Engineering Encyclopedia
Saudi Aramco DeskTop Standards
CHARACTERISTICS OF VIBRATION
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Engineering Encyclopedia Vibration Measurement and Diagnostics
Characteristics of Vibration
Section Page
WHAT IS VIBRATION? .................................................................................................. 2
MACHINE & VIBRATION ............................................................................................... 2
VIBRATION INDICATES MACHINE CONDITION ......................................................... 4
VIBRATION LEVELS ..................................................................................................... 5
VIBRATION MOTION CHARACTERISTICS & PARAMETERS ..................................... 5
Amplitude............................................................................................................. 5
Displacement ............................................................................................ 7
Velocity ..................................................................................................... 7
Acceleration .............................................................................................. 8
Frequency.......................................................................................................... 11
Phase Angle ...................................................................................................... 12
Vibration Waveforms ......................................................................................... 13
List of Figures
Figure 1. Simpliest Form of Vibrating System ............................................................... 3
Figure 2. Typical Frequency Spectrum........................................................................... 4
Figure 3. A Complex Waveform and its Sinusoidal Component ..................................... 6
Figure 4. Conversion From Displacement to Velocity and Acceleration ......................... 8
Figure 5. Conversion From Acceleration to Velocity and Displacement ......................... 9
Figure 7. Relative Phase Angle .................................................................................... 12
Figure 8. Absolute Phase Angle ................................................................................... 13
Figure 9. Time Base Presentation ................................................................................ 14
Figure 10. Orbital Presentation .................................................................................... 15
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Characteristics of Vibration
WHAT IS VIBRATION?
Vibration is the effect, or the object response to an applied
oscillating, pulsating, random, or steady forces. This could be
any force transmitted from the surrounding to the machine, the
structure, or the rotating machine itself. From a machinery
viewpoint, vibration is the periodic motion of a machine or
machine part, back and forth from its position of rest.
Vibration can be considered to be the oscillation or repetitive
motion of an object around an equilibrium position. Figure 1
shows the simpliest form of vibration.
MACHINE & VIBRATION
In practice, vibration occurs as a by-product of the normal
transmission of cyclic forces through the internal or external
mechanism. Machine elements react against each other and
energy is dissipated through the structure in the form of
vibration.
A good design should produce low levels of inherent vibration.
But as the machine deteriorates in use, its foundation settles
and parts deform. Subtle changes in the dynamic properties of
the machine begin to occur like; shaft becomes misaligned,
rotor becomes unbalanced and clearances opened-up. These
factors may excite resonance that puts considerable extra
dynamic loads on the bearings. An increase in vibration will be
expected which is dissipated throughout the machine.
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Characteristics of Vibration
Figure 1. Simpliest Form of Vibrating System
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Characteristics of Vibration
VIBRATION INDICATES MACHINE CONDITION
Machine elements which constrain the transmitted forces, for
example bearing housings, are usually susceptible to the
excitation forces, therefore, vibration can be measured at these
points. As long as excitation forces are constant, or vary within
certain limits, the vibration level measured will also be constant
or vary within similar limits.
Furthermore, when the machine is in good condition, the
vibration level and its frequency spectrum has a typical shape
characteristic, as shown in Figure 2. This frequency spectrum is
a plot of vibration amplitude against frequency and is known as
the vibration signature of the machine, which is obtained by
using a spectrum analyzer.
Figure 2. Typical Frequency Spectrum
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Characteristics of Vibration
VIBRATION LEVELS
There are four factors that control the vibration levels measured
on a machine or a structure. First, is the excitation force. High
excitation force tends to produce high vibration response levels.
The machine will respond to excitation force depending on the
other three factors which are:
• System effective mass.
• System effective stiffness.
• System effective damping.
VIBRATION MOTION CHARACTERISTICS & PARAMETERS
The fundamental characteristics of vibration are: amplitude,
frequency, phase, and wave form.
Amplitude
The amplitude of the dynamic motion, whether expressed in
displacement, velocity, or acceleration, is generally an indicator
of the severity of vibration. It attempts to answer the question:
“Is this machine running smoothly or roughly?” Amplitude must
be specified in terms of peak-to-peak, zero-to-peak, rms, or
average. Its periodic motion can be represented theoretically as
the summation of many sinusoidal waves with different
frequencies.
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Figure 3 shows a complex waveform and its sinusoidal
component.
dt
Figure 3. A Complex Waveform and its Sinusoidal Component
The peak-to-peak amplitude represents the total distance
moved from the extreme positive peak to the extreme negative
peak between the two ends of oscillation.
The zero-to-peak amplitude is a measure of the maximum
amplitude from the zero reference position. In the periodic
sinusoidal signal the zero-to-peak value equals half the peak-to-
peak value.
The overall amplitude refers to the amplitude of the total
periodic motion, while the term running speed amplitude refers
to the amplitude of the sinusoidal component that has the same
frequency as the running speed of the equipment in question.
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RMS is an abbreviation of Root Mean Square and is a measure
of the energy content of the signal. The mathematical formula is
shown below.
T
1
RMS = ∫ [x (t )]2 • dt
TO
t = time
x(t) = amplitude function
T = signal period
Displacement
The change in distance or position of an object is called
displacement. Typically the displacement in oscillatory motion is
measured as the total distance moved from the two ends of
oscillation, i.e.; peak to peak motion. The Displacement unit
used are either mils (1 inch = 1000 mils) or micro-meter (µm) in
SI units also called micron. In rotating machines the typical
displacement measurement device is the Eddy current
(proximity) probe and is sometimes called the non-contact
probe. Others are optical, lasers, and conductive. Displacement
can also be derived from velocity or acceleration measurement
by performing a single or double integration of the waveform.
Velocity
Velocity is the time rate change of displacement. Velocity is
often expressed as V or dx/dt. The velocity units used are
either in/sec or mm/sec in SI units. Since the maximum velocity
in oscillatory motion occurs at the zero displacement reference,
velocity is sometimes expressed as the maximum amplitude or
zero-to-peak value. The Root Mean Square (RMS) is now
recommended to express the velocity amplitude as it represents
the energy content in the signal and is sometimes called the
effective amplitude.
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Acceleration
Acceleration is the time rate change of velocity. It is often
expressed as a or dv/dt. The acceleration units used are either
ft/sec2 or m/sec2. G’s are commonly used which relate the
vibration acceleration to the gravitational acceleration of the
earth, G = 9.81 m/s2 or 32.17 ft/sec2. Acceleration
measurements are generally made with piezoelectric
accelerometers and are typically used to evaluate high
frequency machine casing or bearing housing response
characteristics. As in velocity, acceleration is measured in 0-pk
or RMS. Figure 4 & 5 shows the relationship between
displacement velocity, and acceleration.
Figure 4. Conversion From Displacement to Velocity and Acceleration
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Figure 5. Conversion From Acceleration to Velocity and Displacement
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Selection of vibration measurements type is affected by the
expected frequencies generated by the machine as shown in
Figure 6.
Figure 6. Relative Amplitude for Acceleration,
Velocity and Displacement vs Frequency
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Frequency
The frequency of vibration is a term used to express the number
of events (periodic oscillations) per unit time. The frequency of
vibration usually indicates the cause of the vibration and the
excitation force. It is most commonly expressed in multiples of
the rotative speed of the machine. This is primarily due to the
tendency of machine vibration frequencies to occur at direct
multiples or sub-multiples of the rotative speed of the machine.
It also provides an easy means to express the frequency of the
vibration.
The frequency can be presented relative to time such as cycles-
per-minute (cpm), cycles-per-second (cps), or hertz (Hz) which
is another notation for cps. When references to the shaft, it is
called harmonics or orders. It is necessary only to refer to the
frequency of vibration in such terms as one time rpm, two times
rpm, 43 % of rpm rather than having to express all vibrations in
terms of cycle-per-minute or hertz.
The frequency within the signature indicates causes of
malfunctions or the exciting forces. Machinery malfunctions
tend to occur at certain frequencies and this helps to segregate
certain classes of malfunction from others. Frequency is an
important piece of information when it comes to analyzing
vibration related problems. But all data should be looked at
before arriving at any conclusion.
Synchronous frequency vibration occurs at a frequency
that varies in direct proportion to changes in rotative
frequency. Usually synchronous components are whole
multiples, or integer fractions of rotative speed and they
maintain that relationship regardless of speed.
Sub-synchronous frequency vibration occurs at a
frequency which is some direct integers fraction of the
rotative speed, i.e.; 1/2X, 1/3X etc.
Non-synchronous frequency vibration occurs at some
frequency other than the multiples or fractions of running
speed frequency.
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Phase Angle
The phase angle is a measure in degrees of the timing
relationship between two events. It is a mean of describing the
location of the rotor at a particular instant in time. Accurate
phase angle measurement are extremely important in the
balancing. The phase angle of the rotor as determined by
various transducers attached to a machine train can provide
valuable information about the performance of that machine
train.
Phase angle is also important in determining the natural rotor
balance resonance, or “critical speed.” The most accurate and
reliable means of measuring phase angle is with the use of a
Keyphasor (shaft reference). The keyphasor can be set-up
using either a proximity probe or an optical transducer.
The unit of phase measurement is degree (2π = 360º).
When the phase angle is measured between two signals (i.e., x
and y or inboard and outboard), it is called relative phase angle,
as shown in Figure 7.
Figure 7. Relative Phase Angle
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Absolute phase (see Figure 8) refers to the timing difference
between keyphasor pulse and the next peak of the signal.
Figure 8. Absolute Phase Angle
Vibration Waveforms
The waveform of the vibration is perhaps the most important
means of presenting vibration data for analysis. The machine’s
behavior can be analyzed through good data presentation of the
raw waveform. The oscilloscope is used to present the raw
waveform instantaneous or analog form.
Vibration time domain can be separated into two separate
categories: Time Base presentation and Orbital presentation.
Refer to Vibration Signature Plots.
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Time Base presentation (see Figure 9) is provided by displaying
transducer input on the oscilloscope in the time base mode.
Figure 9. Time Base Presentation
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Orbital presentation (see Figure 10) is provided by displaying
the output from two orthogonal separate proximity probes at 90°
angles to one another in the X-Y mode of the oscilloscope. In
cases where the angle between the two probes are not 90°,
then special equipment should be used other than the
oscilloscope but it will be digital presentation.
Figure 10. Orbital Presentation
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