FAUJI FERTILIZER COMPANY LIMITED

Technical Training Centre

Machinery Vibrations

PREPARED BY : TAUFEEQ ARSHAD MIR

Table of Contents
CHAPTER – 1
Introduction
 Vibration
 Amplitude
 Frequency
 Phase Angle
 Phase Angle Measurement
 Time and Frequency Domain

CHAPTER – 2
Vibration Plots
 BODE Plot
 Polar Plat
 Waterfall Plot
 Orbit

CHAPTER – 3
Source of Vibration
 Imbalance
 Misalignment
 Soft Foot & Sprung Foot
 Looseness
 Bearings
 Rubbing
 Oil Whip Instability
 Oil Whirl Instability
 Gear Mesh Frequency
 Vane Pass Frequency
 Resonance
 Cavitation
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Introduction
Amplitude
Amplitude, whether expressed in displacement, velocity, or acceleration, is
generally an indicator of severity. It attempts to answer the question, “Is this
machine running smoothly or roughly?” The ability to measure the shaft with
proximity probes has helped greatly in providing more accurate information
with regard to the amplitude of vibration.

n. In the past, when only casing measurements were available, amplitude of the
casing vibration was the only available parameter for severity. Whereas the
casing measurement were able to indicate the presence of some machinery
malfunction conditions, by and large, the casing measurement proved
inadequate for proper machinery protection..

Amplitude of vibration on most machinery is expressed in peak-to-peak mils

displacement. With proximity probes mounted at or near the bearings,
vibration tolerances can be established which provide for the maximum
excursion that the shaft makes with respect to the bearing. Today, most
continuous monitoring of critical machinery is provided with a peak-to-peak
displacement measurement either in mils or micrometers.

Frequency
The frequency of vibration (cycles-per-minute) is most primarily due to the
tendency of machine vibration frequencies to occur at direct multiples or sub-
multiples of the rotational speed of the machine. It is necessary only to refer to
the frequency of vibration in such terms as one time rpm, two times rmp
rather than having express all vibrations in cycles-per-minute or hertz.

Also, the tendency of certain malfunctions to occur at certain frequencies has

helped to segregate classes of malfunctions from others. It is extremely
important to note, however, that the frequency / malfunction relationship is
not mutually exclusive. This means, a vibration at one particular frequency
often has more than one malfunction associated with it. There is no one-to-
one relationship between malfunction and frequencies of vibration.

Frequency is an important piece of information with regard to analyzing

rotating machinery, and can help to classify malfunctions. However, frequency
is only one piece of data and is necessary to evaluate all other pertinent data
before arriving at any conclusion.

Phase Angle
Phase is the relative shift of a vibrating part to a fixed reference point on
another vibrating part. That is, phase is a measure of the vibration motion at
one location relative to the vibration motion at another location.

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Figure 1 shows the two systems in-place with each other or vibrating at the
same rate with 0 phase difference and the resulting time waveform.

Figure 2 shows two masses vibrating with 90-phase difference. That is mass
#2 is one-fourth of a cycle ahead of mass #1.

Figure 3 shows the same two masses vibrating with a 180-phase difference.
That is , at any instant of time, mass # 1 moves downwards at the same as
mass # 2 moves upwards, and vice versa.

Figure 4 shows how phase relates to machine vibration. The left sketch shows
a 0 phase difference between bearing position 1 and 2 (in-phase motion); while
the right sketch pictures a 180 out-of-phase difference between these positions
(out-of-phase motion).

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Phase can be measured in angular degrees by using a strobe light or electronic

photocell. Figure 5 illustrates a typical strobe light method for taking phase
measurements. In this method, the strobe light must first be “tuned” to the
speed of the rotating shaft and thereafter the vibration amplitude and phase
must be recorded. The transducer should be moved from one bearing to
another taking data in horizontal, vertical and axial directions. One will have to
find and record the new position of the reference mark each time the
transducer is moved to a new location or direction. Manipulation of the strobe
light can be made in any way to see the reference mark, but the transducer
must be firmly mounted and kept in place for each reading. However, if a
photocell is being used, both the photocell and transducer will have to be
locked down; with each subsequent measurement, only the transducer will be
moved to the next location.

The photocell method shown in figure 6 utilizes a stationary photocell targeted

at a piece of reflective tape mounted to the rotating component of interest.

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The photocell method is more accurate than hand held strobe light since the
instrument measures the phase angle within very accurate tolerances, whereas
the strobe light method include human error in attempting to accurately read
the angular position of the reference mark.

Time and Frequency Domain

There are two ways to look vibrations.
 Time Domain
 Frequency Domain

In the former case, amplitude is on the vertical axis, and time is on the
horizontal axis; whereas in the frequency domain display, frequency is
exhibited on the horizontal axis. The frequency domain display is one of the
most powerful windows into machine monitoring. All machine diagnostics and
predictive maintenance instruments display vibrations in the frequency
domain.

Figure 5 illustrates this concept of separating a complex wave into its

components. Figure shows two pure waves. The upper wave is four times the
frequency of the lower wave and one-fourth its amplitude. When these two
waves are mixed together, the result is shown in Figure 5-b. Both waves can
still be visually seen in the resultant wave pattern.

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Figure 6 shows the segregation of more complicated waveform. Note that the
total waveform is actually made up of a series of smaller waveforms, each of
which correspond to an individual frequency (1 X RPM, 2 X RPM, 3 X RPM,
etc.). Each of these individual waveforms then algebraically adds to one
another to generate the total waveform. In the same figure, a view looking
along each individual waveform is shown allowing the analyst to see the
frequency domain of amplitude versus frequency.

The frequency domain view of the time waveform visually shows each simple
sine wave as a vertical line that has amplitude (determined by its height) and
frequency (determined by its position along the frequency axis). The frequency
domain representation of a time waveform is called spectrum. A spectrum is
sometimes referred to as a “signature” or an “FFT”.

Bode`, Polar, and Waterfall Plots

The Bode and Polar plots are just different ways of looking at the same
vibration data. The Bode plot is a graph of amplitude versus shaft revolutions
per minute and phase versus shaft revolutions per minute. Figure 6.12 is a
hypothetical Bode plot, showing how the phase angle data is presented above
the vibration amplitude with speed as the horizontal axis. A tracking filter is
needed to obtain this plot. The tracking filter locks onto the shaft revolutions
per minute and stays with it as it changes. In this way it records the amplitude
and phase at different speeds. This is very useful in finding shaft resonances.
At resonances, the amplitude peaks and the phase changes. The shaft
revolutions per minute can then be read from the horizontal axis, and the
critical speeds or resonances are identified. Figure 6.13 is a Bode plot acquired
from a small machine during its run-up. Resonances are identified as peaks at
646 and 1418 rpm, with corresponding phase changes. There appears to be
another, highly damped, resonance at 2921 rpm.

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The polar plot of Fig. 6.14 contains the same machine run-up data as the
previous Bode plot. Each loop represents a resonance of some kind because
the phase angle underwent a 180º reversal before continuing. The polar plot is
a graph of amplitude versus phase using polar coordinates. Polar coordinates
identify a point on a plane by a vector from the origin. The two numbers
needed to identify the point are the length and angle of the vector.

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For example, point A, in Fig. 6.15a, can be identified in the normal Cartesian
coordinate system by its x and y coordinates: 7.07x and 7.07y. In polar
coordinates, in Fig. 6.15b, the same point is identified as 10<45º - a distance of
10 from the origin at an angle of 45º. The polar data must also be gathered
with a tracking filter.

The Polar plot is used frequently for balancing large flexible rotors; typically
for turbines in the power utilities. The size of the large loop is a direct measure
of the amount of imbalance present. The Polar plot allows balancing to be
done at, or close to, the critical speed where a reduction in amplitude is the
objective.

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Both the Bode and Polar plots are used for machine run-up and coast-down.
As such, they both require a tracking filter to lock onto the shaft speed and
stay with it. They both look at only one frequency – the shaft speed as it
changes. They are blind to every thing else going on because it is filtered out.
There is another type of plot that is useful for viewing run-up and coast-down
that does not require a tracking filter. This is a waterfall diagram (Fig. 6.16),
sometimes called a cascade plot or a 3-D plot.

The waterfall diagram is a series of spectrums stacked on top of each other.

Each subsequent spectrum is stepped along in time. The waterfall diagram,
unlike the Bode and polar plots, looks at all frequencies simultaneously, so no
information is lost. The waterfall diagram does not require a tracking filter. It is
three-dimensional in amplitude, frequency, and time.

The waterfall diagram in Fig. 6.16 was taken during the start-up of a laser
printer. The oldest data is at the bottom, with most recent data at the top of
the diagram. Very little vibration was present prior to turning on the power
switch. The small vibrations present were probably coming from the adjacent
computer on the same table. Upon energizing the printer, the 120 Hz appears
immediately and does not change much in amplitude or frequency. There is a
significant amount of vibration during start-up, which mostly settles out. The
peak at 52.5 Hz is probably a motor at 3150 rpm. The 152.5- and 172.5-Hz
vibrations are possible Bearing frequencies since they clearly change with the
rotational speed. The remaining small peaks in the top 15 spectrums are
probably resonances, because they come and go.

Source of Vibration
Vibration itself is not a problem; rather it is a caveat of impending problem.
Vibration signature and relevant data help the machine specialists in identifying
and locating the source. Identifying the source means to perform a frequency

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analysis to tag the offensive frequency, and then locate the source by tracking
this frequency to its origin. The amplitude is then measured to judge the
severity. The said technique is not as simple as it sounds. It is due to the fact
that each vibration is a new situation, and it is possible that that particular set
of parameters has never been encountered before or described in the literature.
However, typical machine problems and their spectra are described in this
chapter for quick and easy reference.

Imbalance
Mass imbalance is at the top of the list because it is the most common cause of
vibration and the easiest to diagnose. Imbalance is a condition where the
center of mass is not coincident with the center of rotation. The reason for this
is a nonuniform mass distribution about the center of rotation. This can be
viewed as an imaginary heavy spot on the rotor. The heavy spot pulls the rotor
and shaft around with it causing a deflection that is felt at the bearings.

Following are the causes of imbalance:

 Porosity in casting
 Nonuniform density of material
 Gain or loss of material during operation
 Loose material moving around, like water in cavities
 Keys & Couplings

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In this case, vibration frequency exactly equal to the rotational speed with an
amplitude proportional to the amount of imbalance. A typical spectrum of an
out of balance rotor is shown in the figure.

Misalignment
Coupling misalignment is a condition where the shafts of the driver machine
and the driven machine are not on the same centerline. There are two types of
misalignment:
 Radial Misalignment
 Axial Misalignment

Accounting the plane in which the misalignment exists, the above-mentioned

types of misalignments can be further sub classified as under:
 Horizontal Radial Misalignment
 Vertical Radial Misalignment
 Horizontal Axial Misalignment
 Vertical Axial Misalignment

The time domain view is not very helpful for diagnosing misalignment.
Spectrum (frequency domain) of Misalignment shows a series of harmonics of
the running speed. The harmonics occur because of the strain induced in the
shaft. The harmonics are not really vibrations at those frequencies, but fallout
of the digital signal process when motion is restricted. If the two shafts are not
aligned and not coupled, then they can rotate freely on their own axis as shown
in the figure.

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When the two shafts are coupled together, they are now strained toward each
other as shown in the figure. When coupled and rotated together, the two
shafts are cyclically strained at running speed. Though shafts are generally
made of stiff material, but still they deflect a small amount. This deflection
creates forces on the nearby bearings and sets the entire housings of both
machines into cyclic motion.

The housings and bearings create reactionary forces that prevent the shaft
from moving as much as it would tend to. These restrictions prevent the
normal sine wave motion from achieving its full excursion in amplitude. In
other words, the sine wave motion of shaft deflection is distorted at the
extremes as shown in the figure. It is thus distortion that generates the
harmonics. The acceleration display is the best place to see the harmonics of
misalignment as the acceleration emphasizes the higher frequencies over
velocity and displacement.

This same pattern of harmonics appears for bearing misalignment also. Some
further analysis needs to be done to separate the two. On running the motor
solo, if the harmonics disappear it is the indication of coupling misalignment.

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If they persist, then the problem is in the motor bearings and not in the
alignment of the two machines. Misalignment is temperature dependent. All
materials grow with increasing temperature, and metal is no exception.
Therefore, a change in vibration, and specifically in the harmonics, during
temperature changes is a strong indication of misalignment.

Further distinguishing between angular and radial misalignment spectrum, it is

to be noted that angular misalignment can be best detected by 180º phase
change across the coupling in the axial direction as shown in the figure. If each
of the bearing on one of the side is moving one way, while those on the other
side are moving in the opposite direction, angular is highly suspected. Radial
misalignment primarily affects radial vibration in contrary to angular, which
affects axial. Moreover, radial misalignment also causes phase to approach 180º
difference across the coupling, but in the radial direction (horizontal or
vertical). The difference will rarely be exactly 180º. It may be 160º, 140º, or
may be even only 110º. But the point is that there will be a significant
difference in the phase.

Recognizing Imbalance from Misalignment

Imbalance Misalignment

High 1X rpm High harmonics of 1X rpm

Low axial readings High axial readings

In phase About 180 out of phase

Temperature dependent; therefore,

Temperature independent
vibration changes on warm-up.

Speed dependent due to centrifugal Less sensitive to speed changes.

force. Vibration at 1X rpm increases Forces due to misalignment remain
as the square of the speed. constant with speed.

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Soft Foot & Sprung Foot

Machinery soft foot is a phenomenon in which a machine’s vibration level can
be decreased dramatically by loosening one
or more hold-down bolts. Figure shows
motor feet. Three out of four are in one
plane whereas the fourth foot is slightly
higher. A fourth foot therefore distorts
something when it is clamped down, as it
does not lie perfectly in the plane of the
other three feet. When the fourth hold-
down bolt is tightened, the machine casing
gets distorted. This changes its stiffness and
could shift its response to a region of
resonance. It also disturbs alignment, either
internal or external alignment.

Soft foot often affects vibration at 1 X RPM, but can also do so at 2 X RPM, 3
X RPM.

When balancing or alignment cannot reduce a machine’s vibration level, the

following procedure is recommended:
 While monitoring the vibration level, loosen and retighten each bolt, one
at a time.
 Note which ones produce a dramatic decrease in vibration.
 When finished with all the bolts, go back to the ones noted and see if the
decrease is consistently persisted.
 If so, shim that foot. Determine the amount of shimmimg with a dial
indicator.
 Repeat the above procedure again until there are no more dramatic
vibration decreases.

Sprung foot cab also cause great frame distortion, resulting in increased
vibration, force and stress in the frame, bearing housing. This can occur when
a hold-down is forceably torqued down on the sprung foot in an attempt to
level the foot. Likewise, Soft Foot, Sprung Foot affects vibration at 1 X RPM,
but can also do so at 2 X RPM, 3 X RPM.

Looseness
Mechanical looseness generally can be classified into three types:

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A. Structure Frame / Base Looseness.

B. Looseness due to Rocking Motion or Cracked Structure / Bearing
Pedestal.
C. Loose Bearing in Housing or Improper Fit between Component Parts.

One of the important facts about each type of mechanical looseness is that it
alone is not a cause of vibration. Instead, looseness is a reaction to other
problems, which are present such as unbalance, misalignment, eccentricity,
bearing problems, etc.

Type A looseness spectra are generally dominated by high 1 X RPM vibration

and appear identical to that for an unbalance or eccentric rotor conditions.
Often, high vibration is pretty well confined to only one rotor (that is the
driver or driven component or the gear box). This
is unlike unbalance or misalignment in which high
vibration levels are not confined to just one of the
rotor. Two different phase behaviors can occur
with Type A Looseness:

When comparing vertical and horizontal phase on each of the bearing

housings, the vibration will sometimes be found to be highly directional with
phase difference of either 0º or 180º depending on whether or not the
horizontal reading was taken on one side or the other (either a phase difference
of 0º or 180º means that the motion is directly up and down or side to side).
This does not normally occur with simple unbalance in which horizontal and
vertical phase usually differs approximately 90º.

When this first phase behavior occurs (0º or 180º phase difference in
horizontal and vertical), the analyst should not confine his measurements to
the bearing housings alone, but move on down to the machine foot, base-
plate, concrete base and surrounding floor as shown in the figure. Here
comparative amplitude and phase measurements should show relatively
identical amplitude and phase at 1 X RPM at each location. If there is a great
difference in amplitude and phase, this will suggest relative motion. Using the

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point where this great phase change occurs, one can locate where the problem
exists. For example, the measurements in the above figure show a problem
between the baseplate and concrete base indicated by the great difference in
phase (180º out of phase with the other two measurements). This indicates
structural looseness / weakness allowing relative movement in machine
components which may be due to a problem with the grouting between the
baseplate and concrete base; or broken or cracked foundation, etc. On the
other hand, if a great phase difference occurred between machine foot and
baseplate, this might suggest looseness of the mounting bolt. Either of these
two problem conditions can cause a great vibration at 1 X RPM.

In case of Type B Looseness, spectrum exhibits significant amplitude at 1 X

RPM and 2 X RPM. However, amplitude at 2 X
RPM exceeds about 50 % of that at 1 X RPM in
the radial direction. It can therefore be concluded
that in case of Type B Looseness, 2 X RPM
dominates the spectrum. Also amplitudes are
somewhat erratic.

Type C is the most common mechanical looseness and may be of any of the
following forms:
 Bearing loose in the Housing
 Excessive Internal Bearing clearance
 Loose Rotor
 Bearing loose and turning on the Shaft.

Spectrum (frequency domain) of this type of mechanical looseness shows large

number of harmonics of running speed up to 10 X or even 20 X RPM when
lightly loaded. One will also find ½ harmonics, as 1 ½ X, 2 ½ X, etc. The
harmonics show up because of clipping of the waveform when the loose parts
hit against their limits of movement. Figure shows an illustration of sine wave
that has been clipped. The vibrating part is not allowed to swing to the full
extreme of motion that it would like because it hits up against physical stops.
The sine wave of its motion is clipped and the resulting spectrum of looseness
is shown in the figure.

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In the case of a loose rotor such as a loose pump impeller, phase will vary
from one startup to the next. On all kinds of machines, looseness can be
confirmed by changing the load and observing the vibration.

Bearings
Ninety percent of bearing failures can be predicted months beforehand. There
are still 10 % of bearing failures that are abrupt and unforeseen. The primary
causes of bearing failures are:
 Contamination, including moisture.
 Overstress
 Lack of lubrication
 Defects created after manufacturing

All vibration occurs at some frequency, which are known in case of bearings
and this helps a lot in diagnosing the real problem. All anti-friction bearings
emanate specific vibration frequencies, or tones, that are unique. The
amplitude of these tones is an indication of their condition. Ball bearings give
off following four distinct frequencies:
Outer Race Defect Frequency (Non-Synchronous) 5 ?/?
Inner Race Defect Frequency (Non-Synchronous) 8 ?/?
Cage Defect Frequency (Sub-Synchronous) < ½(0.34 – 0.47)
Ball Spin Defect Frequency (Non-Synchronous) 2 ?/?

It may be noted that each of the bearing defect frequencies are noninteger
multiples. That is, they are one of the few machinery vibration sources that do
not generate integer multiples of the rotational speed. Moreover, bearing
defect frequencies are different from other vibration sources in view of the fact
that they are defect frequencies. In other words, they should not be present

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at all. When they are present, they signal at least an incipient problem. On the
other hand, other common frequencies such as 1 X RPM are always present
whether or not there is satisfactory or unsatisfactory balance or alignment;
pumps always show vane pass frequencies; spectrum of the mating gears
always shows gear mesh frequency. However, the presence of these other
frequencies does not mean there is necessarily a defect or problem. The
appearance of bearing defect frequencies do send a message to the analyst to
“pay attention” to the imminent problem.

All these frequencies can be calculated using the following formulae:

Outer Race Defect Frequency = Nb/2 {1-Bd/Pd ( Cosθ )}
Inner Race Defect Frequency = Nb/2 {1+Bd/Pd ( Cosθ )}
Cage Defect Frequency = 1/2 {1-Bd/Pd ( Cosθ )}
Ball Spin Frequency = Pd / 2Bd {1-(Bd/Pd)2 ( Cosθ )2 }
Where Nb → Number of Balls
Bd → Ball Diameter
Pd → Pitch Diameter
θ → Contact Angle

Following approximation can also be used for calculating Outer and Inner
Race Frequencies in case if bearing manufacturer and bearing number are not
known
Outer Race Frequency = Nb X 40 %
Inner Race Frequency = Nb X 60 %

Tables of tabulated bearing frequencies are now days available with the
machine analysts. Frequencies of bearing SKF 6311 can be found in the table.
This table points out another feature of bearing tables, i.e., the same bearing
number from different manufacturers may produce different frequencies. The
discrepancies may be larger than this. Bearing tables assumes that the shaft
rotates and that the outer race is stationary. If these conditions do not exist,
then the tabulated numbers do not apply.

Bearing Frequency Factors

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CF BSF ORF IRF

FAG 6311 0.378 1.928 3.024 4.976

SKF 6311 0.382 2.003 3.057 4.943

NTN 6311 0.384 2.040 3.072 4.928

The bearing frequencies can be found by multiplying the numbers given in the
table by the rotational speed. For example, take the data of SKF bearing from
the above table. And suppose it is fitted in the machine, which runs at 1715
rpm. Bearing defect frequencies can be calculated as under:
Outer Race Frequency 3.057 x 28.58 = 87.37 Hz
Inner Race Frequency 4.943 x 28.58 = 141.27 Hz
Cage Frequency 0.382 x 28.58 = 10.92 Hz
Ball Spin Frequency 2.003 x 28.58 = 57.25 Hz

These frequencies can be noticed in the frequency domain spectrum shown in

the figure except Cage Frequency, as it rarely appears, unless a serious cage
defect exists. The vibration peaks at 57 and 87.5 Hz are likely the ball spin and
outer race frequencies, but they could also be harmonics of running speed. The
harmonics of running speed are as under:
2 x 28.58 = 57.16 Hz
3 x 28.58 = 85.74 Hz

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Bearing frequencies cab be separated from the harmonics by zooming the

spectrum. This has been done in Figure 5.23. It may be noted that the 57 Hz
peak divide into two prominent vibrations at 55.5 and 57.25 Hz. The 57.25 Hz
is most likely a combination of ball spin plus a harmonic of running speed. The
two frequencies are too close and overlap. Further zooming will separate the
two. The 87.5 Hz peak divides into a vibration at 85.75, which is certainly the
3X harmonic of running speed, and a peak at 87.5 Hz, which is clearly the
outer race frequency.

For high-frequency measurements, the acceleration display is a better choice.

Bearing defect frequencies are generally of higher order; therefore it can be
viewed only in the acceleration display. These bearing defect frequencies may
not appear in the displacement or velocity displays. The accelerometer should
be mounted in a vertical direction. This is the best orientation to monitor
bearing vibrations on horizontal shaft machines because the accelerometer-
sensitive axis is in line with the bearing load zone.

The very first indications of bearing wear are metal-to-metal impact shocks.
These metal impacts are the balls or rollers, making contact with the races or
cage assembly. They cab be viewed as shock pulses in the time domain with a
frequency between 1000 and 10,000 Hz. They can also be seen in the
frequency domain as random peaks that come and go. They average out to
some broadband vibration in the frequency domain, so it is best to view them
in the time domain with an accelerometer as a transducer. The presence of
these shock pulses does not necessarily indicate a bad bearing. What they do
indicate is metal-to-metal impacts due to defects, high loads, or lack of
lubrication. If this condition is left to continue, it will most certainly lead to
accelerated wear and premature failure.

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Shock pulses in the time domain emanating from a “bad” and “good” bearing
are shown in the figures below.

Bearing can be installed in a misaligned condition, i.e., its axis not being
perpendicular to the housing bore as shown in the figure. The vibration
spectrum of a misaligned bearing looks just like a misaligned coupling, with
harmonics in the spectrum. The other diagnostic indicators of misalignment
are also present; high axial vibration at 1 X RPM and 180º phase differences.

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It is difficult sometimes to separate the two, coupling alignment versus bearing

misalignment. Following additional analysis techniques help the analyst to
locate the true fault:
 Run driver solo.
 Measure shaft run out with a dial indicator while hand turning.
 Carefully inspect shaft and bearing surfaces visually for contact points
and wear patterns.

Rubbing
Rubbing between the rotor and a stationary part of the machine is a serious
malfunction that may lead to a catastrophic failure. Rubbing involves several
physical phenomena, such as friction, stiffening, coupling effect, and may
affect solid / fluid / thermal balance in the machine system. Rubbing always
occurs as a secondary effect of a primary malfunction, such as unbalance,
misalignment, or fluid induced self excited vibrations, which results in high
lateral vibration amplitudes and / or changes in the shaft centerline position.

Rotor rub produces similar spectra to Mechanical Looseness when rotating

parts contact stationary components. Rub may be either partial or throughout
the whole revolution. Usually generate a series of frequencies, often exciting
one or more resonances. Often excites integer fraction sub harmonics of
running speed (1/2, 1/3, ¼, 1/5,……,1/n), depending on location of natural
frequencies. Rotor rub can excite many high frequencies (similar to wide-band
noise when chalk is drug along a blackboard). It can be very serious and of
short duration if caused by shaft contacting bearing babbit; but less serious
when shaft rubbing a seal, an agitator blade rubbing the wall of a tank, or a
coupling guard pressing against a shaft. Rotor rub causes significant
instantaneous changes in phases.

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Oil Whirl Instability

Oil Whirl instability occurs at .42 x RPM and is often quite severe. Considered
excessive when amplitude exceeds 50% of bearing clearances. Oil Whirl is an
oil film excited vibration where deviations in normal operating conditions
(attitude angle and eccentricity ratio) cause oil wedge to “push” shaft around
within bearing. Destabilizing force in direction of rotation results in a whirl (or
precession). Whirl is inherently unstable since it increases centrifugal forces
which increase whirl forces. Can cause oil to no longer supports shaft, or can
become unstable when whirl frequency coincides with a rotor natural
frequency. Changes in oil viscosity, lube pressure and external preloads can
affect oil whirl.

Oil Whip Instability

Oil Whip may occur if machine operated at or above 2X rotor critical
frequency. When rotor brought up to twice critical speed, whirl will be very
close to rotor critical and may cause excessive vibration that oil film may no
longer be capable of supporting. Whirl speed will actually “lock onto” rotor
critical and this peak will not pass thru it even if machine brought to higher
and higher speeds.

Gears
Gears transmit power from one rotating shaft to another. The full power
generated by the prime over, less minor losses, is transmitted by the gear teeth
in contact. Consequently, significant forces are present at the surfaces of the
mating teeth. These forces cause the teeth to deflect under load, and then
rebound when unloaded. The local stress level is high and fatigue damage
accumulates. If the teeth were of perfect form and without defects, this cyclical
loading and unloading would cause very little vibration. The presence of non-
perfect gears is what gives rise to vibration.

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The spectral pattern of gear vibration is the crucial information to

understanding their defects. A single defect on a single gear tooth will cause a
force perturbation at 1X running speed. Figure 5.31a is a time domain view of
a 30-tooth gear with 1 defective tooth. The defective tooth was created by
filing flat a tooth face. A shock pulse clearly arises every time this defective
tooth comes in contact. The speed of the gear was 1200 rpm (20 Hz), and the
period of one rotation is 50 msec. However, unless the defect is large, the
energy generated by this defect is of short duration and looks like a transient. It
may not show up at all at 1X running speed. And, in fact, this defective tooth
caused no noticeable change in the vibration at running speed. Figure 5.31b is
the frequency spectrum of this same gear. The vibration at running speed is
very small at 20 Hz. It will, however, modulate the gear-mesh frequency and
appear as a 1X sideband of gear mesh. Needless to say, gear-mesh frequencies
are high, typically above 1000 Hz, so an accelerometer is necessary to detect
them, and the acceleration display is necessary to see them. The gears of Fig.
5.31 generated a gear-mesh frequency of 600 Hz. This is calculated by
multiplying the rotational speed of the gear times the number of teeth. In this
case
20 Hz x 30 teeth = 600 Hz gear-mesh frequency

It should be made clear that there is only one gear-mesh frequency for two
mating gears. The high-speed shaft has fewer teeth, and its product of speed
times number of teeth will yield the same gear-mesh frequency of 600 Hz.

The 2X gear-mesh frequency of 1200 Hz is also present. The 2X gear mesh

usually shows up larger than the 1X in the acceleration display and is a better
indicator of developing gear problems. As mentioned earlier, sidebands of the
gear-mesh frequency contain significant information about the condition of
individual gear teeth. Zooming on the gear-mesh frequency is usually necessary
to clearly see these sidebands. The amplitude of vibration at gear-mesh
frequency does vary with load. Therefore, when judging the condition of gears

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using the vibration amplitude, it is important to take measurements under the

same load conditions to obtain comparative data. Excessive backlash does
cause an increase in the amplitude at gear-mesh frequency when unloaded.

A broken gear tooth obviously cannot carry any load. This momentary lapse in
torque transmission causes a 1X-rpm abnormality that shows up as sidebands
of the gear-mesh frequency. The sideband spacing is the running speed. These
kinds of defects, broken, cracked, or chipped gear teeth, show up best in the
time domain as in Fig. 5.31a. There is metal-to-metal contact either at this
defective tooth or when the next mating abruptly takes up the load. These
metal crashes appear as shock pulses in the time domain. The time interval
between shock pulses is the time interval between defect encounters. For
example, Fig. 5.32 is a hypothetical time plot of a mating spur gear set. The
rotational speed is 1800 rpm (30 Hz) which corresponds to a period of 33.3
milliseconds. This is the time interval between shock pulses of similar patterns.
There are two separate patterns, therefore, two teeth have abnormalities. The
time interval x is proportional to the arc distance along the circumference
between the bad teeth. Serious gear problems will cause accelerated wear of
metal particles and should be confirmed with a wear particle analysis.

Gears, when produced, are not perfect with respect to tooth profile. During
the early few hours of operation, the teeth wear in and the gear-mesh
frequency can be expected to decrease. As gears wear, the frequencies remain
the same, but the amplitudes increase. The peaks at gear-mesh frequencies
broaden and develop sidebands of the primary rotational speed.

It is important to mention two facts concerning gear faults. The first one is
that as these load-bearing members wear, they get louder and louder (increased
amplitude), but they will continue to carry the load. At some point cracks begin
to develop, and these are the first signs leading to a catastrophic failure. It is
sufficient, usually, to monitor the gear frequencies and watch their amplitudes
grow due to normal wear. With experience, and a previous history to rely on,
you will be able to predict at what level a gear will fail. A sudden change is very
significant. The change may be an abrupt decrease to a lower plateau. Figure
5.33 shows such a change. The abrupt drop is not good news. It indicates that
a dramatic decrease in stiffness has attenuated the force transmission path. The
crack has propagated much more, leaving the gear or shaft very flexible and
able to absorb the forces by bending more. Catastrophic failure is eminent.
The second fact concerning gears is that they are designed to last the life of the
machine. If they do not, then suspect some other cause, such as imbalance,
misalignment, or improper lubrication.

Vane Passing
A phenomenon similar to gear-mesh frequency is vane passing frequency on
fluid-handling machines. This occurs on pumps and fans. The source of the
vane passing frequency is a pressure fluctuation as a vane passes a
discontinuity within its chamber. This discontinuity is usually the edge of the
discharge opening, but it could also be a structural support on a propeller fan,
or the trailing edge wake of an airfoil fan. The vane passing frequency is always

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the product of the rotational speed times the number of vanes. Figure 5.34is a
vibration spectrum of a small centrifugal fan with 24 blades. The speed of the
fan was measured with a strobe light to be 3355 rpm, or 56 Hz. The vane
passing frequency is therefore calculated to be

56 Hz X 24 blades = 1344 Hz

The existence of vane passing frequencies can be expected as a fact of

operation of all pumps and fans. They are usually not a problem unless they
excite a structural resonance or cause an acoustical problem on fans.

Resonance
Resonance is a
condition whereby the
driving force applied to
a structural part is close
to its natural frequency
and amplification
occurs. The source of
the driving force is
most likely residual
imbalance in a rotating
machine attached to the
structure (Fig. 5.16). This small imbalance is transmitted throughout the
machine, and attached parts, as a vibratory force. If that force encounters a
structural part that is tuned to that frequency by virtue of its mass and
stiffness, then that part will be excited into resonance. Its vibration amplitude
can be 10 to 100 times the amplitude of the input force, depending on
damping.

The equation for resonance is wn = k/m. This says that the resonant
frequency, in radians per second, is equal to the square root of the stiffness
divided by the mass.

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Beams, plates, and other objects also have resonant frequencies. Figure 5.17
shows the first, second, and third modes of vibration of simple beams. The
points where no motion is taking place are called nodes. For the first mode of
vibration, the beam supports are nodes. Each successive higher mode of
vibration has one additional node.

Rotors also have resonances, called critical speeds. According to the formula
for centrifugal force, F = mrw2, the vibratory force should increase as the
square of the speed. This is true in the low-speed range. When approaching
resonance, or critical speed, the vibration increases much more than expected
by the centrifugal force formula. It peaks at the critical speed; then, at higher
speeds, it smooths out. The reason for this is because of the 180 phase shift at
resonance. The response of the rotor to the residual imbalance is delayed 180
and causes the mass center to be pulled in closer to the center of rotation.
Rotors run smoother above the first critical speed than below it. However,
they must pass through that first critical speed for every run-up and coast-
down.

Resonances are more typical on stationary parts than on the rotating parts.
Rotating parts are in the fluid stream, and this usually provides sufficient
damping to keep amplification down. Except for critical speeds of high-speed
rotors, resonances on rotating parts are rare.

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A single impulse will excite a system to vibrate at its natural frequency (Fig.
5.18). The vibration amplitude dies away because of damping, but the
frequency of vibration is the same – its natural, or resonant frequency.

In the frequency domain, a resonance appears as a discrete peak unrelated to

the running speed (unless the running speed or a harmonic coincides with the
resonance). A resonance coincident with a driving frequency will have a
relatively constant amplitude.

Figure 5.19 is a resonant vibration from an aluminum wheel. The wheel is

pictured in Fig. 5.15 as one of the larger wheels. The wheel was not rotating
but was excited into resonance by striking it with a wooden dowel. The
vibration was measured on the adjacent bearing block. It “rang” like a bell and
was clearly audible. The “ringing” continued for about 10 sec before finally
fading away. Very little damping was present here. The period of this sine wave
was 0.000 859 sec, which corresponds to 1164 Hz.

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Figure 5.20 is the frequency domain view of this same aluminum wheel
vibrating in resonance. The resonant frequency is 1170 Hz, as measured in the
frequency spectrum.

The key indicators of resonance are;

1. An audible pure tone
2. A clean sine wave in the time domain
3. A single tall peak in the frequency domain

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Cavitation
Cavitation is the vaporization of fluid within the pump. It occurs when the
fluid pressure is less than the vapor pressure at that temperature. Technically,
cavitation is the boiling of fluid at ambient temperature due to reduced
pressure. Prolonged cavitation will cause erosion damage to a pump impeller.
The causes and correction of cavitation is beyond the scope of this book, but
cavitation can be recognized as a broadband vibration in the 3- to 5-kHz range
(Fig. 5.38). With a spectrum analyzer monitoring the pump vibration, the
controls and operating parameters can be varied to find the conditions of least
cavitation and minimum vibration.

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Table 7.1 Common Machinery Faults

Cause Frequency Amplitude

Less than 1X rpm
Beats Difference Frequency Comes and goes; caused by two machines
running at close rpm.
Loose journal bearing Subharmonics ½, 1/3, etc. Decreases with load. Applicable to high-
Oil whirl Approx. 45% of rpm. speed machines with journal bearings.
Looseness Belts ½, 1 ½, 2 ½, etc. Decreases with load. Strobe light helps to
Belt rpm plus harmonics see defect. Slipping belts can cause a
periodic buildup and decline.
1X rpm
Unbalance 1X Mostly radial; a common fault.
Misalignment 1X plus harmonics High axial, high 2X and 3X; a common
fault.
Eccentricity 1X Looks just like unbalance; can be corrected
by loosening belts.
Bent shaft / bowed rotor 1X Looks just like unbalance; can be corrected
with massive balancing weights.
Soft foot Variable Dramatically decreases by loosening one
hold-down bolt.
Reciprocating 1X plus harmonics Cannot be easily corrected; isolate machine
better or provide inertia base.
Medium frequencies 1X to 10X rpm
Misalignment 2X, 3X, plus harmonics High axial; a common fault.
Motor (Electrical) 120 Hz; also 60 and 240 Hz Stops immediately upon disconnecting
power; also causes 120-Hz sidebands at
higher frequencies. Not usually destructive;
an indication of the quality of construction.
Present to some degree in all motors and
transformers.
Looseness ½, 1 ½, 2 ½, etc. Decreases with load.
Bearings 4-10X FTF = 0.4 x rps
OR = 0.4 x rps x N
IR = 0.6 x rps x N
N = number of balls
rps = rev/sec
High-frequency shocks in time domain.
High frequencies
Gears Gear mesh = rpm x no. of Sidebands at tooth mesh 2X gear mesh
teeth typically larger.
Blades Blade passing = rpm x no. Not usually destructive.
of blades.
Resonance Discrete peaks A serious condition; usually high amplitudes;
slight speed changes cause a dramatic
decrease.
Cavitation Broadband 3-5 kHz Changing operating conditions
(i.e. pressures) alleviates problem.
Cracking Unexplained drop in Amplitude changes are insignificant.
frequencies. Phase changes are significant.

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