measurement of vibration
TRANSCRIPT
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Measurement of Vibration
A.Rama Rao
Vibration Laboratory SectionReactor Engineering Division
Bhabha Atomic Research CentreMumbai-400085
E-Mail: [email protected]
There are three quantities, which are of interest in vibration studies. In the case of
sinusoidal motion, the three quantities are related by the frequency of oscillation. The
instantaneous position or displacement of a body can be mathematically described as,
X = Xpeaksin( 2t/T) = Xpeaksin (2ft) = Xpeaksin(t)
where = 2f = angular frequency.
Xpeak=Maximum displacement.
f = 1/T and T = period of oscillation
As the velocity of motion is the time rate of change of motion, it can be expressed as,
v = dx/dt = Xpeakcos (t) = Vpeakcos(t) = Vpeaksin(t+ /2)
and acceleration which is again time rate of change of velocity, it can be express as,
a = dv/dt = dx2
/dt2
= - 2
Xpeaksin(t) = - Apeaksin(t) = Apeaksin(t+ )
It can be seen that the form and period of vibration remain the same except that the
velocity leads the displacement by a phase angle of 90 o and acceleration leads velocity
again by 90o
1.0 Amplitude quantification
Common sense says that vibration severity is indicated by correct measurement of
vibration amplitude. Figure 1 shows a sinusoidal signal with amplitude, period and phase.
The peak amplitude is used to describe for example the displacement of a shaft, which
helps in estimating the position of the shaft with respect to the clearance of the bearing
supporting the shaft. Whenever there is vibration of a body within a given clearance, peak
value measurement is advisable.
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Figure-1 A Periodic signal
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Figure-2 Amplitude Characteristics of a Periodic Signal
Measurement of Root Mean Square value of a signal has important significance in
expressing the power content of the vibration and hence the damage potential of
vibration. It gives the DC equivalent of oscillating or alternating signal. It is
mathematically expressed as
PEAKRMSXX
2
1
Other amplitude quantifications are Form factor (Ff) and Crest factor (Fc).
Ff= RMS/AVERAGE
Fc = PEAK/RMS
These factors give some indication of the wave shape. For example for pure harmonic
motion Ff= 1.11 and Fc = 1.41. Deviation from these numbers indicates that the signal is
not pure harmonic. Of the two factors, crest factor has important diagnostic importance.
For example, while monitoring health of bearings, if the crest factor shows an increasing
trend then it is considered to be an indication of impending damage to the bearing. This
happens for example when there is single vibration component caused by a faulty
bearing. This defect goes undetected by RMS measurement but crest factor easily picks
up the in defect in the bearing. Figure 2 illustrates the relative significance of these
measurement quantities.
2.0 Transducer specification
Transducers help us in making dependable measurement when their selection for a
particular type of measurement is carefully followed. A very common mistake made in
this regard is that one transducer is used for all types of measurement. During normal
operating condition this mistake may not be too costly but when vibration severity
increases, the error may be too big. For example, transducer tuned to measure machinery
vibration strictly cannot be used for assessing piping vibration. The error will be highly
non-conservative.
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2.1 Eddy Current Probes
Eddy current probes, which measure displacements with out contacting the vibrating
surface, have been standardized in terms of gap between the target and the probe, its
measurement range, sensitivity and the connecting electronics. The probe design that
follow standard API 610 give an out put of 8 V/mm for a three meter cable between the
probe and the proximeter that supplies to the probe the carrier signal for modulation
during vibration of the target. The proximeter also demodulates the measured signal and
gives voltage out put. The proximeter is supplied with external DC voltage of 18 to 24 V.
Figure 3 shows typical mounting details of the probe inside a bearing housing. Care must
be taken while positioning the tip of the probe with respect to the shaft. As shown in
Figure 4, no metal should be present within 4 mm of the probe face except the target
surface.
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Figure-3 Eddy Current Probe Mounting within the Bearing Housing
Figure 4 Schematic of Proper installation of Eddy Probe.
Eddy probes are also available to measure the nano micron deflection of the outer race of
the ball bearings. These probes are highly sensitive and also require special mounting
within the bearing housing. Figure 5 shows high sensitivity probe to measure nano level
deflection of outer race of a bearing.
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Figure-5. High Sensitivity Eddy current Probe
The probe tip diameter basically decides the range of measurement. They normally are in
the range of 6mm to 12mm. The magnetic field generated at the tip of the probe need to
be directed towards the target with out much of loss. If 12 mm probe is used for
measuring vibration of 30 mm shaft then there is a possibility of error in measurement.
The orbit plot has very high potential in machinery diagnosis. For example, figure 6
shows the orbit plot of a shaft measured in x-y direction as shown in figure 3.
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Figure-6 Orbit plot or X-Y from Eddy Probes
Figure 6 shows some of the orbit shapes indicating severity of misalignment between to
coupled rotors and figure 7 shows 3-D plot along with orbit plot used for recognizing
resonance during start trial of a machine.
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Figure-7 Orbit plots indicating severity of misalignment
Figure-8 3-D plot and orbit plot.
2.2 Accelerometers
As brought out earlier, accelerometers are widely used for measuring all the three
vibration quantities. Piezoelectric based accelerometers are widely used type of sensors.
The piezo material develops charge when subjected to force. Quartz and Rochelle salt are
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when excited from low frequency up to its resonance frequency. Normally for
general-purpose accelerometers the resonance frequency is in the range of 30
to 90 KHz. As a thumb rule the upper limit of the useful range is taken as 1/3rd
the resonance. That is 10 to 30 KHz. Figure shows the band useful frequency
range. Accelerometers are not capable of a true DC response. The
preamplifier decides the lower limit of the frequency.
Figure-10 Frequency response of an Accelerometer
Up to 1 Hz is normally considered acceptable without any amplitude or phase
distortion. If a measurement involves higher frequencies than 30 KHz, then
accelerometers with resonance frequency higher than 100 KHz must be used
and if low frequency measurement is to be carried out involving low
displacements, then accelerometers are not suitable. Double integration of
acceleration signal for estimating low displacement gives unreasonably high
displacement, which is due to noise in the integration. This is one commonly
made mistake and so there is a need to exercise caution.
2.2Sensitivity: It is the magnitude of voltage developed across its outputterminals when subjected to certain acceleration. This is specified as V/m/s
2
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or pico coulomb/ m/s2. Ideally, the general feeling that higher the sensitivity
the better suits low level of acceleration. However for measurements
involving vibration and intermittent shock for example in automobile on a
bumpy road, high sensitivity could lead to saturation of input signal and hence
distortion. High sensitivity accelerometer normally has limited high frequency
range and accelerometers suited for high frequency measurement are of lower
sensitivity. What is important is to make an estimation of what is the likely
level of voltage that may be received from the accelerometer. Based on this
the electronics, and other condition for storage device may be adjusted.
2.3Dynamic Range: When it is required to measure abnormally low and highvibration levels, the dynamic range needs to be considered. Now-a-daysaccelerometers are available with dynamic range from 60dB to 100 dB.
Dynamic range of 60 dB measures from says 1mm/s2 to 1000 mm/s2and 100
dB range measures up to 100,000 mm/s 2. The dynamic range must be seen in
combination with sensitivity to assess the performance of the sensor in the
lower or upper range of the amplitude. Figure 11 shows the illustration of
dynamic range.
Figure-11 Illustration of dynamic range of accelerometer
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Upper limit of the dynamic range is determined by structural strength of the
accelerometer. Accelerometers are available to measure up to 100,000 g,
which is well into the range of mechanical shock.
2.4Mass: Normally accelerometers are lightweight and compact in design.However when they are used in large numbers say on aeroplane wings or
panels, the mass loading could be an issue. Additional mass changes the level
response and the frequency of the structure thus invalidating the measurement
results. The change in the response can be corrected with the following
formula.
as = am (ms+ma)/ms and fs =fm {(ms+ma)/ms }
1/2
where
as = acceleration with out mass loadingfs = frequency with out mass loading
ms = effective mass of the structure
ma = mass of accelerometer
As a general rule, mass of the accelerometer should not be greater than one
tenth of the effective (dynamic) mass of the structure.
2.5Transient Response: Accelerometers are also used for measuring shortduration shocks caused by impact of two bodies or say during drop testing of
packages etc. The two shock parameters that need to be accurately measured
are time duration of shock and the amplitude of shock. The shock duration
could be smaller than the natural period of the system. The most likely error
could be in estimating the time duration due to retention of charge by the
accelerometer when shock is suddenly applied and in estimating the amplitude
when the resonance of the accelerometer is excited. The supplier provides the
safe lower and upper limit of shock measurement.
2.6Temperature limits: Since property of the piezo material is dependent on thetemperature, it is advisable to stick to the specified limit. Beyond the limit the
piezo material depolarizes causing permanent loss or change in sensitivity.
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Some times heat sinks (finned washer) or mica washers are used to reduce
heat transmission. Sensitivity versus temperature curves is provided by the
suppliers to estimate the error in measurement due to temperature effect.
2.7Phase Response: Any shift in the phase between mechanical input andresulting electrical output of the accelerometer indicates time delay between
input and output and hence distortion of the mechanical input. At frequencies
below the mounted resonance there should be no phase shift. Figure 12
illustrated the phase and amplitude relationship.At resonance frequency, the
motion of the seismic mass inside the accelerometer lags that of the base
resulting in phase distortion
Figure-12 Phase and amplitude relation
2.8 Environmental condition: Most of the accelerometers withstand accumulated
gamma radiation dose of 2 M Rad with out significant degradation. For
permanent installation under nuclear radiation, accelerometers to withstand
accumulated dose of 100 M Rad is available. Magnetic sensitivity of piezo
sensors is very low. Measurements on power generators and magnetic devices
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are possible with out distortion. Acoustic noise present in the machine is not
sufficient to induce any error in the measurement.
3.0 Piezoelectric Accelerometers
Since accelerometers are widely used in the industry, let us understand its
working. Figure 13 shows a general arrangement of measurement using an
accelerometer.
Figure-13 General scheme of measurement using accelerometer
The output impedance of a piezo element is very high and so cannot be directly
connected to a read out device, which normally have low input impedance. When
connected, it can greatly reduce the sensitivity as well as its frequency range. To
eliminate this connectivity problem, the accelerometer out put is connected to a
pre amplifier, which has high input impedance and low output impedance. Figure
14 shows the equivalent circuit diagram of an accelerometer, which is basically a
charge generator q coupled with an internal capacitance C. e is the voltage
across the capacitor. Figure 15 show the equivalent diagram of accelerometer plus
cable plus charge amplifier.
Figure-14 Equivalent circuit for an Accelerometer
Vibration Preamplifier Analyzer Recorder
Pick-up
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Figure-15 Equivalent diagram for an Accelerometer + Cable + Charge Amplifier
The pre amplifiers are either voltage type in which the out put voltage is
proportional to input voltage from the sensor or charge type in which the out put
voltage is proportional to input charge. When voltage amplifier is used, the
overall system is very sensitive to changes in cable capacitance that is changes in
the cable length between the sensor and the pre amplifier. However, with charge
pre amplifiers the out put remains unaffected by the length of the cable. Hence
one has to be careful in knowing the type of preamplifiers before the
measurement or even while specifying for purchase of vibration equipments.
Some preamplifier includes integrators to convert acceleration signal to velocity
or displacement proportional signal.
4.0 Cables
The signal carrying cables are one of the loose links in the chain of vibration
measuring setup. They have to be correctly and carefully used for dependable
diagnostics. There are many instances wherein bad cables have given wrong
reading. In spite of standardized connecting cables, over the years of use,connecting errors creep in. Since accelerometers are high impedance device,
certain problem may also arise due to cable noise. The noise can originate either
from mechanical motion of the cable, also called tribo-electric effect or from
the ground loop. Mechanical motions of the cable during the measurements result
in change in the charge. Such an effect disturb cause disturbance in the low
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frequency range. This can be avoided by the practice of clamping the cable firmly
to arrest relative movement between several layers of insulation in the cable as
shown in figure 16.
Figure-16 Illustration of fastening cables to eliminate triboelectric noise
The second source of noise is the hum picked up from the mains supply by
ground loop in the chain of measuring device. Ground loop currents flow in the
shielded layer of the cables because of slight difference in the electrical potential
of grounding points such as at the accelerometer base and the electrical ground of
the read out device. The best way to eliminate ground loop is to ensure that the
entire system is grounded at one point meaning electrically isolate the base of the
accelerometer as shown in figure 17.
Figure-17 Proper connection to avoid Ground loop
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Electromagnetic noise can also pose problem when the cable is laid in the vicinity
of running electrical machinery. If this cannot be avoided, then at least double
shielded cable must be used to reduce the pick up noise.
5.0 Mounting the accelerometer
Selection of the correct mounting arrangement plays a significant roll in the use of
vibration measurement as its mounting decides the mounted resonance frequency
and hence its useful frequency range of measurement.The popular methods are
stud mounted, wax mounted magnet mounted, adhesive mounted and hand probe
type. The mounting type also depends on the size of the accelerometers and
position of measurement. For example big size accelerometer cannot be mounted
with wax when it has to be used for measuring on inclined or vertical plane of a
machine for the fear of dislodging or slipping downward. However miniature
sensors can be mounted with wax in any plane. The most popular method is probe
type mounting because it needs minimum preparation and is quick to use.
However it is most error prone especially when the measurement involves high
frequency. Probe type mounting drastically reduces the useful frequency range.
Figure-18 Illustration of Probe type and Stud Mounting
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Figure-19 Change of Response of Accelerometer for different type of mounting
Figure 18 and 19 illustrate the two extreme mounting methods of accelerometer
and its effect on the frequency response. Looking at the reduction of high
frequency response during probe type of mounting of accelerometers, one has to
be careful. Due to ease of measurement with probe type of mounting, there is a
tendency to make error especially while monitoring high frequency vibration say
in a bearing.
6.0 Accelerometer Calibration
Accelerometer calibration is to ensure the accuracy, reliability and repeatability of
measurement. Calibration helps to trace measured vibration values to the physical
standard. There are several reasons for performing a calibration. The most
important being the contractual reasons as an evidence of the accuracy of the
sensor, possibly with reference to international standards. At times calibration is
required to when performance of the sensor in a particular environment has not
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been documented. System checking also forms an important part of the calibration
process, particularly in measurement systems consisting of many instruments.
The most common question raised by users is how often the sensor should be sent
for calibration. While the manufacturers say that ideally accelerometers do not
need calibration for several years if they are used as per the manufactured
specification. However, we know that the accelerometers are subject to rough
handling in shop floor. If not the sensor per se, at least the connected cables,
connectors, switches in the readout meters get bad. At least for the system as a
whole recalibration is required. Then the question is how often the calibration
should be done. This is best judge is the user himself. Depending on the usage and
duty cycle of the accelerometer and its electronics, recalibration can be carried at
least once in year or earlier.
There are different levels of calibration possible such as primary, secondary, and
working reference type. In primary calibration, the sensitivity of the
accelerometer is established in terms of fundamental or derived units for physical
quantities of SI systems. Such transducers are kept in National Standard Institutes.