect vibrations
Analyzers are used to quantify the amplitude and
frequency of vibrations

Chapter II -
Basic Machinery Vibrations
Table
2.1.
Vibration
Units
The
basic
units
used
in
this
book
to
describe
vibratory
forces

and
motions,
from
the
English
system,
are
pound
(lb),
inch

(in.),
and
second
(see).
Amplitudes of
vibrating
motion
are
described
using
the

following
units:
displacement,
mils-‐peak
to
peak
(1,000
mils
=
1
inch)
velocity,
in./sec-‐peak
or
rms (IPS-‐peak
or
rms)
acceleration,
gs peak
or
rms (386.1
in./sec2
=
1
g)
Frequencies are
expressed
in
cycles/minute
(CPM)
or

cycles/second
(Hertz,
Hz),
or
orders
(multiples
of
operating

speed).
Speeds are
expressed
in
revolutions/minute
(RPM).

Vibration cause and effect

Vibration Measurement
Mechanical vibration is measured by a
transducer (also called sensor) that converts
vibratory motion to an electrical signal. The
units of the electrical signal are volts (v) or,
more typically, millivolts (mv). There are 1,000
millivolts per volt (mv/v)

Vibration
Example
2.2.
Measurement
Units
400
mv-‐pk to
pk was
measured
by
a
displacement

transducer
that
has
a
scale
factor
of
200
mv/mil.
Then
the

displacement
amplitude
equals

400
mv − pk
to
pk
200
mv/mil
= 2
mils
pk − pk
Example
2.1.
Voltage
Units
Convert
253
millivolts
to
volts
123
45
6777
45/5
= 0.253
v
Convert
0.342
volts
to
millivolts

0.342
𝑣
6777
45
5
= 342
mv

Proximity Probe
Proximity probes, also termed noncontacting
eddy current displacement transducers, are
attached to the bearing housing and measure
shaft vibration relative to the mounting position
of the probe. Two probes are usually mounted
at a 90° angle to each other

Vibration
Magnetically
Mounted
Accelerometers
on
a
Fan
Pedestal.

Vibration motion
Three fundamental properties that describe vibration
are frequency, amplitude, and phase. Frequency is
defined as the number of cycles or events per unit
time. It is expressed as cycles per second (Hertz,
Hz), cycles per minute (CPM), or orders (multiples)
of operating speed

Vibration motion
Amplitude is the maximum value of vibration at a
given location on the machine. When the vibration is
displayed as displacement and measured in mils (1
mil =1/ 1,000 in.), the amplitude measured is peak
to peak.

Vibration motion
For example, in Figure 2.6, one cycle of vibration is
made in 32.8 milliseconds (mSec) or 0.0328 sec.
Therefore, one cycle divided by 0.0328 sec. equals
30.48 cycles per second. ).

Vibration motion
Example
Period
and
Frequency
From
Figure
2.6,
Period
(τ)
=
32.8
mSec/cycle
τ =

31.=
4>?@
6777
4>?@/A?@

=
0.0328
sec/
cycle
Frequency
(f)
=

6
B?CDEF
(H)
Then
f
=

6
H
=
6
7.731=
A?@/@J@K?
=
30.49
Hz(cycles/sec)
f
=
30.49
Hz
x
60
sec/min
=
1,829
cycles/minute
(CPM)

Vibration motion
For example, in Figure 2.6, Velocity equals 0.6 IPS-
Peak.

Vibration motion
Also, the velocity amplitude can be reported in root-
mean-square (RMS) units. If the data are harmonic
(one-frequency) as they are in Figure 2.7, then the
RMS is equal to 0.707 times the peak or 0.424 IPS-
RMS. If the data are not harmonic, no simple
mathematical relationship holds between RMS and
peak and an electronic circuit must be used to get
the RMS. The advantage of the peak unit is that it
always can be obtained from the time waveform.

Vibration
Vibration Measures.
Measure Units Description
displacement mils
p-‐p*
motion
of
machine,

structure,
or
rotor;

relates
to
stress
velocity in./sec,
IPS
time
rate
of
motion;

relates
to

component
fatigue
acceleration gs**
relates
to
forces

present
in

components
*1
mil
=
0.001
inch;
p-‐p
=
peak
to
peak

**1
g
=
386.1
inches/sec2

Vibration
Displacement. Displacement (D) is the
dominant measure at low frequencies and is
related to stress in flexing members. It is
expressed in mils peak to peak because the
total excursions of the machine motions are
measured. It is normally nonharmonic but
periodic and will therefore yield different
positive and negative peaks. Displacement is
used as the measure for low-frequency
vibration [less than 600 CPM (10 Hz)] on
bearing caps and structures.

Vibration
Displacement is also commonly used to determine
the relative motion between a bearing and its
journal or between the machine casing and its shaft
to assess whether or not rubbing may occur. Figure
shows vibration data plotted in the displacement
measure that is symmetrical originating from a
harmonic force like mass unbalance.

Vibration
Velocity (V) is the time rate of change of displacement.
Velocity cannot be sensed by touch - only changes in it.
Basically, it is displacement times frequency and is a
measure of fatigue in machines. The greater the
displacement and/or frequency of vibration, the greater is
the severity of machine vibration at the measured location.
Velocity is used to evaluate machine condition in the
frequency range from 600 CPM (10 Hz) to 60,000 CPM
(1,000 Hz).

Vibration
Figure 2.8 is a plot of velocity versus time. The amplitude is
measured in peak units positive or negative, whichever is
larger. In Figure 2.8 the negative peaks are larger;;
therefore, the peak velocity is 0.42 inches per second, IPS-
peak.

Vibration
Acceleration is the dominant measure at higher
frequencies. Because it is related to force it can be
sensed by touch. It is proportional to the force on a
machine component such as a gear and is used to
evaluate machine condition when frequencies
exceed 1,000 Hz (60,000 CPM) in gears and
bearings. Acceleration is the time rate of change in
velocity.

Vibration
Figure shows acceleration measured on a gearbox;;
the peak amplitude is 10 gs.

Vibration
If the vibration is harmonic (one frequency), the
amplitudes of the velocity and acceleration are
directly related to displacement by frequency. If the
frequency is known and, the measures-
displacement, velocity, and acceleration - are
related by frequency. If a measure and the
frequency is known, the two other measures can
be calculated using the formulas provided below.
V = 2𝜋fD and A=2𝜋fV

Vibration
To calculate velocity, displacement must be changed from
mils-peak to peak to inches-peak. This requires division by
two (2) and by one thousand (1,000 mils = 1 inch). To obtain
acceleration in gs, divide the value in in/sec2 by 386.1
in/sec2 per g. For example, a vibration displacement of 5
mils-pk to pk becomes 5/2000 = 0.0025 inches-peak. For a
frequency of 100 Hz, the velocity is V = 2 x 𝜋x 100 x 0.0025
in/sec-peak. V = 1.57 IPS-pk. The acceleration A = 2 x 𝜋x
100 x 1.57/386.1 = 2.55 gs-peak. A displacement of 6.4
mils-pk to pk relates to a velocity of 0.2 IPS-peak at 10Hz
whereas the acceleration is only 0.03 gs peak.
An acceleration of 3.2gs at 1,000 Hz relates to a
displacement of 0.064 mils-pk to pk. Therefore,
displacement and acceleration measures are restricted to
low- and high-frequency applications respectively.

Vibration Analysis
The basic vibration data (waveforms) collected by sensors
and displayed by instruments must be broken down into
frequency components in order to perform a detailed
vibration analysis.

Vibration Analysis
Vibration signals are usually composed of multiple
frequency components with different amplitude. The
amplitude of the lower plot (time waveform) is 3.6 mils peak-
to-peak;; the period is 18.7 mSec (53.5 Hz). The upper plot,
which is called a spectrum, is the breakdown of the time
waveform in mils peak-to-peak versus frequency. The
spectrum is obtained from the waveform using a
mathematical procedure called an algorithm. This allows the
analyst to determine the dominant source of the problem.
The fundamental frequency, 53.3 Hz, of the data in Figure
2.10 is equal to the operating speed of the driven pump
(3,198 RPM).

Vibration
The data shown in Figure 2.11 were obtained from
a velocity sensor mounted on a generator exciter
bearing with a magnet.

Vibration
The amplitude of the time waveform is 0.73
inch/second (IPS)-peak. The amplitude in the
spectrum can be given in spectral component
peaks (0.275 IPS at 60 Hz and 0.24 IPS at 120 Hz)
or in overall root-mean-square (RMS), which is
0.283 IPS

Vibration
The RMS measure of a complex waveform cannot
be obtained from the peak value. If the vibration
waveform is not harmonic (one frequency), the
RMS cannot be obtained by multiplying the peak
value by 0.707 as shown in Example 2.4. Note that
the two RMS peaks in the spectrum do not add up
to the actual RMS values.
Example
2.4.
Peak
and
RMS
Measurements.
From
Figure
2.11
At
60
Hz
RMS
=
0.275
x
0.707
-‐ 0.194
IPS
At
120
Hz
RMS
=
0.24
x
0.707
-‐ 0.170
IPS
Total
RMS
in
the
spectrum
-‐ 0.283
IPS

Excitation
The purpose of vibration analysis is to identify
defects and evaluate machine condition.
Frequencies are used to relate machine faults
to the time-varying forces, termed forcing
frequencies, that cause vibration. It is therefore
important to identify the frequencies of machine
components and machine systems before
performing vibration analysis. The forces are
often the result of defects or wear of
components or are due to equipment design or
such installation problems as misalignment,
soft foot, and looseness.

Vibration
Example Machine Forcing Frequencies.
Mass
unbalance shaft
rotational
frequency
(RPM)
Misalignment two
times
RPM
Bent
shaft RPM
Vane
and
blade number
of
vanes/blades
x
RPM
Electromagnetic two
times
line
frequency

NATURAL FREQUENCIES AND CRITICAL
SPEEDS
Natural frequencies are determined by the design of
a machine or component. For example, the shape of
a bell will determine its natural frequency. The
sound of the bell when it is rung is its natural
frequency. How long it rings is a measure of its
damping. Natural frequencies are properties of a
system and are dependent on the distribution of
mass (material) and stiffness (elasticity). Every
system has a number of natural frequencies.
However, they are not multiples of the first natural
frequency (with the exception of rare instances of
simple components).

NATURAL FREQUENCIES AND CRITICAL
SPEEDS
Natural frequencies are not important in machine
diagnostics unless a forcing frequency occurs at or
close to a natural frequency or impacts occur within
the machine. If a forcing frequency is close to a
natural frequency, a resonance exists, and the
vibration level is high because the machine absorbs
energy easily at its natural frequencies. If the forcing
frequency is an order of the operating speed of the
machine, the resonance is termed a critical speed.
Only natural frequencies in the range of forcing
frequencies are of interest in the vibration analysis
of machines.

REVIEW
• Two important characteristics of vibration are frequency
and amplitude.
• The frequency is the number of cycles per unit of time.
• The period is the time required for one cycle of vibration;; it
is the reciprocal of frequency.
• Amplitude is the maximum value of vibration at a given
location on a machine. It is expressed in mils (displacement),
in.!sec (velocity), or gs (acceleration).
• The amplitude of vibration is expressed in units of peak,
peak to peak, or rms.
• Peak and rms are used with velocity and acceleration;; mils
peak to peak are used with displacement.
• The measures of vibration - displacement (stress), velocity
(fatigue) and acceleration (force) - can be converted one to
the other if the vibration is a single frequency (harmonic).

REVIEW
• A force, or excitation, causes vibration.
• Vibratory forces arise from process variable, improper
design, bad installation, and defects.
• Vibrations are analyzed in the time waveform and the
frequency spectrum.
• Natural frequencies are a property of a machine system
and depend on mass and stiffness.
• Resonance occurs when a forcing frequency is equal to or
close to a natural frequency.
• Vibration is amplified at resonance.

This chapter involves the acquisition of data which will be
analyzed and used to make maintenance or acceptance
decisions on the operability and efficiency of machines.
Sources of data
• physical observations of persons walking through the plant
• periodic collection of vibration data, oil samples, and
thermography snapshots
• continuous vibration monitoring with permanently
installed sensors
• periodic or continuous acquisition of process data like
temperature, pressure, and flow
• design and installation drawings and procedures
• maintenance records
Chapter III – Data Collection

Vibration
The procedures and processes of obtaining
data, types of data, sensors and instruments
for collection of data, and computers for
analyzing and displaying data will be
discussed.
Any vibration analysis is only as good as
the data collected.
This is a very important task and as such good
procedures should be observed.

PHYSICAL OBSERVATIONS by Human
Senses
While there are several types of recorded data
that form the basis for machine fault and
condition analysis, among the most basic data
are direct observations by the person doing the
data collection based on human senses -
hearing, sight, touch, smell, and taste. Human
sensory capabilities, although not analytical,
cannot be underestimated in the machine
analysis process.

Noise
Unusual noises can indicate rubs, bearing
defects, looseness, improper assembly, lack of
lubrication, and any other metal to metal
contact problems. A listening rod or screw
driver can be used to detect a bearing defect or
rubbing in a low speed machine. In pumps, a
sign of flow problems is a noise that sounds
like gravel in the piping. Motors and generators
may emit high frequency whining noises when
they are subject to excessive vibration due to
casing distortion, misalignment, or coupling
unbalance.

Noise
High pitched noise from new gears indicates
bad construction and machinery quality or
design (low contact ratio). Rubbing of guards
by pulleys and belts will cause impacting and
noise. Lack of lubrication in oil starved bearings
or bearings with excessive clearance means
that the bearing needs attention. Excessive
noise is almost always an indicator of trouble.
The experienced data collector will be able to
enhance their analytical capability by learning
to identify noise sources and associate the
physical problem with them.

Sight
The use of sight is an even more powerful tool for
data collectors. Smoke, fire, and catastrophic
failures need and get immediate attention. However,
other mundane faults may go unnoticed for months.
Foundation and bearing pedestal faults are the
source of many cases of excessive vibration.
A flashlight and feeler gage or knife help to root out
these type problems. Squishing oil between joints is
a certain clue of looseness.
Cracks in ducting and piping and other machine
components provide clues to the presence of
excessive vibration. Vibration analysis will confirm
these faults

Sight
Vibration analysis will confirm these faults. The data
collector may have to go off route to measure these
cases.
Hammered
and
Torched
to
Fit.

Smell and Touch
The senses of smell and touch are less important but
should not be neglected. Unusual, abnormal odors are
easily detected by the human sense of smell. Oil
smoke can be smelled long before an oil fire. Ammonia
and other chemical and gas leaks are best detected by
the nose. Even small quantities can be detected. Hot
bearings or other machine parts that are not normally
operating above ambient temperature can be identified
by touch. However, the data collector needs to exercise
extreme caution. A steaming or red hot machine should
not be touched. The water can confirm the
temperatures are above 100⁰ C.
The use of taste is not recommended in this work.

PERIODIC AND CONTINUOUS DATA
COLLECTION
Periodic and continuous non-intrusive data
collection provide current and trended information
about the condition of a machine. The procedure
involves the use of sensors to acquire data, meters
to quantify the measured data, and instruments to
store, manipulate, and present the data. Periodically
acquired data provide an intermittent record of what
is happening in the machine. Whereas continuous
data monitoring and collection provides continuous
surveillance along with the ability to protect the
machine through data based automatic shutdown.

COLLECTION
Measurement of vibration for analytical use is
performed by a sensor, sometimes called a
transducer or pickup, and is nonintrusive to the
machine or process, Figure 3.2. The sensor
transforms the vibration (mechanical motion) of the
mounting location to an electrical voltage which
varies with time, Figure 3.3.

COLLECTION

Selecting a Measure
A measure is a unit or measures of vibration are
standard of measurement that provides a means for
physical evaluation. Examples of measures are
pounds for weight and feet for height. Three basic
available displacement, velocity, and acceleration.
Ideally the sensor would directly provide the
selected measure. Unfortunately, sensor limitations
do not always allow direct measurement of vibration
in the proper measure. Other predictive
maintenance based measures are temperature,
pressure, and viscosity.

Selecting a Measure
The measure is selected on the basis of the
frequency content of the vibration present, the type
of sensor, the design of the machine, the type of
analysis to be conducted (e.g., faults, condition,
design information), and the information sought.

Selecting a Measure
Relative shaft displacement
which is measured with a noncontacting relative
displacement sensor, proximity probe, shows the
extent of bearing clearance taken up by vibration
and is used over a frequency range as wide as the
shaft speed. This permanently mounted probe
measures the relative motion between the point of
mounting and the rotor.

Selecting a Measure
Absolute displacement
which is used for low-frequency vibration (0 to
10Hz) measured on the bearing pedestal, relates to
stress (shaft or structure) and is typically measured
with a double integrated accelerometer. It is called
seismic vibration. Absolute displacement of a shaft
must be measured with either a contacting sensor
or a noncontacting sensor in combination with a
seismic sensor mounted on the bearing pedestal.

Selecting a Measure
Velocity
For general machinery monitoring and analysis in
the span from 10 Hz to 1,000 Hz, velocity is the
default measure. Velocity as a time rate of change
of displacement is dependent upon both frequency
and displacement and related to fatigue. It has been
shown to be a good measure in the span for 10Hz
to 1,000 Hz because a single value for rms or peak
velocity can be used in rough assessments of
condition without the need to consider frequency.
Most modem data collectors use accelerometers but
the signal must be integrated to obtain velocity.

Selecting a Measure
Acceleration
is the measure used above 1,000 Hz;; it relates to
force and is used for such high- frequency vibrations
as gearmesh and rolling element bearing defects.
Acceleration and velocity are absolute measures
taken on the bearing housing or as close to the
bearing as possible.

Selecting a Measure
.
Measure
Useful

Frequency

Span
Physical

Parameter Application
Relative
displacement

(Proximity
probe)
0
– 1000
HZ stress/motion
relative
motions

in

bearings/casings.
Absolute
displacement

(seismic)
0
– 10
Hz stress/motion machine
condition
Velocity
(seismic)
10
– 1000
Hz energy/fatigue
general
machine,

medium-‐
frequency

vibrations
Acceleration
(seismic)
>1000
Hz force
general
machine,

medium-‐high-‐
frequency

vibrations

Selecting a Measure
The rule of thumb for measure selection is that
velocity is used for bearing pedestal measurement
up to 2,000 RPM and acceleration is used above
that machine speed. If the machine has permanent
non-contacting displacement sensors, then
displacement is acquired.

Selecting a Measure
FREQUENCIES
Bearing Frequencies
FTF =
Ω
2
1 −
B
P
cos CA
BPFI =
N
2
Ω 1 +
B
P
cos CA
BPFO =
N
2
Ω 1 −
B
P
cos CA
BSF =
P
2B
Ω 1 −
B
P
1
cos1
CA
FTF = fundamental train frequency CA = contact angle
BPFI = ball pass frequency, inner race Ω = machine speed
BPFO = ball pass frequency, outer race N = number of
rolling elements
BSF = ball spin frequency P = pitch diameter,
in
RPM = shaft speed
B = ball or roller diameter, in
Bearing defect frequencies are same units as machine speed

Selecting a Measure
FREQUENCIES
Bearing Frequencies
General Guideline Bearing Frequencies
(for use in maximum Frequency selection ONLY)
BPFO = 0.41 x RPM x N
BPFI = 0.59 x RPM x N
FTF = 0.41 x RPM
BSF = 0.22 x RPM x N
FAN
blade pass frequency = no blades x RPM

Example
3.1.
Measure
and
Sensor
Selection
-‐ Fan.
Select
a
measure
and
sensor
for
a
fan
operating
at
950
RPM.
The
fan
has

seven
(7)
blades
and
fifteen
(15)
rolling
elements
in
its
bearings.

The
frequencies
of
interest
are
operating
speed
and
orders,
blade
pass

frequency
and
multiples,
and
rolling
element
fault
frequencies,
and
multiples.

operating
speed
frequency
=

]27
^_`
a7
=
15.83
Hz
and
orders
blade
pass
frequency
=
no
blades
x
RPM

blade
pass
frequency
=

]27
^_`
a7
×7
=
110.8
Hz
and
multiples

ball
pass
frequency
of
inner
race
=
0.6
x
no.
balls
x
RPM
bearing
fault
frequency
=

]27
^_`
a7
×0.6×15
=
142.5
Hz
and
multiples
The
majority
of
the
frequency
activity
is
between
150
and
1425
Hz,
if
ten

multiples
are
used.
Therefore,
velocity
measure
will
provide
the
best

information.
An
integrated
accelerometer
or
velocity
sensor
can
be
used
to

acquire
the
data.

Example
3.2.
Measure
Selection
-‐ Low
Speed
Roll
Select
measure(s)
for
low-‐speed
200
RPM
dryer
roll.
The
multi-‐
ton
roll
is
mounted
on
large
rolling

element
(26)
bearings.
Because
the
roll
operates
at
such
a
low

speed,
mass
unbalance
is
not
a
major

consideration
since
the
force
is
small.
The
highest
rolling
element

bearing
frequency
is
the
ball
pass

frequency
of
the
inner
race.
It
can
be
estimated
as

BPFI
=
(0.6)
(RPM)
(N)
BPFI
=
(0.6)
200
(26)
=
3,120
CPM
(52
Hz)
Therefore,
the
frequency
span
is
520
Hz
if
ten
multiples
are
used.

This
value
is
within
the
velocity
range
(see
Table
3.1).

Example
3.3.
Measure
Selection
-‐ Motor
Select
measure(s)
for
a
200
HP-‐four
pole
induction
motor
with
eight
rolling

elements
in
the
bearings.
The
operating
speed
vibrations
have
a
frequency
of

1,800
CPM
(30
Hz)
and
a
frequency
span
of300
Hz,
which
is
within
the
velocity

range.
For
ten
multiples,
the
bearing
frequency
span
is

(BPFI)
(10)
=
(0.6)
(8)
(1,800)
(10)
=
86,400
CPM
(1,440
Hz)
Because
the
majority
of
the
activity
is
in
the
velocity
range,
a
velocity

transducer
can
be
used
even
though
some
activity
is
above
1,000
Hz.
The

useful
frequency
spans
of
all
measures
overlap.
Therefore,
the
measure

should
be
selected
from
the
predominant
portion
of
the
frequency
activity
of

the
component.
For
example,
if
the
default
frequency
span
for
the
bearing

had
been
2,880
Hz
(16
rolling
elements),
acceleration
would
have
been

selected
as
the
measure
for
the
bearings.
Unfortunately,
the
shaft
vibration

frequency
span
of300
Hz
remains
within
the
velocity
range.
Therefore,
two

measures,
velocity
and
acceleration,
are
required.

Vibration Sensors
Magnitude, frequency, and phase between two
signals are used for evaluation. Sensor
selection is based on sensitivity, size required,
selected measure, frequency response, and
machine design and speed. The sensor should
be mounted as close to the source of vibration
as possible.

Proximity probes
The proximity probe (non-contacting eddy current
displacement transducer) shown in Figure 3.5
measures static and dynamic displacement of a shaft
relative to the bearing housing. It is permanently
mounted on many large (greater than 1,000 HP)
machines for monitoring (protection and trending) and
analysis.

Proximity probes
The probe generates a negative DC voltage
proportional to the distance of the shaft from the sensor
(gap). The typical gap is 40 mils or at 200 mv/mil, 8
volts. The negative voltage decreases as the shaft gets
closer to the probe. The probe generates an AC voltage
proportional to the vibration with a scale factor of 200
mv/mil. Therefore, the voltage measured is divided by
the scale factor to obtain the vibration level (Example
3.4). The probe does require an 18 or 24 volt power
supply.

Example
3.4
Assuming the data on Figure 3.3 were taken from
a proximity probe with a scale factor of 200 mv/mil
(0.20 Volts/mil), the peak to peak displacement
would be 1.58 volts divided by 0.2 volts per mil or
7.9 mils-pk to pk. If the measured gap voltage was
7.6 volts, then the gap (distance from the probe to
the shaft) would be 7.6 volts divided by 0.2
Volts/mil or 38 mils.

Velocity transducers
Velocity transducers. The velocity transducer (Figure
3.6) is a seismic transducer (i.e., it measures absolute
vibration) that is used to measure vibration levels on
casings or bearing housings in the range from 10 Hz to
2,000 Hz. The transducer is self-excited - that is, it
requires no power supply. The self-generated signal
can be directly passed to an oscilloscope, meter, or
analyzer for evaluation. A typical velocity transducer
generates 500 mv/(in./sec).

Accelerometers
Accelerometers are used to measure vibration levels
on casings and bearing housings;; they are the
transducers typically supplied with electronic data
collectors. An accelerometer (Figure 3.7) consists of a
small mass mounted on a piezoelectric crystal that
produces an electrical output proportional to
acceleration when a force is applied from the vibrating
mass.

Accelerometers
The size of an accelerometer is proportional to its
sensitivity. Small accelerometers (the size of a pencil
eraser) have a sensitivity of 5 mv/g (1 g = 386.1
in./sec2) and a flat frequency response to 25 kHz. A
1,000 mv/g accelerometer, which is used for low-
frequency measurement, may be as large as a velocity
sensor;; however, the limit of its usable frequency span
may be to 1,000 Hz. The analyst should be aware of
the properties of each accelerometer being used.

Accelerometers
If vibration velocity is desired, the signal is usually
integrated, which electronically converts acceleration to
velocity, before it is recorded or analyzed;; an analog
integrator/power supply is shown in Figure 3.8.
Analog
Integrator
and
Power

Accelerometers
Accelerometers are recommended for permanent
seismic monitoring because of their extended life and
because their cross sensitivity is low. (Cross sensitivity
means that the transducer generates a signal in
horizontal direction from vibration in the vertical
direction.)
However, cable noise, transmission distance, and
temperature sensitivity of the accelerometer must be
carefully evaluated. Excellent guidelines are available
from vendors for accelerometer use.

Sensor Selection
Important considerations in sensor selection include
frequency response, signal-to-noise ratio, size, thermal and
amplitude sensitivity of the sensor, and the strength of the
signal being measured. The frequency range of the sensor
must be compatible with the frequencies generated by the
mechanical components of the machine. Otherwise, another
transducer must be selected and the signal converted to the
proper measure. For example, if the velocity measure is
desired at frequencies above 2,000 Hz, an accelerometer
integrated to velocity should be selected to obtain the
signal. If the time waveform of the velocity measure is
desired, the signal must be acquired from a velocity pickup
or analog integrated signal from an accelerometer, either
within or external to the data collector.

Sensor Selection
The cable that transmits the signal to the data collector can
cause erroneous readings. Many standard cables are
specially wound cords that are more convenient than the
standard coaxial construction. But, because many
conductors are flexible at the core, individual strands may
fail at stress points as a result of handling or packing in a
carrying case. In addition, the terminals must be handled
carefully.

Sensor Mounting
The method used to mount a vibration sensor can affect the
frequency response because the natural frequency of an
accelerometer can decrease, depending on the mounting
method used - hand-held, magnetic, adhesive, threaded
stud (Figure 3.9).
Method Frequency
Limit
Hand
Held 500
Hz
Magnet 2,000
Hz
Adhesive 2,500-‐4,000
Hz
Bees
Wax 5,000
Hz
Stud 6,000-‐10,000
Hz
Approximate
Frequency
Spans
for
100
mv/g

Accelerometers.

Sensor Location
The key to accurate vibration measurement is placement of
the sensors at a point that is responsive to machine
condition. In any event the sensor should be placed as
close to the bearing as is physically possible and in the load
zone. Figure 3.10 shows the optimum points for mounting
sensors for data acquisition in a normal bearing mounting

Sensor Location
The horizontal and vertical locations at the bearing
centerline are shown. These locations are used to sense
the vibrations from radial forces such as mass unbalance.
Vibrations from axially-directed forces such as gearmesh
and bearing faults are measured in the axial direction in the
load zone.

Sensor Location
The sensor must be placed as close to the bearing as
possible, even though placement is restricted by such
components as housings, coupling guards, and fan covers.
In general, radial readings are taken on radial bearings;; that
is, any antifriction bearing with a contact angle of 0°.
Radial bearings are used in electric motors, in medium- to
light-duty fans, and in power transmission units not subject
to axial loading.
Angular contact bearings or any bearing absorbing thrust
have a radial-to-axial coupling that requires an axial
measurement for accurate condition monitoring.

Review
Measure: a unit or standard of measurement
Frequency Span: Fmax or frequency range in the
spectrum
Sensor: device that senses mechanical
vibration and emits an electrical
signal
Frequency Response: amplitude out of an
electrical device such as a
sensor as a function of
frequency

Chapter 4 – Machine Characteristics
The design and function of machines and their
peripheral equipment determine the basic
vibration characteristics encountered in
machine condition monitoring and diagnostics.
Manufacturing and installation quality may alter
the vibrations of newly installed equipment.
These mechanisms determine the amplitude
and frequency of vibrations measured under a
baseline condition.

Chapter 4 – Machine Characteristics
As the machine continues in service, defects
due to fatigue and wear appear as part of the
aging process. The severity of these defects is
dependent on load, lubrication, contamination,
and machine speed. These defects often cause
vibrations at unique frequencies and increases
in the amplitudes of vibrations at existing
frequencies such as operating speed and its
orders.

General Characteristics
It is important to know the connection between
measured vibrations and the function and
operating mechanisms of the machine. By
knowing how the machine works and what can
go wrong the analyst can better determine what
a measured vibration pattern means. Vibrations
are generated by forces which are caused by
mechanisms involved in the design,
manufacturing, installation, and wear and
structural failures of the machine.

The more information available about the
machine design, construction, supports,
operational responses, and defect responses,
the easier will be the diagnosis of defects and
malfunctions. All service equipment should be
cataloged and the following data listed.

• broad characteristics such as rotational frequencies,
gear mesh, vane pass, and bearing defect frequencies.
• vibration, temperature gradients, or pressure initiated
by an operating component or system.
• vibration responses to process changes.
• characteristics identified with the specific machine
type.
• known natural frequencies and mode shapes.
• sensitivity to vibration from mass unbalance,
misalignment, distortion, and other malfunction/defect
excitations.
• sensitivity to instability from wear or changes in
operating conditions.

SOURCES OF VIBRATION
Source
Design
and

Function
Manufacturing Installation Defects
mass

unbalance
•
• •
eccentricity • • • •
misalignment • • •
looseness • • •
distortion • • •
cogging •
gear
defects • • •
bearing

defects
•
•
•
electrical • • • •
flow
noise •

SOURCES OF VIBRATION
Source
Design
and

Function
Manufacturing Installation Defects
natural

frequency
• •
thermal • •
bad
grout • •
reciprocating •
flexible • •
oil
whirl • • •
excessive

clearance
•
•
•
•
poor
quality • •
overstressed •
hydrodynamic • • •
acoustic • • •
machining • • •

Design and Function
Mass unbalance occurs when the mass center of a
rotating part is not located at the geometric center.
However, it may result from unsymmetrical design of
a part such as a coupling hub. Normally
components and parts would have a symmetrical
design to avoid this problem. The frequency of mass
unbalance is the shaft operating speed and the
amplitude is dependent on the mass unbalance and
speed squared.

Design and Function
Mass unbalance
. However, mechanisms such as the cam in Figure
are likely to be unbalanced because the mass
center is not at the geometric center.

Design and Function
Cogging of chain links of a sprocket, Figure 4.4,
occurs because of the intermittent forces generated
from the sprocket teeth entering and exiting the
chain. The cogging frequency is the number of
sprocket teeth times the RPM of the sprocket.
Similarly, the frequency of a timing belt is the
number of grooves in the pulley times the RPM of
the pulley.

Design and Function
Flow noise is normally generated from inlet
conditions (mixed flow from elbows, reducers, or
increasers) or operating off the best efficiency point,
BEP, of the pump. Straight flow is usually ensured
by having at least ten (10) pipe diameters of
straight, constant diameter pipe prior to the pump
inlet. BEP operation is designed into the system by
proper system design. Too little back pressure
causes cavitation while too high back pressure
causes recirculation of the flow at the inlet. Both
conditions cause random noise and vibration and
sound like gravel circulating in the pump.

Design and Function
Certain responses (Table 4.2), including vibration,
temperature, and pressure can be related to
components of the system

Design and Function
Component Frequency
antifriction
bearings ball
pass
frequency,
outer
race
ball
pass
frequency,
inner
race
fundamental
train
frequency
rotating
unit
frequency
ball
spin
frequency
hydrodynamic
journal
bearings frictional
frequency,
whirl
frequencies
gears rotating
unit
frequency

gear-‐mesh
frequencies
and
harmonics

harmonics
of
gear-‐mesh
frequencies

assemblage
frequencies

system
natural
frequencies
(gear-‐
tooth
defects)
Blade
wheels
and
impellers Rotating
unit
frequencies
vane
and
blading
frequencies

harmonics
of
vane
and
blading

frequencies

Design and Function
Component Frequency
rotors trapped
fluid
rotational
frequency

directional
natural
frequencies

higher
harmonics
couplings
and
universal
joints orders
of
rotating
frequency
reciprocating
mechanisms rotating
frequency
and
its
orders
Electric
motor
rotors sidebands
at
no
poles
x
slips

Chapter 5 – VIBRATION INSTRUMENTS
The sensor which changes the mechanical
motion of the machine to an electrical signal is
connected to an instrument which provides an
analytical read out and/or print out. The read
out can be as simple as a single number from a
meter or a waveform from an oscilloscope.
More elaborate analyzers provide spectra
(amplitude versus frequency) and digital time
waveforms. Data collectors provide overall
values, filtered values, phase readings,
spectra, and time waveforms.

Figure
5.1.
Time
Waveform

Figure
5.2.
Spectrum
(Top)
and
Waveform
(Bottom).

Figure.
Trend
on
Three
Bearing
Pedestals.

Data Collectors and Analyzers
The data collector (and analyzers are all Fast
Fourier Transform (FFT) based calculated off a
digitized waveform that is obtained from a
sensor.

Data Collectors and Analyzers
The spectrum of Figure
5.10 (upper plot) has
400 lines (bins) and a
frequency span of
1,000 Hz. Therefore,
there are 400 divisions
across the horizontal
frequency scale where
data can be located.
Any frequency
between these lines is
included in the closest
adjacent bin.

Chapter 6 – VIBRATION TESTING
Basically there are four types of vibration tests
that the machine analyst conducts
• periodic monitoring
• fault and condition analysis
• Acceptance
• design.

Periodic monitoring
serves a predictive maintenance program by
acquiring vibration data on a routine basis on
organized routes with data point specific
collector setups. The data collected on the
route are compared against previous data and
alarm settings to evaluate the machine's
change in condition. Data are downloaded into
a computer for trending and analysis.

Machine analysis
is conducted when trended data exceed alarm
levels. Frequencies and amplitudes are
evaluated to determine the fault and severity of
the problem.

Acceptance testing
is used to determine whether a new or repaired
machine meets the specification in the
purchase agreement. Usually decisions are
made on the basis of agreed upon
measurements and vibration levels according
to specified procedures.

Design testing
Basic tests for design characteristics are
conducted to determine machine dynamic
properties such as natural frequencies,
damping, and critical speeds.

PERIODIC MONITORING
Periodic monitoring of machine vibrations is
one of the principal components of any
predictive maintenance program because it
provides information that allows decisions to be
made on production scheduling, minimizes the
occurrence of catastrophic equipment failures,
and provides rational management of assets
and resources. By using the electronic data
collector, an individual can effectively monitor
many machines for signs of equipment
malfunction, wear, and failure during
production.

PERIODIC MONITORING
Machine Knowledge
The person collecting data should have a
working knowledge of the machines being
monitored. This knowledge involves internal
construction, supports, foundations and piping
as well as how the machine works internally
(Chapter 4). The experienced data collector will
be aware of and report unusual physical
behavior (Chapter 3) through senses of touch,
sound, sight, and smell.

PERIODIC MONITORING
Machine Knowledge
These signs of deterioration are often vital in
the process of non-intrusive monitoring.
Knowledge of speeds and characteristics
common to individual machines (Chapter 4) is
absolutely essential. There are many texts and
magazines on machine function which can heIp
the data collector continuously expands
machine knowledge. Viewing the machine
being repaired or having a background as an
operator, millwright, or mechanic provide
invaluable experience.

PERIODIC MONITORING
Data Collection Procedures
The data collection route can be based on plant
layout, machine train, machine type, or data
type. Whatever the criterion used for route
design, it should allow efficient movement of
the data collector from machine to machine and
data point to data point. Figure 6.1 shows a
route for a 4,000 HP motor driven boiler feed
pump while Figure 6.2 shows a schematic
diagram of the location of measurements.

PERIODIC MONITORING
Figure
6.1.

Example
of
a

Route
for
Motor

Driven
Boiler

Feed
Pump

PERIODIC MONITORING
Figure
6.2.
Location
of
Measurement
Points.

PERIODIC MONITORING
Transducer Positioning and Mounting.
While collecting data on a route, the data
collector programming should be consistent
with transducer positioning and mounting - the
measured position relates to the data collector
recorded position. For this reason, the machine
measurement positions should be permanently
marked.

PERIODIC MONITORING
Transducer Positioning and Mounting.
Magnet mountings require some care in
attaching the transducer. The transducer needs
to be mounted so that it does not rock or is not
loose - this may cause erroneous, noisy data. It
is a good idea to try to move the transducer
after it is magnetically attached. If it rocks, turn
it until it does not move when you put a minor
force on it.

PERIODIC MONITORING
Some
general
recommendations
should
be
considered
when
vibration
is

sampled
on
equipment
with
known
faults:

1.
Never
stand
next
to
drive
couplings
or
other
locations
where

components
would
likely
come
out
in
the
event
of
failure.

2.
If
temporary
test
equipment
is
setup
for
extended
monitoring,
locate
the

equipment
on
the
end
of
the
machine
train,
usually
on
the
drive
end.

3.
Plan
an
escape
route
when
approaching
the
machine.

4.
Determine
a
threshold
vibration
level
above
which
continued
testing
will

not
be
performed.
Discuss
this
level
with
plant
personnel
prior
to
testing

if
necessary
so
that
appropriate
action
can
be
quickly
taken
to
shut
the

machine
off
if
the
threshold
values
are
exceeded.

5.
Be
prepared
at
all
times
to
stop
testing,
move
to
a
lower
risk
area,
and

possibly
shut
the
machine
down
if
conditions
change
so
that
noise
or

vibration
levels
obviously
increase.

PERIODIC MONITORING
Some
general
recommendations
should
be
considered
when
vibration
is

sampled
on
equipment
with
known
faults:

6.
NEVER
stay
around
a
machine
that
has
known
faults
with
increasing

severity.

7.
NEVER
continue
testing
once
the
pre-‐determined
safe
vibration

threshold
has
been
identified
to
be
exceeded
on
any
sample
point.

8.
NEVER
continue
operating
a
machine
with
an
obvious
mechanical
fault

such
as
loose
hold
down
bolts,
coupling
element
progressing
damage

(rubber
material
falling
under
coupling),
metal
shavings
or
bolts
failing

from
the
machine,
etc.

PERIODIC MONITORING
Figure.
Possible
Unsafe
Data
Acquisition
Locations

PERIODIC MONITORING
Screening and Trending
The central tasks of periodic monitoring are
screening and trending. Screening is the process of
routine data sampling and comparison of that data
to alarms to determine if the condition of the
machine has changed.

PERIODIC MONITORING
This process typically involves amplitude changes
using overall peak or RMS values of velocity or
acceleration. Changes in vibration levels can be
attributed to long- and short-term changes in
machine speed, production conditions, mechanical
defects, thermal conditions, product buildup, and
alignment and foundation function.

PERIODIC MONITORING
A change in measured value of two to two and one-
half usually indicates a genuine change in
condition leading to more detailed analysis, more
frequent monitoring, shut down for inspection or
parts replacement. The severity of the problem and
management procedures dictate what combination
of these actions will be followed.

PERIODIC MONITORING
Unfortunately, there are cases where trending of
overall amplitude values of vibration does not work.
Typically, the problem is either lack of signal
strength (very low amplitudes), noise problems, or
masking of the low amplitude important data by
normal vibration levels. For example, low amplitude
rolling element bearing defect frequencies may be
sending a very important message about an
impending bearing failure. However, there is a much
higher amplitude component of vibration due to
mass unbalance or gearmesh present (Figure 6.8).

PERIODIC MONITORING
Bearing
Frequencies
Masked
by
Gearmesh and
Mass
Unbalance
Frequencies.

PERIODIC MONITORING
Changes in overall amplitude due to the bearing
defect may be a small percentage of the existing
vibration amplitude. Trending of overall amplitude
values in this case is useless. Bearing failures will
be missed. There are three ways of dealing with this
problem.

PERIODIC MONITORING
The first method involving moderately low (0.05 IPS-
peak) bearing defect frequency amplitudes uses
RMS trending of band filtered values (Figure 6.8)
which eliminate the higher amplitude normal
vibration levels. In other words, only the data
important to failure are being trended. In actual point
of fact, usually band (filtered) trending is an adjunct
to overall trending. For example, a trend chart like
Figure 6.7 would be recorded for Bands 2,4, and 6
in Figure 6.7.

PERIODIC MONITORING
The second method involves routine high resolution
spectrum analysis where important bearing defect
frequency amplitudes are very low (less than 0.02
IPS-peak). Here the severity of the problem is
defined by the presence of frequencies (defect
frequencies and sidebands, Figure 6.8).

PERIODIC MONITORING
The third and last method of dealing with low
amplitude signals involves the use of procedures
that filter out low frequency high amplitude portions
of the vibration data prior to processing. The
peakness and enveloping methods depend on high
frequencies to carry the failure oriented information
to the analyst. Because of transducer mounting
uncertainties and design natural frequency variance,
these methods in general do not yield trendable
results or indicate the severity of the problem. They
do, however, indicate the presence of a problem.

PERIODIC MONITORING
Therefore, providing a message to management to
analyze further or go into the machine and
determine the severity. These methods will indicate
where the problem is located so that minimum
energy will be exhausted.

MACHINE ANALYSIS
Machine testing for in-depth analysis has two levels
• Fault analysis - what and where is the problem
(Chapter 7)
• Condition evaluation - what is the severity of
the problem (Chapter 8).

MACHINE ANALYSIS
Fault analysis
In the time waveform, the data sample is essentially
unprocessed raw data that has information about
the condition of the machine. The analyst obtains an
overview of what is at fault and the severity of the
problem from the periodicity, shape, and amplitude
of the time waveform, Figure 6.9 - lower plot.

MACHINE ANALYSIS
Fault analysis
The waveform contained in Figure 6.9 shows a
shape and periodicity that indicates vibration of one
and two times operating speed (small peak within
the period) is present. The amplitude of 1.39 IPS
indicates that it is a serious problem.

MACHINE ANALYSIS
Fault analysis
For more analytical details, the spectrum, amplitude
versus frequency - Chapter 7, is examined.
Frequencies in the spectrum, Figure 6.9 - upper
plot, confirm that the frequencies of operating speed
and twice operating speed are present. Since this is
a generator where vibration generated by two times
operating speed (mechanical) and two times line
frequency (electrical) can be present, the fault
cannot accurately be defined through the use of
frequency matching without further in- depth
analysis.

MACHINE ANALYSIS
Fault analysis
Most spectrum analysis is done through frequency
matching - known machine frequencies such as
operating speed are matched to frequencies present
in the vibration spectrum. The problem in Figure 6.9
is that the frequencies of twice operating speed
7,200 cpm - 120 Hz (mechanical- indicating
misalignment) and twice line frequency (electrical -
indicating air-gap or stator faults) are equal. Thus
one or the other or both faults could be present.

MACHINE ANALYSIS
Condition Evaluation
Condition Evaluation is the process of determining
the severity of the vibration and what it means in
terms of machine condition. Most condition
evaluation is done with charts and graphs where
overall RMS or peak values of vibration are
matched against the standard chart. For example,
the value of 1.39 IPS on Figure 6.9 (lower plot) time
waveform would be compared to a chart.

MACHINE ANALYSIS
Condition Evaluation
Unfortunately, this provides only a rough
assessment of condition and more detailed analysis
is usually required because these charts are not
machine specific. However, some charts do have
adjustments of allowable values for type, mounting,
and size of machines.

MACHINE ANALYSIS
ACCEPTANCE TESTING
Acceptance testing of new and repaired equipment
provides some assurance of the quality of
workmanship provided the purchase specification is
properly written. The acceptance test is based on a
purchase specification that includes procedures,
measurement locations, process conditions,
measures and how they are processed, and
acceptable levels of vibration. Acceptance testing
may be conducted in the shop prior to equipment
release or it may be conducted in the field.

MACHINE ANALYSIS
ACCEPTANCE TESTING
Due to mounting, process activation, and other
differing conditions, levels of vibration will differ in
these methods. If no specification exists, a baseline
test should be conducted and the data compared
with general vibration standards. The baseline test
should reflect the operating conditions of the
machine and its environment to the best extent
possible.

MACHINE ANALYSIS
ACCEPTANCE TESTING
The purchase specification should include testing
procedures as well as acceptable levels of vibration;;
that is, it should be similar to ISO, IEC, or OM
standards. For example, ISO 10816 contains
information about equipment mounting, the
measures to be used, transducer locations, and
acceptance levels.

MACHINE ANALYSIS
Procedure for Acceptance Testing
1.

Read
the
specification
and
determine
what
is
legally
required
for

acceptance.

2.

If
no
specification
exists,
determine
what
the
owner
expects.

3.

Based
on
available
information
determine
the
measurement
locations,

type
of
data
to
be
evaluated,
data
processing
if
any,
machine
speeds,
and

process
conditions.

4.

Select
transducers
and
set
up
the
data
collector,
analyzer
or
tape
recorder

to
acquire
data.

5.

Check
the
mounting
conditions
-‐make
sure
loose
bolts
or
safety
issues
do

not
exist.

6.

Conduct
the
machine
test
keeping
records
of
data
acquired.

7.

Evaluate
the
data
for
acceptance
and
give
reasons
if
the
machine
should

not
be
acceptance.

8.

Write
a
brief
report.

MACHINE ANALYSIS
DESIGN TESTING
Design characteristics of the machine such as
natural frequencies, critical speeds, and damping
levels are important factors in vibration analysis.
Specialized tests have been designed to determine
this information because of the influence of design
on vibration severity. Abnormally high vibration
levels cause bearing failures, rubs, and shaft and
structural fatigue failure. In addition, high vibration
levels may affect process quality - imaging and
printing are two examples

MACHINE ANALYSIS
DESIGN TESTING
Resonance - matching natural frequencies to forcing
frequencies - cannot be tolerated in most machines.
Therefore, special vibration tests have been devised
to determine the common design parameters -
natural frequencies and critical speeds. These
advanced tests will be covered in subsequent books
at advanced levels.

Chapter 7 – BASIC ANALYSIS
Vibration analysis is conducted to determine
the origin of the vibration. Vibration sources
include mechanical and electrical defects,
normal functioning of the machine or its
process, installation problems, and faulty
design. These sources all involve the
generation of forces which cause vibrations.

SPECTRUM ANALYSIS
Basic vibration analysis is about matching
frequencies - that is known machine frequencies are
related to those of the measured vibration. The
typical vibration analyzer provides the vibration
waveform (usually called the time waveform) and a
spectrum - a plot of vibration level versus frequency.
Figure 7.1 (lower plot) shows a data sample
obtained by a sensor from a generator exciter
pedestal measurement.

SPECTRUM ANALYSIS
The lower plot, called the time waveform, shows the
data as it was acquired from the exciter by the
sensor. It has a period (repeat cycle) of 16.7 mSec
or 0.0167 see per cycle of vibration.
by using the formula f = 1/T = 60 Hz = 3600 RPM.
Note the time waveform in Figure 7.1 has a second
peak in between the principal peaks. This indicates
that another vibration frequency is present.

SPECTRUM ANALYSIS
The spectrum, upper plot, is required because the
relative size (amplitude) of the two peaks cannot be
readily determined from the time waveform.
The spectrum displays the amplitude and frequency
of each vibration component is required for analysis.
In this case the frequency of the second vibration
component is 120 Hz or exactly twice the first
vibration component which is equal to operating
speed.

SPECTRUM ANALYSIS
FAST FOURIER ANALYSIS
The spectrum (a plot of amplitude versus frequency
- upper plot of Figure 7.1) is computed from the time
waveform by a numerical process called an
algorithm. The process commonly used is the fast
Fourier transform.

SPECTRUM ANALYSIS
When the analyst is setting up the analyzer, three
decisions have to be made.
1. Fmax is the maximum frequency measured -
1,250 Hz in Figure 7.1.
2. The number of lines which is tied to the number
of data points - 400 lines in Figure 7.1.
3. The window which is related to the type of
analysis - Hanning in Figure 7.1.
The number of lines and window are not shown on
the plot.

SPECTRUM ANALYSIS
Fmax
The Fmax should be set for the maximum frequency
desired but should not be excessively high;;
however, it must cover the frequency range of
spectral activity. The Fmax is determined from the
design of the machine.

SPECTRUM ANALYSIS
The number of lines determines the detail of the
spectrum. The fact that Figure 7.1 has 400 lines
means 400 discrete points are plotted across the
frequency axis - no information is provided between
the lines. If a frequency does not fall on a line, then
it will be included in the closest line with an
amplitude error dependent on the window used. If
two vibration components are close together and fall
in the same bin (the area around the line - Figure
7.2), they are summed and a true picture is not
obtained.

SPECTRUM ANALYSIS
Figure
7.2.
Bins
and
Lines.

SPECTRUM ANALYSIS
However, the penalty for more lines is data
acquisition time. Thus it takes more time to acquire
data when using a large number of lines.
Data Acquisition Time =
ef4g?C
Eh
iDj?A
(e)

klmn

For example, in the spectrum of Figure 7.1 (upper
plot), the data acquisition time per sample was 400
lines/1,250 Hz or 0.32 sec. Ten averages were
made - thus the total data acquisition time for the
spectrum was 3.2 sec (3,200 mSec).

SPECTRUM ANALYSIS
Without the window, the resolution (ability to resolve
and display closely spaced frequencies) would be
the Fmax divided by the number of lines or Fmax
/N= 3.125 Hz/line in Figure 7.1. But the window,
which is required because the FFT process
degrades the resolution by spreading vibration
component energy into adjacent bins, lowers the
ability to resolve closely spaced frequencies. The
amount of actual resolution then is equal to two
times the Fmax and the window factor divided by
the number of lines as shown below.

SPECTRUM ANALYSIS
Resolution (Hz) =
The Hanning window which was used in Figure 7.1
has a window factor (WF) of 1.5.
2 ×
Fmax

(Hz)

N
× WF

ANALYSIS TERMINOLOGY
Operating Speed and Orders
The frequency of operating speed is the foundation
of spectrum analysis of mechanically generated
vibrations. Many other frequencies in the spectrum
are related to the operating speed - being multiples
(orders) or non-multiples.

Figure 7.3 shows a spectrum from a generator
pedestal with one component (0.263 IPS-peak) at
60 Hz - the frequency of operating speed.

Vibrations shown in Figures 7.3 is symptomatic of
mass unbalance

Figure 7.4 shows a spectrum with operating speed
vibrations 60 Hz and a second order 120 Hz.

Vibrations shown in Figures 7.3 is symptomatic of
misalignment

Electrical Frequencies
Line frequency is the basic frequency of AC electric
power and electrically generated vibration. Line
frequency is 60 Hz in North America and 50 Hz in
the remainder of the world. Line frequency will not
be 60 Hz when variable frequency drives are
analyzed. In each case the base frequency must be
obtained prior to analysis.

Figure 7.5 shows data from a motor operating at
3,588 RPM.

The second order is dominant (upper plot) but may
contain mechanical (2x operating speed) and/or
electrical (2x line frequency) vibration.

The lower plot of Figure 7.5, which is a zoom
(increased resolution) of the data on the upper plot,
shows mechanical (119.6 Hz) and electrical (120
Hz) symptoms.

COMMON MACHINE FAULTS
Table
7.4.
Common
Machine
Faults.
•

Resonance
and
critical
speeds

•

Mass
unbalance

•

Misalignment

•

Looseness

•

Distortion

•

Beats

•

Rolling
element
bearing
defects

•

Gear
defects

•

Motor
faults

•

Pumps

•

Fans

Resonance and Critical Speeds
All systems have natural frequencies that are
not active unless they are excited by some
force. When a forcing frequency such as
operating speed is close to or equal to a natural
frequency, the condition of resonance occurs
and the vibration is amplified beyond what
would normally be obtained for that force.
When the rotor of the system excites the
natural frequency, the frequency of the rotor
that matches the natural frequency of the
system is called a critical speed.

Figure 7.8 is an example of a resonance in a
vertical pump support structure.
Figure
7.8.
Vertical
Pump
Resonance.

The operating speed of the pump is close to
the natural frequency of the pump frame and
support. This is a common problem with pumps
driven by variable frequency driven motors. It is
difficult to design a system where no natural
frequencies will occur in a wide speed range.
Natural frequencies usually respond
directionally. Therefore, if the vibration level is
high in one direction but not 90° from it, that is
an indication that it may be resonant.

Mass Unbalance
Mass unbalance occurs when the geometric center
(shaft centerline) and the mass center of a rotor do
not coincide. Unbalance is a once-per-revolution
fault - that is, it creates vibration at the frequency of
rotor speed.

Mass Unbalance
it creates vibration at the frequency of rotor
speed
Figure
7.9.
Mass
Unbalance
of
a
Generator.

Mass Unbalance
This can be done with phase analysis because
the nature of the forces is different. The
spectrum for mass unbalance normally has a
high amplitude component at a frequency of
operating speed (Figure 7.9 - 3,600 RPM) and
low amplitude orders of operating speed. Mass
unbalance appears to be similar to resonance;;
however, by moving the sensor 90° the
vibration should be similar in amplitude.

Misalignment
The magnitude of the resulting vibration is
dependent on the radial stiffness of the components
(bearings, shafts, seals, couplings) in the system.
It is characterized by two peaks at 1x and 2x.
The second order component of vibration in cases
of severe misalignment can exceed the first order.
High first-order axial vibration is also a symptom of
misalignment.

Misalignment
Figure
7.9.
Generator
Misalignment.

Looseness
Excessive bearing clearances and untightened bolts cause
impacts that can be identified in the spectrum as once-per-
revolution vibration plus orders of operating speed
Figure
7.11.

Fan

Looseness.

Rolling Element Bearing Defects
When a rolling element passes over a bearing defect in the
races or cages (Figure 7.14), pulse-like forces are generated
that result in one or a combination of bearing frequencies.
This causes pulses in the time waveform and bearing
frequencies and harmonics in the spectrum (Figure 7.15) at
nonsynchronous (not an order of operating speed) frequency
and resonance.

Figure
7.14.
Nomenclature
of
Rolling
Element
Bearings.

Figure
7.15.
Rolling
Element
Bearing
Defects.

Figure 7.15 shows the spectrum from a bearing supporting a felt
roll (530 RPM)). It has a fundamental ball pass frequency of the
outer race of 56.25 Hz or 6.37 times operating speed. The bearing
frequencies would be calculated using the above formulas or
would be given by the bearing manufacturer as a multiple of
operating speed - in this case BPFO = 6.37 x operating speed. In
Figure 7.15 the third harmonic has sidebands (small peaks) at
operating speed frequency (530 RPM/60 = 8.83 Hz).

• ball pass frequency of the outer race (BPFO);; generated by balls
or rollers passing over defective outer races.
• ball pass frequency of the inner race (BPFI);; generated by balls
or rollers passing over defective inner races.
• ball spin frequency (BSF);; generated by ball or roller defects.
• fundamental train frequency (FTF);; generated by cage defects
or improper movements.
• ∅ = contact angle;; angle between lines perpendicular to the
shaft and from the center of the ball to the point where the arc of
the ball and the race make contact (Figure 7.14c).
• N = number of rolling elements (balls or rollers).
• P = pitch diameter, in.
• B = ball or roller diameter;; average value for tapered bearings,
in.
• RPS = speed of rotating unit in revolutions per second.

Ω =
RPM/60
=
RPS
FTF =
Ω
2
1 −
B
P
cos∅
BPFI =
N
2
Ω 1 +
B
P
cos∅
BPFO =
N
2
Ω 1 −
B
P
cos∅
BSF =
P
2B
Ω 1 −
B
P
1
cos1
∅

Gear Defects
Gearboxes generate high-frequency vibrations as a result of the
gearmeshing function of the box. The greater the number of gear
teeth in mesh at any instant the smoother the performance of the
box. Gearbox faults fall into two categories - gear meshing and
broken teeth. Gearmesh frequency is number of teeth on the
pinion times speed of the pinion or number of teeth on the gear
times gear speed. These frequencies will be equal.
The gearmeshing problem occurs because of uneven local wear,
pitting, roughness, and/or machine gear tooth quality. As the teeth
go through mesh the vibration varies because the surface quality
of the teeth vary. This causes vibration with amplitude modulation
(change) which results in gearmesh frequency and sidebands in
the spectrum

Fans
On fans, pumps, and other bladed machines, look for frequencies
that are multiples of operating speed that relate to the number of
blades or vanes. Figure shows data from a six (6) bladed fan.

Fans
The spectrum (upper plot) shows vibration at 92.8 Hz which is
close to six (6) times the operating speed (15.6 Hz). This vibration
is generally caused by the blades passing the discharge duct.

CHAPTER 8- VIBRATION SEVERITY
BEARING HOUSING EVALUATION
Table 8.2 shows peak and RMS velocity levels for machine
vibrations based on evaluation of operating speed faults.
MACHINE
CONDITION
ACCEPTABLE
LEVELS
(IPS)
RMS PEAK
Acceptance less
than
0.08 less
than
0.16
Normal less
than
0.12 less
than
0.24
Surveillance 0.12
to
0.28 0.24
to
0.7
Unacceptable more
than
0.28 more
than
0.7
Table
8.2.
Acceptable
Levels
of
Machine
Vibrations
for
Operating
Speed
Faults.

CHAPTER 8- VIBRATION SEVERITY
BEARING HOUSING EVALUATION
Figure 8.1 shows vibration data acquired from a lobed blower operating at 3,563
RPM.

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