Chemical Engineering January 2011 - 38

CASE 2. Bad antifriction thrust bearing
1.5
1.2
0.8
0.4
500
1,000
Frequency, Hz
1,500
2,000
10
5
-5
-10
-15
50
100 150
200 250 300 350 400
Time, milliseconds
Details:     (that is, no thrust bearing in the drive end), horizontal-center-line-mounted centrifugal pump
  
FIGURE 4. These plots of vibration signature and time-wave-form distribution were produced as a result of a bad anti-friction
bearing. The raised spectrum loor spread (from low order to very high order of operating harmonics) suggested a damaged bearing,
helping the operators to locate a broken bearing cage
acquisition of phase data. Of all crosschannel
measurements, cross-channel
phase is the most sensitive vibration
parameter because errors in mounting
positions for the sensors can lead
to erroneous conclusions.
Some multi-channel Fast Fourier
Transformatiom (FFT) analyzers require
a specific input channel (FFT
analysis is a mathematical operation
that extracts the frequency information
from a time-domain signal and
transforms it to the frequency domain).
This allows one sensor to be
configured as a reference input during
phase-difference checking.
If the channel is set up incorrectly,
cable changes will be required. One
way to sidestep this problem is to
take the orientation into account and
add 180 deg. Other multi-channel
FFT analyzers provide the ability to
determine which input signal can be
the reference without changing
cable connections. Listed next are
some basic considerations that must
be taken into account when acquiring
multi-channel phase data:
* An accelerometer is the only true
phase transducer
* The multi-channel FFT analyzers
have no internal phase shift between
channels
* Depending on the type of fault, a
machine's structure will either be
moving as one unit (in phase) or not
as one unit (out of phase)
Vibration excitation
For vibration excitation to happen,
two types of forces - namely the exciting
forces and the restraining forces
- are at work. In general:
Exciting force = Stiffness force + Damping
force + Inertial force
This can be expressed as:
F(t) = Kx (t) + Cv(t) + ma(t)
or
F(t) = Kx (t) + C.dx/dt (t) + m.d2 x/dt2(t)
(4)
where:
F(t) = a measure of the exciting force
K = stiffness constant (depends upon
physical and dimensional properties
of component)
C = dampening force per unit velocity
(depends upon dampening system
engaged)
m = Mass of the component subjected
to the exciting force
All the forces are expressed as a function
of time. (The equations shown
are for illustrative purposes, so showing
specific units here is not relevant.
During the actual calculations, units
are required.)
The static deflection is controlled by
the stiffness force alone. At a low-speed
frequency range, the response (that
is, the vibration) is dominated by the
spring force and is in phase with the
excitation force.
As frequency increases, the inertial
force of the mass has an increasing influence
[because by definition, force =
(mass)(acceleration)]. At a particular
frequency (called the undampened
natural frequency,) the mass and
spring terms cancel each other out. The
system is easily excited into motion
and the response is controlled only by
the dampening.
At the natural frequency, the response
lags the excitation by 90 deg.
At frequencies greater than the natural
frequency, the mass term exerts
increasing control and the system begins
to behave as a moving mass; in
these situations, the response lags the
excitation by 180 deg.
The general rule of thumb is that for
any rotating mass, the stiffness of the
system (imparted by physical properties
of material and dimensional
geometry) counters the frequency of
vibration, and the amplitude of any
vibration that does occur is controlled
by any dampening device in the system
(such as the dampening provided
by the foundation and any supports).
38 CHEMICAL ENGINEERING WWW.CHE.COM JANUARY 2011
Direction of measurement
To be of greatest utility, vibration data
must be collected at the right place,
under the right conditions, using the
right procedure. For relatively large
(Class IV and above) machines, online
vibration data are typically collected
using an integrated monitoring
and display system that captures radial
displacement data using sensor
probes mounted close to the rotating
body through the support housing.
For smaller units, vibration data are
typically collected off line at a preset
frequency using portable vibrationmonitoring
devices. Care must be
taken during the manual collection of
vibration data to reduce the chance of
error and ensure the most comprehensive

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Chemical Engineering January 2011

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