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VIBRATION TESTING
Vibration is either the obvious cause or the prime
symptom of problems in many different industrial
situations. Solutions must be found. Increasingly,
engineers are required to measure and analyze
vibration, to find engineered solutions, and to show
and document improvement. This article, the first
of a three-part series, explores the different types
of instruments available for measuring vibrations.
Subsequent articles will discuss the gathering and
analysis of data, and solution to vibration problems.
Displacement and Velocity Sensors
If a structure is steadily vibrating with a large
amplitude, its approximate amplitude can be meas­
ured by holding a scale alongside it. But for small
displacements—say a double amplitude of only 200
/tin. produced by a 10-g acceleration at 1000 Hz—
such simple methods are entirely inadequate.
More sophisticated nonelectrical methods, such
as optically magnified scales, offer certain advan­
tages; primarily, they magnify the amplitude so
that it can be seen by the naked eye. Electrical
sensors, however, are generally required to meas­
ure the tiny, high-frequency displacements that
originate in such components as bearings and gears.
Displacement sensors convert changes in posi­
tion into electrical signals, utilizing variations in
resistance, capacitance, inductance, or eddy cur­
rents caused by changes in distance. These instru­
ments excel in sensing relative, rather than ab­
solute, displacements. One unit, for example,
threads into the frame of a machine so that its
sensing end is close to a rotating shaft. If motion
is eccentric, a signal proportional to the relative
motion between shaft and frame is obtained.
Velocity sensors, Fig. 1, detect velocity, which
is then converted electronically into displacement.
Velocity pickups require no external source of
power. Because of their low electrical impedance,
the readout instrument can be some distance from
the sensor.
Disadvantages of velocity pickups are: They are
generally large and heavy, compared to accelerom­
eters. They cannot be used to measure amplitudes
greater than the free-motion amplitude of their
magnets or coils, whichever are free. Since they
will sometimes experience motion close to their
natural frequencies, some form of damping must
be used; this introduces phase-shift problems in
measurement of nonsinusoidal motions.
Accelerometers
Accelerometers are sensors whose output signal
is proportional to the instantaneous value of ac­
celeration. Most vibration and shock measurements
today are made with accelerometers.
Strain-gage accelerometers provide one of the
118
Visualize a cork bobbing and drifting
on a pond; this is an example of
whole-body motion. If the cork also
were bent by the waves, as the hull
RY of a ship might be, this deformation
would exemplify relative motion of
the parts. Both types of motion are
forms of vibration that must be con­
sidered in engineering designs. Prin­
ciples of whole-body motion can be
THEO illustrated by an idealized spring­
mass damped system.
N
< > >
TIO
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A /////////////^
R
IB A simplified mechanical system, con­
strained to motion along one axis, con­
sisting of Weight W, a spring of stiff­
V ness K, and a viscous damper of
damping constant C, is shown above.
(Such systems are never found in
practice, but many systems approxi­
mate this ideal over small ranges of
AT frequency.) A load of K pounds will
deflect the spring by 1 in. Without
weight W, the spring would have a
length L. When the spring supports
W, its length becomes L + 8. 8 is
called the static deflection and is
equal to W/K.
LOOK
Free Vibration: If W is disturbed,
the system will oscillate at its natural
frequency, fy, where fy = 3.13/8%.
(Temporarily ignore the effect of the
damper.) The double amplitude of
the oscillations will remain constant
if there is no damping. If damping
is present, the motion gradually de­
creases as kinetic energy is converted
into heat energy.
BRIEF If a vibration pickup located on
weight W were connected to an os­
cilloscope, the screen would show pat­
terns like this;
A
Machine Design