vibration

ED 7104 –VIBRATION ANALYSIS & CONTROL
NOTES ON
UNIT 4 - VIBRATION CONTROL
UNIT 5 - EXPERIMENTAL METHODS IN
VIBRATION ANALYSIS

ANNA UNIVERSITY SYLLABUS
REG- 2013
UNIT IV VIBRATION CONTROL
Specification of Vibration Limits –Vibration severity standards-
Vibration as condition Monitoring tool-Vibration Isolation methods-
-Dynamic Vibration Absorber, Torsional and Pendulum Type
Absorber- Damped Vibration absorbers-Static and Dynamic
Balancing-Balancing machines-Fieldbalancing – Vibration Control by
Design Modification- - Active Vibration Control
2

UNIT 4 : VIBRATION CONTROL
S.NO CONTENTS PAGE NO
1 Specification of Vibration Limits. 4
2 Vibration severity standards. 7
3 Vibration as condition Monitoring tool. 11
4 Vibration Isolation methods. 15
5 Dynamic Vibration Absorber. 23
6 Torsional and Pendulum Type Absorber. 31
7. Damped Vibration absorbers. 33
8. Static and Dynamic Balancing. 37
9. Balancing machines. 41
10. Field balancing 66
11. Vibration Control by Design Modification 67
12. Active Vibration Control 70
UNIVERSITY QUESTIONS
PART-A 76
PART-B 76
3

1. SPECIFICATION OF VIBRATION LIMITS
Design and control procedures of vibration have the primary objective of
ensuring that, under normal operating conditions, the system of interest does not
encounter vibration levels that exceed the specified values. In this context, then,
the ways of specifying vibration limits become important.
This section will present some common ways of vibration specification
1.1 PEAK LEVELSPECIFICATION
Vibration limits for a mechanical system can be specified either in the time
domain or in the frequency domain. In the time domain, the simplest
specification is the peak level of vibration (typically acceleration in units of g,
the acceleration due to gravity). Then, the techniques of isolation, design, or
control should ensure that the peak vibration response of the system does not
exceed the specified level. In this case, the entire time interval of operation of
the system is monitored and the peak values are checked against the
specifications. Note that in this case, it is the instantaneous peak value at a
particular time instant that is of interest, and what is used in representing
vibration is an instantaneous amplitude measure rather than an average
amplitude or an energy measure.
1.2 RMS VALUESPECIFICATION
The root-mean-square (rms) value of a vibration signal y(t) is given by the
square root of the average (mean value) of the squared signal:
 1.1
Note that by squaring the signal, its sign is eliminated and essentially the energy
level of the signal is used. The period T over which the squared signal is
averaged will depend on the problem and the nature of the signal. For a periodic
signal, one period is adequate for averaging. For transient signals, several time
constants (typically four times the largest time constant) of the vibrating system
will be sufficient. For random signals, a value that is as large as feasible should
be used.
In the method of rms value specification, the rms value of the acceleration
response (typically, acceleration in gs) is computed using equation (1.1) and is
then compared with the specified value.
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In this method, instantaneous bursts of vibration do not have a significant effect
because they are filtered out as a result of the integration. It is the average
energy or power of the response signal that is considered. The duration of
exposure enters into the picture indirectly and in an undesirable manner. For
example, a highly transient vibration signal can have a damaging effect in the
beginning; but the larger the T that is used in equation (1.1), the smaller the
computed rms value.
Hence, the use of a large value for T in this case would lead to diluting or
masking the damage potential.
In practice, the longer the exposure to a vibration signal, the greater the harm
caused by it. Hence, when using specifications such as peak and rms values,
they have to be adjusted according to the period of exposure. Specifically, larger
levels of specification should be used for longer periods of exposure.
1.3 FREQUENCY-DOMAIN SPECIFICATION
It is not quite realistic to specify the limitation to vibration exposure of a
complex dynamic system by just a single threshold value. Usually, the effect of
vibration on a system depends on at least the following three parameters of
vibration:
1. Level of vibration (peak, rms, power, etc.)
2. Frequency content (range) of excitation
3. Duration of exposure to vibration.
This is particularly true because the excitations that generate the vibration
environment may not necessarily be a single-frequency (sinusoidal) signal and
may be broad-band and random; and
Fig 1 Shows Operating vibration specification (nomograph) for a machine
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furthermore, the response of the system to the vibration excitations will depend
on its frequency transfer function, which determines its resonances and damping
characteristics. Under these circumstances, it is desirable to provide
specifications in a nomograph, where the horizontal axis gives frequency (Hz)
and the vertical axis could represent a motion variable such as displacement
(m), velocity (m·s–1), or acceleration (m·s–2 or g). It is not very important
which of these motion variables represents the vertical axis of the nomograph.
This is true because, in the frequency domain,
and one form of motion can be easily converted into one of the remaining two
motion representations. In each of the forms, assuming that the two axes of the
nomograph are graduated in a logarithmic scale, the constant displacement,
constant velocity, and constant acceleration lines are straight lines.
Consider a simple specification of machinery vibration limits as given by the
following values:
This specification can be represented in a velocity vs. frequency nomograph
(log–log) as in Fig 1.Usually, such simple specifications in the frequency
domain are not adequate. As noted before,the system behavior will vary,
depending on the excitation frequency range. For example, motion
sickness in humans might be predominant in low frequencies in the range of 0.1
Hz to 0.6 Hz, and passenger discomfort in ground transit vehicles might be most
serious in the frequency range of 4 Hz to 8 Hz for vertical motion
Fig 2 A severe-discomfort vibration specification for ground transit vehicles.
and 1 Hz to 2 Hz for lateral motion. Also, for any dynamic system,
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particularly at low damping levels, the neighbourhoods of resonant frequencies
should be avoided and, hence, should be specified by low vibration limits in the
resonant regions. Furthermore, the duration of vibration exposure should be
explicitly accounted for in specifications. For example,
Fig2 presents a ride comfort specification for a ground transit vehicle, where
lower vibration levels are specified for longer trips.
The system should perform below (within) these specifications
under normal operating conditions. The test should be conducted at or above
these vibration levels so that the system will meet the test specifications.
Fig Represents the vibration on several vibration limits
2. VIBRATION SEVERITY STANDARDS
Standard are intended:
· To setup criteria for rating or classifying the performance of
equipment or material
· To provide a basis for comparison of the maintenance
qualities of pieces of equipment of the same type
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· To test equipment whose continuous operation in
necessary for industrial or public safety
· To provide a basis for the selection of equipment or material
· To setup a procedure for the calibration of equipment
ISO 2372 (10816) Standards provide guidance for evaluating vibration severity
in machines operating in the 10 to 200Hz (600 to 12,000 RPM) frequency
range.
• Examples of these types of machines are small, directcoupled, electric motors
and pumps, production motors, medium motors, generators, steam and gas
turbines, turbocompressors, turbo-pumps and fans.
• Some of these machines can be coupled rigidly or flexibly,
or connected though gears.
• The axis of the rotating shaft may be horizontal, vertical or inclined at any
angle. Use the chart below combined withadditional factors described in this
manual to judge the overall vibration severity of your equipment.
Vibration Severity Level ISO 10816-1
Shaft Speed (RPM)
Less than 2,000 Greater than 2,000
Mounting Drive Category Mounting Drive Category
Rigid Mounting Rigid Drive I Rigid Mounting Rigid Drive II
Flex Drive II Flex Drive III
Flexible Rigid Drive II Flexible Rigid Drive III
8

Mounting Fle Mounting
ISO 10816 was released in August 2000, establishes the general conditions and
procedures for measurement and evaluation of vibrations using measurements
made on the non-rotating parts of machines. It also provides general evaluation
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criteria related to both operational monitoring and acceptance testing
established primarily with regard to securing reliable long term operation of the
machine.
· ISO 10816-3 separates the working conditions into four zones:
· Zone A Green: Vibration values from machines just put into operation.
· Zone B Yellow: continuous operation without any restrictions.
· Zone C Orange: condition is acceptable only for a limited period of
time.
· Zone D Red: Dangerous vibration values - damage could occur at any
time.
· It also defines four groups of machines, according to their size, base
and purpose.
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3. VIBRATION AS CONDITION MONITORING TOOL
CONDITION MONITORING
• Condition Monitoring and Machinery Vibration Analysis
• Condition Monitoring (CM) - a maintenance process where the condition of
equipment with regard to overheating and vibration is monitored for early
signs of impending failure.
• Equipment can be monitored using sophisticatedinstrumentation such as
vibration analysis equipment or the human senses. Where instrumentation is
used actual limits can be imposed to trigger maintenance activity.
Condition Monitoring (CM), Predictive Maintenance (PdM) and Condition
Based Maintenance (CBM) are other terms used to
describe this process.
Condition monitoring or CBM (Condition BasedMonitoring ) is an effective
form of predictivemaintenance (PdM) where, as you may have guessed, you
monitor the condition of specific areas of plant and equipment. This can be done
automatically with the use of instrumentation such as machinery vibration
analysis and thermalimaging equipment or manually.
• In automatic CBM when any monitored and predefined condition limit is
exceeded, a signal or output is turned on. This output can be sent directly
to a CMMS so that a work order is generated automatically. This is particularly
suited to continuous process plants where plant failure and downtime can be
extremely costly.
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The most commonly used method for rotating machines is called Vibration
analysis.
• Measurements can be taken on machine bearing casings with seismic or piezo-electric
transducers.
• To measure the casing vibrations, and on the vast majority of critical
machines, with eddy-current transducers that directly observe the rotating
shafts to measure the radial (and axial) vibration of the shaft.
• The level of vibration can be compared with historical baseline values such as
former startups and shutdowns, and in some cases established standards
such as load changes, to assess the severity.
One commonly employed technique is to examine the individual frequencies
present in the signal.
• These frequencies correspond to certain mechanical components (for example,
the various pieces that make up a rolling-element bearing) or certain
malfunctions (such as shaft unbalance or misalignment). By examining these
frequencies and their harmonics, the analyst can often identify the
location and type of problem, and sometimes the root cause as well.
• For example, high vibration at the frequency corresponding to the speed of
rotation is most often due to residual imbalance and is corrected by balancing
the machine. Beside all sensors and data analysis it is important to keep in
mind that more than 80% of all complex mechanical equipment fail
accidentally and without any relation to their life-cycle period.
3.1 PIEZO-ELECTRIC TRANSDUCERS
Some substances, such as barium titanate and single-crystal quartz, can generate
an electrical charge and an associated potential difference when subjected to
mechanical stress or strain. This piezoelectric effect is used in piezoelectric
transducers. Direct application of the piezoelectric effect is found in pressure
and strain measuring devices, and many indirect applications also exist. They
include piezoelectric accelerometers and velocity sensors and piezoelectric
torque sensors and force sensors. It is also interesting to note that piezoelectric
materials deform when subjected to a potential difference (or charge). Some
delicate test equipment (e.g., in vibration testing) use piezoelectric
actuating elements (reverse piezoelectric action) to create fine motions. Also,
piezoelectric valves (e.g., flapper valves), directly actuated using voltage
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signals, are used in pneumatic and hydraulic control applications and in ink-jet
printers. Miniature stepper motors based on the reverse piezoelectric
action are available.
Consider a piezoelectric crystal in the form of a disc with two electrodes plated
on the twoopposite faces. Because the crystal is a dielectric medium, this device
is essentially a capacitor thatcan be modeled by a capacitance C, as in equation
C=kA/x
Accordingly, a piezoelectric sensor canbe represented as a charge source with a
series capacitive impedance shown in fig in an equivalent circuit.
Fig Shows Equivalent circuit representation of a piezoelectric sensor
3.2 EDDY-CURRENT TRANSDUCERS
If a conducting (i.e., low-resistivity) medium is subjected to a fluctuating
magnetic field, eddy currents are generated in the medium. The strength of eddy
currents increases with the strength of the magnetic field and the frequency of
the magnetic flux. This principle is used in eddy current proximity sensors.
Eddy current sensors can be used as either dimensional gaging devices or high
frequency vibration sensors.
A schematic diagram of an eddy current proximity sensor is shown in Figure
3.2(a). Unlike variable-inductance proximity sensors, the target object of the
eddy current sensor does not have to be made of ferromagnetic material. A
conducting target object is needed, but a thin film conducting material — such
as household aluminum foil glued onto a nonconducting target object would be
adequate. The probe head has two identical coils, which will form two arms of
animpedance bridge. The coil closer to the probe face is the active coil. The
other coil is the compensating coil. It compensates for ambient changes,
particularly thermal effects. The other two arms of the bridge will consist of
purely resistive elements [see Figure 3.2(b)]. The bridge is excited by a
radiofrequency voltage supply. The frequency can range from 1 MHz to 100
MHz.
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Fig3.2 Shows Eddy current proximity sensor: (a) schematic diagram, and (b) impedance bridge.
This signal is generated from a radiofrequency converter (an oscillator) that is
typically poweredby a 20-VDC supply. In the absence of the target object, the
output of the impedance bridge is zero, which corresponds to the balanced
condition. When the target object is moved close to the sensor, eddy currents
are generated in the conducting medium because of the radiofrequency
magnetic flux from the active coil.
The magnetic field of the eddy currents opposes the primaryfield that generates
these currents. Hence, the inductance of the active coil increases, creating an
imbalance in the bridge. The resulting output from the bridge is an amplitude-modulated
signal containing the radiofrequency carrier. This signal is
demodulated by removing the carrier.
The resulting signal (modulating signal) measures the transient displacement
(vibration) of the target object. Low-pass filtering is used to remove the high-frequency
leftover noise in the output signal once the carrier is removed. For
large displacements, the output is not linearly related to the
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displacement. Furthermore, the sensitivity of the eddy current probe depends
nonlinearly on thenature of the conducting medium, particularly the resistivity.
For example, for low resistivities, sensitivity increases with resistivity; for high
resistivities, sensitivity decreases with resistivity. A calibrating unit is usually
available with commercial eddy current sensors to accommodate various target
objects and nonlinearities. The gage factor is usually expressed in volts per
millimeter. Notethat eddy current probes can also be used to measure resistivity
and surface hardness (which affects resistivity) in metals.
The facial area of the conducting medium on the target object has to be slightly
larger than the frontal area of the eddy current probe head. If the target object
has a curved surface, its radius of curvature has to be at least four times the
diameter of the probe. These are not serious restrictions because the typical
diameter of the probe head is about 2 mm. Eddy current sensors are medium
impedance devices; 1000 Ω output impedance is typical. Sensitivity is on the
order of 5 V·m/m. Since the carrier frequency is very high, eddy current devices
are suitable for highly transient vibration measurements — for example,
bandwidths up to 100 kHz. Another advantage of an eddy current sensor is that
it is a noncontacting device; there is no mechanical loading on the moving
(target) object.
4 VIBRATION ISOLATION METHODS
Vibration isolation: It is a process of reducing the vibrations of machines and
hence reducing the transmitted force to the foundation using vibration isolating
materials is called vibration isolation.
When the targeted object is rather heavy (e.g. building, bridge or the like),
vibration isolation may be called base isolation. Vibration isolation is a
branch of protective techniques known as vibration control.
METHODS
1. Vibration Isolation with Rigid Foundation.
2. Vibration Isolation with Flexible Foundation.
3. Vibration Isolation System with Partially Flexible Foundation.
4. Shock isolation.
5. Isolation under shock.
6. Vibration under step load.
4.1 VIBRATION ISOLATION WITH RIGID FOUNDATION
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While ω/ωn = r r= Frequency ratio
Vibration of Transmission Ratio
4.2 VIBRATION ISOLATION WITH FLEXIBLE FOUNDATION
17

4.3VIBRATION ISOLATION SYSTEM WITH PARTIALLY
FLEXIBLE FOUNDATION
19

4.6. VIBRATION UNDER STEP LOAD
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5. DYNAMIC VIBRATION ABSORBER
History and Principle of Operation
The dynamic vibration absorber (DVA)was invented in 1909 by
Hermann Frahm. it has been successfully used to suppress wind-induced
vibration and seismic response in buildings. Characteristics of DVA
werestudied in depth by Den Hartog (1985).
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In the industry, it has been primarily used to suppress vibration caused by a
resonance condition in machinery. A DVA, sometimes referred to as a tuned
mass damper, consists of a spring-mass system installed on a vibrating machine.
In its classic form, its natural frequency is tuned to match the natural frequency
of the machine it is installed on. Because of this tuning a DVA exerts a force on
the main system that is equal and opposite to the excitation force, canceling
vibration at the resonant frequency.
DYNAMIC MODEL
For simplicity, we will consider a dynamic model for a machine as a single
degree of freedom system consisting of a single mass and a single spring. We
will use a similar model for the dynamic vibration absorber. When the DVA is
installed on the main system, the result is a two degree of freedom system
whose dynamic model is shown in Fig
In this system, the coordinate x1 corresponds to the displacement of the main
mass M, and the coordinate x2 corresponds to the displacement of the absorber
mass m. The main system’s stiffness is represented by the equivalent spring
K, while the absorber system has the spring k. The absorber system has a
viscous damping element c while the main system is considered undamped. The
main system is excited by a periodic force F that in rotating machines is usually
represented by residual imbalance force, but could be any periodic excitation
originating in the machine, such as vane passing excitation in centrifugal
pumps.
First, a few variables and dimensionless ratios must be introduced, since the
results will be easier to handle in this form
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Now we are ready to plot the results. First,we will evaluate the effect of an
undamped dynamic absorber with the absorber tuned to the main system natural
frequency, so that the tuning ratio f = 1(damping ratio = 0). These results are
shown in Figure 3.
It is notable how the dynamic absorber cancels vibration at the resonance
frequency.
Instead, it creates two new natural frequencies, one below and one above the
original natural frequency. This happens because with the absorber the system
has two degrees of freedom and hence two corresponding natural frequencies.
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The width between the two new natural frequencies depends on the mass ratio
μ. Figure 3 shows the response with two different mass ratios.
With a larger absorber mass the natural frequencies sit wider apart, so a wider
safe operating range around the original resonant frequency can be achieved.
However, the large absorber mass very quickly becomes impractical, especially
for large machinery. Figure 4 shows the two new natural frequencies in relation
to the mass ratio of the absorber.
By changing the tuning ratio of the absorber, the position of the two new natural
frequencies and a usable operating speed range between them can be further
adjusted. Figure 5 shows the effect of tuning on the natural frequencies of the
combined system with an undamped absorber (damping ratio = 0).
Two curves represent two absorber systems: one with the standard tuning ratio
f = 1 (blue lines), and the other one with the tuning ratio f = 1.4, representing
an over tuned absorber system (magenta lines). The over tuned absorber creates
a slightly higher low natural frequency, but significantly extends the range into
the area of high frequencies. Figure 6 shows the two natural frequencies of the
combined system in relation to the tuning ratio. By varying tuning and mass
ratios, a necessary operating speed range free of natural frequencies can be
achieved with an undamped DVA.
This is important because an undamped absorber is simple to design and
manufacture and its adjustment is less complicated than in a damped absorber
that is described below. The tradeoff is that for a wide frequency range a
required undamped absorber may become quite large.
DERIVATION
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6. TORSIONAL AND PENDULUM TYPE ABSORBER
Torsional vibrations
Torsional vibration is angular vibration of an object—commonly a
shaft along its axis of rotation. Torsional vibration is often a concern in power
transmission systems using rotating shafts or couplings where it can cause
failures if not controlled. A second effect of torsional vibrations applies to
passenger cars. Torsional vibrations can lead to seat vibrations or noise at
certain speeds. Both reduce the comfort.
In ideal power generation, or transmission, systems using rotating parts, not
only the torques applied or reacted are "smooth" leading to constant speeds, but
also the rotating plane where the power is generated (or input) and the plane it is
taken out (output) are the same. In reality this is not the case. The torques
generated may not be smooth (e.g., internal combustion engines) or the
component being driven may not react to the torque smoothly
(e.g., reciprocating compressors), and the power generating plane is normally at
some distance to the power takeoff plane. Also, the components transmitting the
torque can generate non-smooth or alternating torques (e.g., elastic drive belts,
worn gears, misaligned shafts). Because no material can be infinitely stiff, these
alternating torques applied at some distance on a shaft cause twisting vibration
about the axis of rotation.
Sources of torsional vibration
Torsional vibration can be introduced into a drive train by the power
source. But even a drive train with a very smooth rotational input can develop
torsional vibrations through internal components. Common sources are:
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· Internal combustion engine : The torsional vibrations of the not
continuous combusion and the crank shaft geometry itself cause torsional
vibrations
· Reciprocating compressor : The pistons experience discontinuous forces
from the compression.
· Universal joint : The geometry of this joint causes torsional vibrations if
the shafts are not parallel.
· Stick slip : During the engagement of a friction element, stick slip
situations create torsional vibrations.
· Lash : Lash in a drive train can cause torsional vibrations if the direction
of rotation is changed
TORSIONAL AND PENDULUM TYPE ABSORBER
Centrifugal pendulum vibration absorbers (CPVA) have been used for a long
time as a method to suppress torsional vibration. Recently, roller type CPVA,
that has a similar characteristic but simpler structure, have been investigated and
started to be used in some automobile engines.
However, only the linear dynamical characteristics of the roller type CPVA
have been focused, and the influence of the nonlinearity affecting on vibration
suppression has not been clarified. This study mainly focuses on the explanation
of nonlinear dynamical characteristics of roller type CPVA.
Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber
used for the attenuation of torsional vibrations in rotating and reciprocating
machines.
• They consist of masses that are constrained to move along specific paths
relative to the rotational axis of the machine.
• Previous analytical studies have considered theperformance of single absorber
systems with general paths and of multi-absorber systems with a specific path
type.
Rotating machines are often subjected to #actuating torsional
loads that can cause noise and vibration difficulties, for
example, gear rattle and fatigue failure.
• Many methods are used to reduce torsional vibrations, including the addition
of wheels and tuned vibration dampers.
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• These methods, however, have some shortcomings. Flywheels increase the
system inertia, which reduces system responsiveness, while torsional dampers
dissipate energy and work at only a single frequency (or a small set of resonant
frequencies).
• method for reducing torsional vibrations is the use of
centrifugal pendulum vibration absorbers (CPVAs)
7. DAMPED VIBRATION ABSORBER
Fig ShowsPrimary system with a damped vibration absorber.
Damping is not the primary means by which vibration control is achieved in a
vibration absorber. As noted before, the absorber acquires vibration energy from
the primary system (and, in return, exerts a force on the system that is equal and
opposite to the vibration excitation), there by suppressing the vibratory motion.
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The energy received by the absorber must be dissipated gradually and, hence,
some damping should be present in the absorber. Furthermore, as one will
notice in the following development, the two resonances created by adding the
absorber have an infinite magnitude in the absence of damping. Hence, damping
has the added benefit of lowering these resonant peaks as well.
The analysis of a vibratory system with a damped absorber is as straightforward
as, but bsomewhat more complex than, that involving an undamped absorber.
Furthermore, an extra design parameter — the damping ratio of the absorber —
enters into the scene. Consider the model shown in above Fig the transfer
function of vibration control can be taken as either ya /f or fs /f, the latter being
simply kp times the former.
Hence, one can consider the dimensionless case of fs /f, but the results are
equally valid for yp/f,except that the responses must be converted from force to
displacement by dividing by kp. There is no need to derive the transfer function
anew for the damped system. Simply replace ka in equation (12.101) by the
complex stiffness ka + jωba, which incorporates the viscous damping
constant ba and the excitation frequency ω. Hence, the transfer function of the
damped system is
From 1 we get 2
1. & 2.
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By solving above 2 eqns we get
12.108
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This result demonstrates that an optimized damped dynamic absorber
suppresses resonance vibration within a wide frequency range. This is a
universal solution as it works for any frequency range. The amplification factor
is controlled by the mass ratio, so an absorber can be designed to meet a specific
vibration limit.
8. STATIC AND DYNAMIC BALANCING.
Balancing is an essential technique applied to mechanical parts of rotational
functionality (wheels, shafts, flywheels…), in order to eliminate the detected
irregularities found within it, and that may cause excessive vibrations during
operation, and act as undesirable disturbances on the system being
in use Such irregularities may rise due to the inhomogeneous distribution of
material within the part, bending and deflection of rotating shafts, and
eccentricity of mass from the axis of rotation of the rotating disks and rotors.
• These irregularities lead to small eccentric masses that disturb mass
distribution of the part, and the lastgenerate centrifugal forces when the part is
in rotation;the magnitude of these forces increases rapidly with speed of
rotation, and enhances vibration.
STATIC BALANCING
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• Static Balancing simply means the insurance of mass distribution about the
axis of rotation of the rotating mechanical part in the radial directions, without
consideration of that distribution in the axial (longitudinal) direction.
Consider a circular disk of perfect mass distribution, with the points A and B are
at two opposite positions on the circumference of the disk, but each is on one
of the faces of the disk, and suppose that a point mass with the same value is
fixed at each of the two points A and B.
CONDITIONS
· The net dynamic forces acting on a shaft is equal to zero.
· It deals only with the balancing of dynamic forces.
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DYNAMIC BALANCING
Dynamic Balancing differs from static balancing in that the mass distribution of
the part is detected in all directions, and not only about the central axis; and so,
not only the magnitude of the unbalanced mass and its distance from the axis of
rotation are to be determined, but also its position in the axial (longitudinal)
direction of the rotational part
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consider a disk rotating with an angular speed , with different out of balance
masses mi, each witheccentricity ei from the axis of rotation. These masses are
not expected to be in the same plane, but in different locations along the disk’s
axial direction; in addition, each mass will produce a centrifugal force making
an angle  i with the reference horizontal direction in its own plane.
Choosing any plane as the reference for the otherplanes containing the eccentric
masses, such that each one of them is at distance ai from that reference plane.
• And for simplicity, choose plane-1 as the reference plane, where a1 becomes
zero.
• The dynamic balancing of a system to be achieved,then:
• “The resultant force of all centrifugal forces caused by the out of balance
masses should be zero (as in static balancing).
· It deals with balancing of dynamic force & balancing of couple due ro
dynamic forces ,in addition to that the
summation of their moments about any point should be also zero”, that is:
And so, after choosing a reference plane, translate all the centrifugal forces in
the other planes to that plane as forces (miei2) and moments (aimiei2), and
there you can apply the vector summation of forces and moments separately to
satisfy the requirements of dynamic balancing mentioned in eqns-1 & 3.
9.BALANCING MACHINES
EXPERIMENTAL PROCEDURE OF BALANCING
The experimental procedure for determining the balancing masses and locations
for a rotating system should be clear from the analytical developments and
examples given above. The basic steps are: (1) determine the magnitude and the
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phase angle of accelerometer signals at the bearings with and without trial
masses at the bearing planes; (2) using this data, compute the necessary
balancing masses (magnitude and location) at the bearing planes; (3) place the
balancing masses and (4) check whether the system is balanced. If not, repeat
the balancing cycle.
A laboratory experimental setup for two-plane balancing is schematically
shown in below Figure 9.1A view of the system is shown in Figure 9.2 The
two disks rigidly mounted on the shaft, are driven by a DC motor. The drive
speed of the motor is adjusted by the manual speed controller.
The shaft bearings (two) are located very close to the disks, as shown in Figure
9.1. Twoaccelerometers are mounted on the top of the bearing housing so that
the resulting vertical accelerations can be measured. The accelerometer signals
are conditioned using the two-channel charge amplifier, and read and displayed
through two channels of the digital oscilloscope. The output of the stroboscope
(tachometer) is used as the reference signal with respect to which the phase
anglesof the accelerometer signals are measured.
In Figure 9.2 , the items of equipment are seen, from left to right, as follows.
The first item is the two-channel digital oscilloscope. Next is the manual speed
controller, with control knob, for the DC motor. The pair of charge amplifiers
for the accelerometers is situated next. The strobelight unit (strobe-tacho) is
placed on top of the common housing of the charge-amplifier pair. The two-disk
rotor system with the drive motor is shown as the last item to the right. Also,
note the two accelerometers (seen as small vertical projections) mounted on the
bearing frame of the shaft, directly above the two bearings.
FIG 9.1 Shows schematic arrangement of a rotor balancing experiment.
In determining an unbalance load, the accelerator readings must be
taken with respect to a body reference on the rotating object. Since this
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reference must always be fixed, prior to reading the oscilloscope data, the
strobe-tacho should be synchronized with the disk rotation with respect to
both frequency and phase. This is achieved as follows. Note that all the
readings are taken with the same rotating speed, which is adjusted by the
manual speed controller.
Fig 9.2 Shows A view of the experimental setup for two-plane balancing. (Courtesy of the University of
British Colombia. With permission
Make a physical mark (e.g., black spot in a white background) on one of the
disks. Aim the strobe flash at this disk. As the motor speed is adjusted to the
required fixed value, the strobe flash is synchronized such that the mark on the
disk “appears” stationary at the same location (e.g., at the uppermost location of
the circle of rotation). This ensures not only that the strobe frequency is equal to
the rotating speed of the disk, but also that the same phase angle reference is
used for all readings of accelerometer signals.
The two disks have slots at locations for which the radius is known and for
which the angular positions with respect to a body reference line (a radius
representing the 0° reference line) are clearly marked. Known masses (typically
bolts and nuts of known mass) can be securely mounted in these slots. Readings
obtained through the oscilloscope are:
1. Amplitude of each accelerometer signal
2. Phase lead of the accelerometer signal with respect to the synchronized and
referencefixed
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strobe signal (Note: a phase lag should be represented by a negative sign in the
data.
TYPES
1. SINGLE PLANE BALANCING.
2. TWO PLANE BALANCING.
9. 1 SINGLE PLANE BALANCING
PROCEDURE
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STEPS REQUIRED TO PERFORM SINGLE PLANE BALANCE
The steps required to perform a single plane balance are the same for
both the Vector and Influence Coefficient solution methods. In the end both
methods will yield the same information. Our data collectors and balance
programs use the Influence Coefficient method so this may be the method
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which the user should get the most familiar with. Now that we are setup and are
prepared
to install a trial weight we are ready to complete the remaining steps. For a
single plane balance the following steps are required to collect the necessary
data to perform the rotor balance.
1. Acquire initial set of 1X amplitude and phase data.
Note: as a good practice log 1X data in vertical, horizontal, and axial directions
at
both bearings.
2. Shut down machine and observe 1X amplitude and phase during shutdown to
assist in trial weight placement
3. Draw initial 1X vector on Polar graph paper
4. Determine trial weight angular placement. Show trial weight magnitude and
placement on polar graph.
5. Attach trial weight to rotor.
6. Run machine and log 1X amplitude and phase at all locations. (Trial Run).
7. Shutdown machine
8. Remove Trial Weight
9. Draw Trial Weight vector on polar graph.
10. Perform balance calculations - determine magnitude and angle of corrective
weight.
11. Attach weight to machine.
12. Run equipment and log 1X amplitude and phase at all locations. Perform an
evaluation of the data. Ask the following questions:
1. Did 1X amplitudes decrease at all locations? If not balance may not be the
only fault.
2. Is a trim run required to further reduce levels?
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16. For trim run use Sensitivity/Response Vector to calculate trim balance
correction.
Repeat steps 13-15. Note: If amplitudes do not decrease following trim balance
other factors may be affecting the rotor. Perform a full analysis and perform
necessary inspection before adding additional weight.
9.2 TWO PLANE BALANCING
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Problem
10 FIELD BALANCING
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Field balancing is a technique used to balance a rotating part in place without
removing the part from the machine. The advantages of field balancing
are apparent, in that time can be saved by not removing the rotating part from
the machine and sending it to a shop for balancing. An additional benefit is
realized in ensuring that the rotating part is balanced as installed.
When field balancing, one must have access to the rotating shaft and have an
area to place trial weights and correction
weights.
A B C D
Fig A Shows the access requirements for field balancing eliminate many machines
Fig B depicts an end view of a rotor
Fig C depicts the trial weight run.
Fig D shows the correction and result
Balancing in its most basic form is a problem of ratios. To simplify, we will use
a one plane example and eliminate the angle calculations by assuming we know
exactly where the heavy spot is located on a rotor. Figure 2 depicts an end view
of a rotor. The amount of vibration is measured and indicates 10-mil of
vibration 90-deg from the 0 angle reference. No weight has been added at this
point and the measurement represents the “as found” condition.
Trial weights provide a method to calibrate the rotor system. A known trial
weight, placed in a known position, will influence the vibration a specific
amount that will permit correcting the measured imbalance.
In this example, we have placed one gram of weight at270-deg. The resulting
vibration was reduced from 10-mil to 5-mil and the angle did not change. This
means we placed the trial weight exactly opposite the heavy spot on the rotor.
Now we can apply the ratio:
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As can be seen from the ratio, if one gram reduced the vibration from 10-
mil to 5-mil, then two grams placed at the same location should reduce the
vibration to 0-mil.
11. VIBRATION CONTROL BY DESIGN MODIFICATION
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The basic design steps for a vibration isolator, in force isolation, are
as follows:
1. The required level of isolation (1 – T) and the lowest frequency of
operation (ω0) are specified. The mass of the vibration source (m) is
known.
2. Use equation (12.11) with ω = ω0 to compute the required stiffness k of
the isolator.
3. If the resulting component k is not satisfactory, increase m by
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introducing an inertia block and recomputed k.
4. Distribute k over several springs. 5. Introduce a mounting pad of known
stiffness and damping. Modify k and b accordingly, and compute T using
equation (12.8). If the specified T is exceeded, modify the isolator parameters as
appropriate and repeat the
design cycle.
12. ACTIVE VIBRATION CONTROL
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IMPORTANT UNIVERSITY QUESTIONS 2 MARKS
1. What is dynamic vibration absorber? What are its characteristics.
2. Difference between passive & active vibration control.
3. What do you understand by field balancing.
4. Different types of vibration isolation methods
5. Define influence co-efficients aij kij.
6. A vibration of harmonic type has a frequency of 10 cps(cycles/sec) & its max
Velocity is 4.5 m/s. Determine its amplitude & time period..
7. What is Static & dynamic balancing.
8. What is field balancing.
9. Name some practical applications of pendulum type absorber.
10.Importance of vibration monitoring
11.Active vibration control.
PART-B
1. Explain specification of vibration limits. (8M)
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2. Different types of vibration isolation methods. (8M)
3. With an example briefly explain static & dynamic balancing(8M)
4. Active vibration control. (8M)
5. What is vibration isolation? When it is required?Name few materials for
achieving vibration isolation (12M)
6. Vibration severity standards (4M)
7. Different types of vibration absorbers (16M)
8. Field balancing with suitable example (8M)
9. Different machine condition monitoring techniques& 2 vibration based
Techniques (16M)
10. Sketch & explain torsional absorbers& mention advantages.(8M)
11. Compare static & dynamic balancing (8M)
12.Explain about vibration Absorbers & vibration control by design
Modification (8M)
Few Solved University Questions PART -A
5. Influence co-efficients aij kij.
Theoritical binary influence co-efficients (aij) is based on the
assumption of total matrix effects on the analyte. i can be expressed as sum of
the effects of each matrix elements j calculated independently.
Where, [aij] = A
Stiffness influence co-efficients(kij)
Stiffness influence co-efficients kij is defined as the relation between
the displacement at a point and the forces acting at a various other points on the
system.
Where, [kij] = k
9. Practical applications of pendulum type absorber
Providing driving pleasure while reducing fuel consumption and CO2 emissions
means, on the one hand,combustion engines that generate high torque at low
speeds and, on the other, transmission concepts with a large spread. For these
developments to exploit their full potential, the comfort objectives at low speeds
must also be achieved. In this case, the performance capability of torsional
vibration dampers like dual mass flywheels plays an important role. As a speed-adaptive
absorber, the centrifugal pendulum-type absorber developed by LuK is
an ideal means of providing the isolation necessary in new drive systems.
CONDITION MONITORING TECHNIQUES
Condition monitoring
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Next we summarize vibration analysis and describe five other technologies that
can be utilized to determine the
health of rotating machinery, and other key assets such as switchgear,
insulators, compressed air systems, and
others. These topics are summarized in order to give the attendee a working
knowledge of each technology.
Acoustic emission (ultrasound):
 What is acoustic emission?
 What can it tell you about rotating machinery?
 How to you detect leaks and electrical faults?
 How can it be used to detect bearing faults?
 We use a simulator to demonstrate visually and audibly how acoustic
emission tests are performed.
Thermography:
 What is thermography?
 How can it be used to detect faults in mechanical and electrical equipment?
 What is emissivity, and how does it affect the accuracy of the measurements?
 What are the key qualities of thermal imaging cameras?
 In addition to lots of thermal images, we have a number of Flash simulations
that clarify the effect
of emissivity and environmental conditions on the test results.
Oil analysis:
 How can it be used to check if the machine has a fault condition,
 How can you test if the lubricant is “fit for purpose”?
 What do viscosity, cleanliness, particle count, and other tests tell you?
Wear particle analysis:
 How are the tests performed?
 How can you learn about the nature of wear?
 How can you determine which components are wearing?
 How does it differ from conventional oil analysis?
Motor testing:
 What are the most common types of faults?
 What can motor current analysis tell you?
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 What other test types tell you about the condition of the rotor, stator, and
insulation
UNIT- V
EXPERIMENTAL METHODS IN
VIBRATION ANALYSIS
Vibration Analysis Overview - Experimental Methods in Vibration
Analysis.-Vibration Measuring Instruments - Selection of Sensors-
Accelerometer Mountings. -Vibration Exciters-Mechanical,
Hydraulic, Electromagnetic And Electrodynamics –Frequency
Measuring Instruments-. System Identification from Frequency
Response -Testing for resonance and mode shapes
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UNIT 5: EXPERIMENTAL METHODS IN
VIBRATION ANALYSIS
S.NO CONTENTS PAGE NO
1. Vibration Analysis Overview 82
2. Experimental Methods in Vibration Analysis. 85
3. Vibration Measuring Instruments 87
4. Selection of Sensors 106
5. Accelerometer Mountings 117
6. Vibration Exciters 126
6A. Mechanical 132
6B Hydraulic 134
6C Electromagnetic and Electrodynamics 135
7 Frequency Measuring Instruments. 143
8. System Identification from Frequency Response 145
9. Testing for resonance and mode shapes 147
UNIVERSITY QUESTIONS
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PART-A 150
PART-B 150
1.VIBRATION ANALYSIS OVERVIEW
1. Increase in demands of higher productivity & economical design lead to
higher speeds of machinery and efficient use of light wt materials. It make the
occurrence of resonant condition during the operation of m/c. Hence,
measurement of vibration character. of m/c becomes essential to ensure
safety margin. Other vibration character. Any shift indicate failure/ need for
maintenance of m/c.
2. Measurement of nat. freq. of m/c is useful in selecting the operational speeds
of m/c.
3. Theoretically computed vibration character May be different from actual
values due to assumptions
4. Measuring of frequency of vibration and forces is necessary in the design
vib isolation systems.
5. To det. the survivability of m/c. If the m/c performs its task under testing
conditions, it is expected to survive in the specified condition.
6. Continuous system –approx. to multi dof. If the measured freq. & mode
shapes are comparable to the computed nat freq. and mode shape, then only
the approx is valid.
7. Measurement of I/P and resulting vibration character helps in identifying the
system in terms of k, m.
8. Information about ground vib. due to earthquake, ocean waves and road
surface roughness is important in design og m/c, structures, and vehicle
suspension systems.
The fundamentals of vibration analysis can be understood by studying the
simple mass–spring–damper model. Indeed, even a complex structure such as
an automobile body can be modeled as a "summation" of simple mass–spring–
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damper models. The mass–spring–damper model is an example of a simple
harmonic oscillator.
A DETAILED PROCEDURE OF VIBRATION ANALYSIS
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2. EXPERIMENTAL METHODS IN VIBRATION ANALYSIS
GAUSSIAN RANDOM PROCESS
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3. VIBRATION MEASURING INSTRUMENTS
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INTRODUCTION TO VIBRATION MEASUREMENT
 A quick introduction to the accelerometer and displacement probes
 A quick introduction to the vibration waveform (via live displays)
 We use a simulator and an Analyser that displays live vibration from an
accelerometer. We use another simulator to show real data from machines
with faults.
How do we measure vibration?
 The non-contact eddy current displacement probe
 The velocity probe
 The accelerometer
 Just wait until you see the 3D animations of the accelerometers, velocity
sensors, and proximity probes.
THEORY OF VIBRATION MEASURING INSTRUMENTS
It is well known that the dynamic forces in a vibratory system depend on the
displacement, velocity and acceleration components of a system:
Spring force ∞ displacement
Damping force ∞ velocity
Inertia force ∞ acceleration
Therefore, in vibration analysis of a mechanical system, it is required to
measure thedisplacement, velocity and acceleration components of a system. An
instrument,which is used to measure these parameters, is referred as vibration
measuringinstrument or seismic instrument. A simple model of seismic
instrument is shown in below fig
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TRANSDUCERS
• Device that transforms values ofphysical variables into equivalent electrical
signals
• Types
– Variable resistance transducer
– Piezoelectric transducers
– Linear Variable Differential transformer Transducer
VARIABLE RESISTANCE TRANSDUCER
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In this m/cal motion produces change in electrical resistance in the o/p volatge
• It consists of fine wire(Cu-Ni alloy known as advance) whose resistance
changes during vib.
• Fine wire is sandwiched b/w 2 thin paper sheet.
• Bonded to surface where the strain is to be measured.
• If surface undergoes a normal strain(ε), the strain gage also undergoes same
strain and the change in resistance is
• K- Gage factor of the wire
• R- Initial resistance
• ΔR- Change in resistance
• L- Initial length of the wire
• ΔL- Change in length of the wire
• ν – poisson’s ratio of the wire
• r- resistivity of the wire
• Δr- Change in resistivity of the wire ≈0 for Advance
The strain gage is mounted on an elastic element of a spring mass system
• Strain is proportional to deflection of mass x(t) and indicated by strain gage
Strain gauge as vibration pick up Wheatstone bridge
The change in resistance ΔR can be measured by Wheatstone bridge
• In the Wheatstone bridge voltage V is applied and the resulting voltage E is
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given by
Initially R1R3=R2R4
When resistance changes, the change in output voltage
Rg-Initial resistance of the gage
O/P voltage is proportional to strain
PIEZOELECTRIC TRANSDUCERS
PIEZOELECTRIC ACCELEROMETER
Quartz, Tourmaline, Lithium sulfate generates electrical energy when subjected
to deformation or m/cal stress.
• Elect. charge disappears when m/cal load is removed
• Such mtls -Piezo electric mtls, -Piezo electric transducers,Piezo electric effect
• Energy generated Qx=kFx=kApx
• k-Piezoelectric constant(2.25X10-12 -Quartz)), A-Area on which the force
applied, px-Pressure
• O/p voltage of the crystal E=vtpx
• V-voltage sensitivity(0.055 voltmeter-Quartz)
LINEAR VARIABLE DIFFERENTIAL TRANSFORMER
TRANSDUCER
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One primary coil and two 2ndary coil
• Magnet core move inside in an axial direction
• When a.c i/p is given to py coil, the o/p is diff. of voltages induced in 2ndary
coil
• o/p depends magnetic coupling b/w coil & core
• Core is in middle-o/p is zero
• On either side-there is o/p
• Range of displacement – 0.0002 cm -40 cm
VIBROMETER(Displacement measuring instrument)
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APPLICATION S
Vibrometer are used in a variety of scientific, industrial and medical fields. Here
are some examples:
· Aerospace - vibrometer are used as tools for non-destructive inspection
of aircraft components.
· Acoustics - Vibrometer are standard tools for the design of
loudspeakers. In addition, they have been used to detect the oscillation
behavior of musical instruments.
· Architecture - vibrometer are used to the vibration behavior of buildings
and bridges (bridge repairs) to record.
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· Automotive engineering - Measurement of vibration modes of individual
components or complete vehicles.
· Particle velocity measurement : A sound velocity brings a thin film to
vibrate. This vibration of the film is measured with a laser Doppler
vibrometer, and the resulting sound pressure determined.
· Biology - vibrometer are for example the investigation of the tympanic
membrane in the ear, or used for the visualization of insect communication.
· Calibration - Since vibrometer be calibrated in relation to the
wavelength of the light, one uses it to calibrate other measuring instruments.
· Hard Drives - Vibromter have been for the study of hard drives,
especially in the positioning of the read head , are used.
· Find Landmines - Vibrometer have shown that they can detect buried
landmines. A noise source, such as a speaker, stimulate the floor for minimal
overshoot. These vibrations are detected by the vibrometer. The soil over a
buried landmine shows another oscillating behavior as a floor without a land
mine. Mine detection with single-beam vibrometers, an array of
vibrometers, and multi-beam vibrometers [13] has been carried out
successfully.
· Safety - Based on your property of non-contact vibration measurement,
Vibromter are also suitable for capturing voices over long distances. Using a
visual sensor (camera), the Vibromter directed to a sound-reflecting surface
in the vicinity of the target, to absorb the acoustic signals.
LASER DOPPLER VIBROMETER (LDV)
A laser Doppler vibrometer (LDV) is a scientific instrument that is
used to make non-contact vibration measurements of a surface. Thelaser beam
from the LDV is directed at the surface of interest, and the vibration amplitude
and frequency are extracted from the Dopplershift of the reflected laser beam
frequency due to the motion of the surface. The output of an LDV is generally a
continuous analog voltage that is directly proportional to the target velocity
component along the direction of the laser beam.
Some advantages of an LDV over similar measurement devices such as
an accelerometer are that the LDV can be directed at targets that are difficult to
access, or that may be too small or too hot to attach a physical transducer. Also,
the LDV makes the vibration measurement without mass-loading the target,
which is especially important for MEMS devices.
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PRINCIPLES OF OPERATION
A vibrometer is generally a two beam laser interferometer that measures
the frequency (or phase) difference between an internal reference beam and a
test beam. The most common type of laser in an LDV is the helium-neon laser,
although laser diodes, fiber lasers, and Nd:YAG lasers are also used. The test
beam is directed to the target, and scattered light from the target is collected and
interfered with the reference beam on a photodetector, typically a photodiode.
Most commercial vibrometers work in a heterodyne regime by adding a known
frequency shift (typically 30–40 MHz) to one of the beams. This frequency shift
is usually generated by a Bragg cell, or acousto-optic modulator.
A schematic of a typical laser vibrometer is shown above. The beam from the
laser, which has a frequency fo, is divided into a reference beam and a test beam
with a beamsplitter. The test beam then passes through the Bragg cell, which
adds a frequency shift fb. This frequency shifted beam then is directed to the
target. The motion of the target adds a Doppler shift to the beam given by fd =
2*v(t)*cos(α)/λ, where v(t) is the velocity of the target as a function of time, α is
the angle between the laser beam and the velocity vector, and λ is the
wavelength of the light.
Light scatters from the target in all directions, but some portion of the light is
collected by the LDV and reflected by the beamsplitter to the photodetector.
This light has a frequency equal to fo + fb+ fd. This scattered light is combined
with the reference beam at the photo-detector. The initial frequency of the laser
is very high (> 1014 Hz), which is higher than the response of the detector. The
detector does respond, however, to the beat frequency between the two beams,
which is at fb + fd (typically in the tens of MHz range).
The output of the photodetector is a standard frequency modulated (FM) signal,
with the Bragg cell frequency as the carrier frequency, and the Doppler shift as
the modulation frequency. This signal can be demodulated to derive the velocity
vs. time of the vibrating target.
APPLICATIONS
LDVs are used in a wide variety of scientific, industrial, and medical
applications. Some examples are provided below:
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TYPES OF LASER DOPPLER VIBROMETERS
Single-point vibrometers – This is the most common type of LDV. It can
measure one directional out of plane movement.
Scanning vibrometers – A scanning LDV adds a set of X-Y scanning mirrors,
allowing the single laser beam to be moved across the surface of interest.
3-D vibrometers – A standard LDV measures the velocity of the target along
the direction of the laser beam. To measure all three components of the target's
velocity, a 3-D vibrometer measures a location with three independent beams,
which strike the target from three different directions. This allows a
determination of the complete in-plane and out-of-plane velocity of the target.
Rotational vibrometers – A rotational LDV is used to measure rotational or
angular velocity.
Differential vibrometers – A differential LDV measures the out-of-plane
velocity difference between two locations on the target.
Multi-beam vibrometers – A multi-beam LDV measures the target velocity at
several locations simultaneously.
Self-mixing vibrometers – Simple LDV configuration with ultra-compact
optical head. These are generally based on a laser diode with a built-in
photodetector.
Continuous Scan Laser Doppler Vibrometry (CSLDV) – A modified LDV
that sweeps the laser continuously across the surface of the test specimen to
capture the motion of a surface at many points simultaneously
SCANNING LASER VIBROMETER
The scanning laser vibrometer is a fast imaging method for contactless
measurement of vibrations , for example in the automotive, aerospace and
mechanical engineering, microsystem and information technology as well as in
the quality and production control. The optimization of resonant behavior and
acoustics (eg operating vibration analysis ) has become in many of these areas
has become an important goal of product development, because the dynamic
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and acoustic characteristics of products are among the key quality
characteristics.
The operating principle is based on the laser Doppler vibrometer: From the
back-scattered from a vibrating structure laser light velocity and displacement
can be determined.
<----3D Scanning Vibrometer
In a scanning vibrometer laser Doppler is vibrometer with a scanning
mirror unit and a video camera integrated into a measuring head. During the
measurement of the laser beam over the surface of the measurement object is
scanned, and provides a very high spatial resolution sequentially a series of
single point measurements. For these sequentially measured vibration data can
be either in the time domain of the simultaneous movement of the structure, or
from the analysis in the frequency domain mode shapes determine and visualize
relevant frequency bands.In contrast to this, the contact measuring method to be
examined, vibration is not affected by the measuring process. The accessible
with today's vibrometers measuring ranges cover the entire area of technically
relevant vibrations completely. Thus, with the Vibrometry one hand motions
ofmicrostructures with swing paths of a few pm at frequencies up to 30 MHz
(and thus v = 0.1 m / s) to analyze, but on the other hand also fast processes in
Formula 1 engines with swing speeds of up to 30 m / s
A 3D scanning vibrometer combines three sensors that detect the oscillating
movement from different directions, and thus completely determine the 3D
vector vibration. In the 3D representation of the vibration data allows the
vibrations of the measurement object observe spatially or individually in the x-,
y-and z-direction, while also in-plane and out-of-plane vector components
clearly distinguishable from each other.
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ACCELEROMETER(Acceleration measuring instrument)
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APPLICATIONS
Engineering
Accelerometers can be used to measure vehicle acceleration. They allow for
evaluation of overall vehicle performance and response. This information can
then be used to make adjustments to various vehicle subsystems as needed.
Accelerometers can be used to measure vibration on cars, machines, buildings,
process control systems and safety installations. They can also be used to
measure seismic activity, inclination, machine vibration, dynamic distance and
speed with or without the influence of gravity. Applications for accelerometers
that measure gravity, wherein an accelerometer is specifically configured for
use in gravimetry, are called gravimeters.
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Notebook computers equipped with accelerometers can contribute to
the Quake-Catcher Network (QCN), a BOINC project aimed at scientific
research of earthquakes.
Biology
Accelerometers are also increasingly used in the biological sciences. High
frequency recordings of bi-axial or tri-axial acceleration (>10 Hz) allows the
discrimination of behavioral patterns while animals are out of sight.
Furthermore, recordings of acceleration allow researchers to quantify the rate at
which an animal is expending energy in the wild, by either determination of
limb-stroke frequency or measures such as overall dynamic body
acceleration Such approaches have mostly been adopted by marine scientists
due to an inability to study animals in the wild using visual observations,
however an increasing number of terrestrial biologists are adopting similar
approaches. This device can be connected to an amplifier to amplify the signal.
Industry
Main article: Condition monitoring
Accelerometers are also used for machinery health monitoring to report the
vibration and its changes in time of shafts at the bearings of rotating equipment
such as turbines, pumps, fans, rollers, compressors, and cooling towers.
Vibration monitoring programs are proven to warn of impending failure, save
money, reduce downtime, and improve safety in plants worldwide by detecting
conditions such as wear and tear of bearings, shaft misalignment, rotor
imbalance, gear failure or bearing fault which, if not attended to promptly, can
lead to costly repairs. Accelerometer vibration data allows the user to monitor
machines and detect these faults before the rotating equipment fails completely.
Vibration monitoring programs are utilized in industries such as automotive
manufacturing, machine tool applications, pharmaceutical production, power
generation and power plants, pulp and paper, sugar mills, food and beverage
production, water and wastewater, hydropower, petrochemical and steel
manufacturing.
Building and structural monitoring
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Accelerometers are used to measure the motion and vibration of a structure that
is exposed to dynamic loads. Dynamic loads originate from a variety of sources
including:
Human activities – walking, running, dancing or skipping
Working machines – inside a building or in the surrounding area
Construction work – driving piles, demolition, drilling and excavating
Moving loads on bridges
Vehicle collisions
Impact loads – falling debris
Concussion loads – internal and external explosions
Collapse of structural elements
Wind loads and wind gusts
Air blast pressure
Loss of support because of ground failure
Earthquakes and aftershocks
Measuring and recording how a structure responds to these inputs is critical for
assessing the safety and viability of a structure. This type of monitoring is called
Dynamic Monitoring.
Medical applications
Zoll's AED Plus uses CPR-D padz which contain an accelerometer to measure
the depth of CPR chest compressions.
Within the last several years, Nike, Polar and other companies have produced
and marketed sports watches for runners that include footpods, containing
accelerometers to help determine the speed and distance for the runner wearing
the unit.
In Belgium, accelerometer-based step counters are promoted by the government
to encourage people to walk a few thousand steps each day.
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Herman Digital Trainer uses accelerometers to measure strike force in physical
training.
It has been suggested to build football helmets with accelerometers in order to
measure the impact of head collisions
Navigation
Main article: Inertial navigation system
An Inertial Navigation System (INS) is a navigation aid that uses a computer
and motion sensors (accelerometers) to continuously calculate via dead
reckoning the position, orientation, andvelocity (direction and speed of
movement) of a moving object without the need for external references. Other
terms used to refer to inertial navigation systems or closely related devices
includeinertial guidance system, inertial reference platform, and many other
variations.
An accelerometer alone is unsuitable to determine changes in altitude over
distances where the vertical decrease of gravity is significant, such as for
aircraft and rockets. In the presence of a gravitational gradient, the calibration
and data reduction process is numerically unstable.
Transport
Accelerometers are used to detect apogee in both professional and in
amateur rocketry.
Accelerometers are also being used in Intelligent Compaction rollers.
Accelerometers are used alongside gyroscopes in inertial guidance systems.
One of the most common uses for MEMS accelerometers is
in airbag deployment systems for modern automobiles. In this case the
accelerometers are used to detect the rapid negative acceleration of the vehicle
to determine when a collision has occurred and the severity of the collision.
Another common automotive use is in electronic stability control systems,
which use a lateral accelerometer to measure cornering forces. The widespread
use of accelerometers in the automotive industry has pushed their cost
down dramatically. Another automotive application is the monitoring of noise,
vibration, and harshness (NVH), conditions that cause discomfort for drivers
and passengers and may also be indicators of mechanical faults.
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Tilting trains use accelerometers and gyroscopes to calculate the required tilt.
Volcanology
Modern electronic accelerometers are used in remote sensing devices intended
for the monitoring of active volcanoes to detect the motion of magma.
TYPES OF ACCELEROMETER
1Bulk micromachined capacitive
2.Bulk micromachined piezoelectric resistive
3.Capacitive spring mass base
4.DC response
5.Electromechanical servo (Servo Force Balance)
6.High gravity
7.High temperature
8.Laser accelerometer
9.Low frequency
10.Magnetic induction
11.Modally tuned impact hammers
12.Null-balance
13.Optical
14.Pendulous integrating gyroscopic accelerometer (PIGA)
15.Piezoelectric accelerometer
16.Resonance
17.Seat pad accelerometers
18.Shear mode accelerometer
19.Strain gauge
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20.Surface acoustic wave (SAW)
21.Surface micromachined capacitive (MEMS)
22.Thermal (submicrometre CMOS process)
23.Triaxial
24.Vacuum diode with flexible anode
1. LASER ACCELEROMETER
A laser accelerometer comprises a frame having three orthogonal input axes
and multiple proof masses, each proof mass having a predetermined blanking
surface. A flexible beam supports each proof mass.
The flexible beam permits movement of the proof mass on the input axis.
A laser light source provides a light ray. The laser source is characterized to
have a transverse field characteristic having a central null intensity region.
A mirror transmits a ray of light to a detector. The detector is positioned to be
centered to the light ray and responds to the transmitted light ray intensity to
provide an intensity signal. The intensity signal is characterized to have a
magnitude related to the intensity of the transmitted light ray.
The proof mass blanking surface is centrally positioned within and normal to
the light ray null intensity region to provide increased blanking of the light ray
in response to transverse movement of the mass on the input axis.
The proof mass deflects the flexible beam and moves the blanking surface in a
direction transverse to the light ray to partially blank the light beam in response
to acceleration in the direction of the input axis. A control responds to the
intensity signal to apply a restoring force to restore the proof mass to a central
position and provides an output signal proportional to the restoring force.
2. PIEZOELECTRIC ACCELEROMETER
A piezoelectric accelerometer that utilizes the piezoelectric effect of certain
materials to measure dynamic changes in mechanical variables. (e.g.
acceleration, vibration, and mechanical shock)
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As with all transducers, piezoelectric accelerometers convert one form of
energy into another and provide an electrical signal in response to a quantity,
property, or condition that is being measured. Using the general sensing method
upon which all accelerometers are based, acceleration acts upon a seismic mass
that is restrained by a spring or suspended on a cantilever beam, and converts a
physical force into an electrical signal. Before the acceleration can be converted
into an electrical quantity it must first be converted into either
a force or displacement. This conversion is done via the mass spring system
shown in the figure to the right.
The word piezoelectric finds its roots in the Greek word piezein, which means
to squeeze or press. When a physical force is exerted on the accelerometer, the
seismic mass loads the piezoelectric element according to Newton's second
law of motion ( ). The force exerted on the piezoelectric material can be
observed in the change in the electrostatic force or voltage generated by the
piezoelectric material. This differs from a piezoresistive effect in that
piezoresistive materials experience a change in the resistance of the material
rather than a change in charge or voltage. Physical force exerted on the
piezoelectric can be classified as one of two types; bending or compression.
Stress of the compression type can be understood as a force exerted to one side
of the piezoelectric while the opposing side rests against a fixed surface, while
bending involves a force being exerted on the piezoelectric from both sides.
Piezoelectric materials used for the purpose of accelerometers can also fall into
two categories. The first, and more widely used, is single-crystal materials
(usually quartz). Though these materials do offer a long life span in terms of
sensitivity, their disadvantage is that they are generally less sensitive than some
piezoelectric ceramics. In addition to having a higher piezoelectric constant
(sensitivity) than single-crystal materials, ceramics are more inexpensive to
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produce. The other category is ceramic material. That uses barium titanate, lead-zirconate-
lead-titanate, lead metaniobate, and other materials whose
composition is considered proprietary by the company responsible for their
development. The disadvantage of piezoelectric ceramics, however, is that their
sensitivity degrades with time making the longevity of the device less than that
of single-crystal materials.
In applications when low sensitivity piezoelectrics are used, two or more
crystals can be connected together for output multiplication. The proper
material can be chosen for particular applications based on
the sensitivity, frequency response, bulk-resistivity, and thermal response. Due
to the low output signal and high output impedance that piezoelectric
accelerometers possess, there is a need for amplification and impedance
conversion of the signal produced. In the past this problem has been solved
using a separate (external) amplifier/impedance converter. This method,
however, is generally impractical due to the noise that is introduced as well as
the physical and environmental constraints posed on the system as a result.
Today IC amplifiers/impedance converters are commercially available and are
generally packaged within the case of the accelerometer itself.
The cross-section of a piezoelectric accelerometer.
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4. SELECTION OF SENSORS
The three parameters representing motion detected by vibration monitors are
displacement, velocity, and acceleration. These parameters can be measured by
a variety of motion sensors and are mathematically related (displacement is the
first derivative of velocity and velocity is the first derivative of acceleration).
Selection of a sensor proportional to displacement, velocity or acceleration
depends on the frequencies of interest and the signal levels involved.
The range of vibration sensors offered is wide, as a vibration sensor has many
different characteristics that may vary, including measurement related factors
such as frequency response, sensitivity and accuracy. Physical characteristics
such as temperature rating, size and connector orientation are also
considerations.
The following is a guide to experience in sensor use in the most common
industrial sectors that employ vibration monitoring.
For each industry, the top four features required of a quality vibration sensor are
stated and explained. Industrial sensor choices are graded as follows:
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Good - A general purpose choice that has adequate measurement and physical
characteristics for condition monitoring programmes, where data is trended for
change and absolute precision is not so important.
Better - A general purpose choice that has adequate measurement and physical
characteristics for condition monitoring programmes, but adds a specific feature
such as an extended temperature range or mounting orientation better suited to
the application.
Best - A premium choice that has optimum measurement and physical
characteristics, but also offers the longest history as evidence of reliability.
These are particularly suited to critical machinery applications where the sensor
may be used in safety-related functions such as machinery protection.
TYPES OF VIBRATION SENSORS
1. DISPLACEMENT SENSORS
Eddy current probes are non-contact sensors primarily used to measure shaft
vibration, shaft/rotor position and clearance. Also referred to as displacement
probes, eddy current probes are typically applied on machines utilizing
sleeve/journal bearings. They have excellent frequency response with no lower
frequency limit and can also be used to provide a trigger input for phase-related
measurements.
These sensors also have the ability to take the output of an accelerometer and
double integrate to obtain a relative displacement; however, except in very
special cases, it is inadvisable because of significant low frequency
instability associated with the integration process. Eddy current probe systems
remain the best solution for shaftposition measurements.
2.VELOCITY SENSORS
Velocity sensors are used for low to medium frequencymeasurements. They are
useful for vibration monitoring and balancing operations on rotating machinery.
As compared to accelerometers, velocity sensors have lower sensitivity to high
frequency vibrations. The mechanical design of the velocity sensor; an iron core
moving within a coil in a limited magnetic field, no clipping of the generated
signal occurs, but smooth saturation.
In an accelerometer with ICPelectronics, sensor resonance excitation can cause
saturation and clipping of the electronic circuit generating false low frequency
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components. Integrating to velocity from the acceleration signal leads to large
low frequency components.
Resonance damping circuits between sensor element and amplifier can
minimize that effect. Traditional velocity sensors are of a mechanical design
that uses an electromagnetic (coil and magnet) system to
generate the velocity signal. Recently, hardier piezoelectric velocity sensors
(internally integrated accelerometers) have gained in popularity due to their
improved capabilities and more rugged and smaller size design. A comparison
between the traditional coil and magnetic velocity sensor and the modern
piezoelectric velocity sensor is shown in Table 1. The electromagnetic
(Inductive) velocity sensor does have a critical place in the proper sensor
selection. Because of its high temperature capability it finds wide application in
gas turbine monitoring and is the sensor of choice by many of the major gas
turbine manufacturers.
The high temperature problems for systems using accelerometers can also be
solved by splitting sensor and electronics (charge amplifiers). The sensor can
have high temperature ranges up to +1,112°F (+600°C).Some methods of
investigating bearing defects and gear problems may require a higher frequency
range and because the signals are generated by impact, the sensitivity should be
lower.
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The basic acceleration sensor has a good signal to noise ratio over a wide
dynamic range. They are useful for measuring low to very high frequencies and
are available in a wide variety of general purpose and application specific
designs. The piezoelectric sensor is versatile, reliable and the most popular
vibration sensor for machinery monitoring.
When combined with vibration monitors capable of integrating from
acceleration to velocity, accelerometers can be a useful component in a Multi-
Parameter Monitoring Program. The user is, therefore, able to determine both
velocity and acceleration values for the same machine point with a single
sensor.
3.PIEZOELECTRIC SENSORS
Accelerometers operate on the piezoelectric principal: a crystal generates
a low voltage or charge when stressed as for example during compression. (The
Greek root word“piezein” means “to squeeze”.) Motion in the axial direction
stresses the crystal due to the inertial force of the mass and produces a signal
proportional to acceleration of that mass. This small acceleration signal can be
amplified for acceleration measurements or converted (electronically integrated)
within the sensor into a velocity or displacement signal. This is commonly
referred as the ICP (Integrated Circuit Piezoelectric) type sensor. The
piezoelectric velocity sensor is more rugged than a coil and magnet sensor, has
a wider frequency range, and can perform accurate phase measurements. Most
industrial piezoelectric sensors used in vibration monitoring today contain
internal amplifiers.
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SELECTION OF SENSORS FOR VARIOUS INDUSTRIES
1. PULP AND PAPER
Following are the top features required of a quality vibration sensor
in the pulp and paper industry, along with the reasons why:
• Low frequency response ≤ 1,0 Hz
– For low rotational speed of rolls
• Elevated temperature 120 to 150 °C (250 to 300 °F)
– For dryer section heat and humidity
• IP 68 cable/connector assembly
– For wet environment and frequent roll changes
• Good signal to noise ratio
– For bearing defect detection
2. GENERAL PURPOSE, FOOD AND BEVERAGE
in the food and beverage industry, along with the reasons why:
– For low rotational speed of machines
• Small physical size
– Small bearing and access restrictions
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• Corrosion precautions
– Cleaning fluid and chemical attack
• Integral cable or IP 68 connector/cable
– Frequent hose-down environment.
3. OIL AND GAS, REFINING, PETROCHEMICALS
Following are the top features required of a quality vibration sensor in the oil
and gas, refining and petrochemicals industries:
• ATEX/NEC certification
– Hazardous area
• Minimum 10 Hz to 10 kHz frequency response
– For turbines, blades and gears
• ±5% sensitivity precision
– May be used for API 670 machine trip
• High EMI/RFI shielding
– May be used for API 670 machine trip.
4. POWER GENERATION (FOSSIL FUEL, NUCLEAR, HYDRO)
in the power generation (fossil fuel, nuclear and hydro) industry:
• Velocity and/or acceleration
– For absolute shaft vibration
• High temperature, ≥ 120 °C (≥ 250 °F)
– For steam leaks
• ±5% sensitivity precision
– May be used for API 670 machine trip
• High EMI/RFI shielding
– High voltage environment.
5.METALWORKING
in the metalworking industry, along with the reasons why:
– For low rotational speed of machines
• Physically robust
– Misuse, abuse and flying debris
• Corrosion precautions
– Hot, dusty and corrosive environment
• Good signal-to-noise ratio
– For bearing defect detection.
5. ACCELEROMETER MOUNTINGS
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An accelerometer is an instrument that senses the motion of a surface to which
it is attached, producing an electrical output signal precisely analogous to that
motion. The ability to couple motion, (in the form of vibration or shock), to
the accelerometer with high fidelity, is highly dependent upon the method of
mounting the instrument to the test surface. For best accuracy, it is important
that the mounting surface of the accelerometer be tightly coupled to the test
surface to ensure the duplication of motion, especially at higher frequencies.
Since various mounting methods may adversely affect accuracy, it is important
to understand the mechanics of mounting the accelerometer for best results.
Figure a illustrates the accelerometer. Its spring-mass analogy is Figure b
and Figure c is a typical frequency response plot for such a system. The plot is
obtained by graphing accelerometer output vs. frequency with input vibration
level held constant at each frequency setting. Every such system has a mounted
resonant (or natural) frequency, fn characterized by a very high peak of output
at resonance. The solution for the differential equation of motion yields the
definitive expression for the resonant frequency as follows:
fn = 1/2π√KM
where: fn= system natural frequency (Hz)
K = spring constant of the crystal stack (lbs/in)
M = mass of the seismic system (Slugs)
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The following mounting methods are recommended for accelerometers:
· Stud mounting with stud bolt, insulating flange or adhesive pad
· Magnetic base
· Adhesive by bee wax, cyanoacrylate (e.g. the gel-like Loctite 454) or epoxy glue
· Mounting cube for triaxial measurement with three uniaxial accelerometers
· Accelerometer probe by hand pressure
· Accelerometer with movable probe tip
Mounting methods for accelerometers
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6.VIBRATION EXCITERS
A vibration exciter is a machine which produces the mechanical motion to
which the best object is subjected. The exciter may be designed to produce a
given range of harmonic or time dependent excitation force and or displacement
through a given range of frequencies. These machines can be mechanical,
Electro dynamic or hydraulic in nature.
Vibration experimentation may require an external exciter to generate the
necessary vibration. This is the case in controlled experiments such as product
testing where a specified level of vibration is applied to the test object and the
resulting response is monitored. A variety of vibration exciters are available,
with different capabilities and principles of operation.
Interactions between major subsystems of an experimental vibration system.
Three basic types of vibration exciters (shakers) are widely used:
1. Mechanical shakers.
2. Hydraulic shakers.
3. Electrodynamic shakers.
Exciters:
– Electrodynamic (high bandwidth, moderate power, complex and
multifrequency excitations)
– Hydraulic (moderate to high bandwidth, high power, complex and
multifrequency excitations)
– Inertial (low bandwidth, low power, single-frequency harmonic excitations).
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Signal Conditioning:
• Filters • Amplifiers
• Modulators/demodulators • ADC/DAC.
Sensors:
• Motion (displacement, velocity, acceleration)
• Force (strain, torque).
Maximum velocity and acceleration are similarly defined. Maximum force is
the largest force that could be applied by the shaker to a test object of
acceptable weight(within the design load). The values given in above table
should be interpreted with caution. Maximum displacement is achieved only at
very low frequencies. Maximum velocity corresponds to intermediate
frequencies in the operating-frequency range of the shaker.
Maximum acceleration and force ratings are usually achieved at high
frequencies. It is not feasible, for example, to operate a vibration exciter at its
maximum displacement and its maximum acceleration simultaneously.
Consider a loaded exciter that is executing harmonic motion. Its displacement is
given by
x = s sinωt
in which s is the displacement amplitude (or stroke). The corresponding velocity
and acceleration are
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x˙ = sωcosωt
˙x˙ = −sω2 sinωt
If the velocity amplitude is denoted by v and the acceleration amplitude by a, it
follows from above equations that
v = ωs
a = ωv
An idealized performance curve of a shaker has a constant displacement-amplitude
region, a constant velocity-amplitude region, and a constant
acceleration-amplitude region for low, intermediate, and high frequencies,
respectively, in the operating frequency range. Such an ideal performance
curve is shown in Figure (a) on a frequency–velocity plane. Logarithmic axes
are used.
Performance curve of a vibration exciter in the frequency–velocity plane (log): (a)
ideal and(b) typical.
In practice, typical shaker-performance curves would be rather smooth yet
nonlinear curves, similar to those shown in Figure (b). As the mass increases,
the performance curve compresses. Note that the acceleration limit of a shaker
depends on the mass of the test object (load).
Full load corresponds to the heaviest object that could be tested. No load
condition corresponds to a shaker without a test object. To standardize the
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performance curves, they usually are defined at the rated load of the shaker. A
performance curve in the frequency–velocity plane can be converted to a curve
in the frequency–acceleration plane simply by increasing the slope of the curve
by a unit magnitude (i.e., 20 dB·decade–1).
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6A MECHANICAL EXCITERS (OR)INERTIAL EXCITERS
130

USES
Uses piston-cylinder arrangement and the movement is controlled by fluid
pressure
• Since the fluid pr can be controlled, widerange of force can be obtained
• Can generate low frequencies
• Used for testing civil engg structures
6C ELECTROMAGNETIC & ELECTRO DYNAMIC EXCITERS
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SIMPLE PROCEDURE
When current passes thro’ a coil passed placed ina magnetic field, force ‘F’
proportional to current ‘I’ and magnetic flux density ‘D’ is produced which
the accelerates the object on the shaker F=DIL (L-length of coil)
• Magnitude of accel. depends max. current & massof object & moving element
of the shaker
• If a.c current is used, forces varies harmonically
• If d.c current is used, const.forces is generated
• Exciter has 2 freq. one corresp. to nat freq of
flexible support an other corresp. To nat. freq. of
moving element
• Operating freq of exciter lies b/w these two freq.
• Used to generate forces upto 30,000N,
displacement – 25 mm, Freq -5 Hz to 20 KHz
ADVANTAGES
· Attaches to solid object and vibrates it to make sound
· Excites multiple oscillation modes for wide directivity
· Easily becomes watertight as it needs no opening as sound outlet
· Rigid structure for robust circuitry
· Light and compact, yet gives high output
PROBLEMS OF VIBRATION EXCITERS
LOW STIFFNESS OF THE EXCITER TABLE
The moving element of a vibration exciter should be as stiff as possible
to work as a rigid body and keep the same motion on its entire mounting area.
Many exciters are built with aluminum alloy moving elements because this
material allows easy machining of relatively lightweight tables. In the case of
back-to-back (BTB) accelerometers, they do not cause many problems because
the reference surface is on the top of the transducer and the piezoelectric
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elements aremounted in an inverted compression configuration. In the case of
single-ended (SE) transfer accelerometers, larger problems can occur because
usually the laser beam has to be focused directly on the exciter table beside the
accelerometer. In addition, accelerometers of this type are usually built in a
compression configuration, which is more sensitive to base bending.
This problem can be verified very easily measuring the sensitivity of the
accelerometer with a single beam laser interferometer focused onto different
points of the table in a radial direction, one that at a time. Sometimes this
problem can be minimized by the use of some stiff adapter between the exciter
table and the accelerometer. Care must be taken when designing these adapters
to get high stiffness and low mass, otherwise the maximum acceleration level
obtainable with the exciter may be unacceptably lowered and heating problems
may appear.
HEATING OF THE MOVING ELEMENT
Electrodynamic exciters can suffer from heating by the driving coil. The
temperature increase on the mounting table depends on the acceleration
amplitude and thus on the driving current. Therefore, this problem usually
shows up at higher frequencies due to the use of higher acceleration levels. This
differential heating from the mounting base induces systematic errors on the
measurement due to the temperature sensitivity of the accelerometer.
Temperature variations of more than 20 oC can be found in some exciters and
no manufacturer states sensitivity changes due to differential heating
on accelerometers specifications. Lower acceleration levels or increasing the air
flow around the driving coil of electrodynamic exciters can minimize
this problem. Another way to deal with this problem is to intercalate low
frequency and high frequency calibrations to keep the temperature rise within
acceptable limits (Lauer, 1995).
ROCKING AND TRANVERSE MOTION
Instead of a piston-like linear motion, the moving table can also
present a rocking behavior. Since the laser is usually focused onto a point away
from the center axis of the accelerometer (or exciter table), an error may occur
when a displacement measurement is made. Transverse motion can also be
coupled to the longitudinal motion of the table.
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Since most accelerometers suffer of some misalignment of the maximum
sensitivity axis, a transverse sensitivity isalways present. Some standard
accelerometers may be bought with the value of its transverse sensitivity and its
maximum direction stated in the calibration certificate, but it’s not a usual
procedure. The coupling of the exciter rocking or transverse motion and the
accelerometer transverse sensitivity axis creates an error on the sensitivity
determination.
Many ways to deal with this problem have been reported. Some authors have
suggested taking the mean of measurements on 3 points; others on 6 points
(Dickinson and Clark, 1999), but measuring on 2 diametrically opposed
points already works very well. These calibrations can be performed in
sequence or simultaneously. Simultaneous measurements are better because
they avoid the effect of drifts in the amplifiers, increase the optical resolution if
a two beam interferometer is used and require a shorter time for the calibration
(Lauer, 1995). On the other hand, the interferometer is a little more complex
and the laboratory needs to have optical lapping capabilities. This is because a
flat polished reference surface is required on the top of the accelerometer, to
allow parallel optical reflections from multiple points. Interferometers with 4
reflections or more (Basile et al, 2004) have already been reported for vibration
measurements.
These methods minimize the errors only in the displacement measurements, and
the effects of the rocking and transverse movement over the output signal of the
accelerometer itself still remain. A suggested solution to minimize
this effect on the final results is to take the mean of two calibrations, which
differ by mounting the accelerometer on two positions, rotated 180o around its
main axis (Lauer, 1995). This simple procedure theoretically cancels out the
influence of the transverse sensitivity component. Residual effects can show up
due to cable influences that are not perfectly canceled, or due to the
accelerometer itself.
RESONANCES
Resonance is the tendency of a system to oscillate with greater amplitude at
some frequencies than at others. frequencies at which the response amplitude is
a relative maximum are known as the system's resonant frequencies, or
resonance frequencies. at these frequencies, even small periodic driving forces
can produce large amplitude oscillations, because the system stores vibrational
energy.
Resonance occurs when a system is able to store and easily transfer
energy between two or more different storage modes (such as kinetic energy
and potential energy in the case of a pendulum).
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Every exciter has resonances and some of them can unfortunately lie
very close to some frequency of interest. Irregularities in the frequency response
function can appear due to resonance of the mass-spring system or of the
suspension system. Most electrodynamic exciters that use flat-spring
suspensions suffer of many internal resonances,which manufacturers try to
dampen out by gluing layers of rubber to the springs. Air bearing exciters that
use O-ring suspensions are also subjected to resonances that can impose
difficulties to the calibration.
Piezoelectric exciters can be used at high frequencies, usually above 3 kHz.
They have the advantages of being very stiff and to easily maintain the optical
alignment. However some care is needed because high voltages are usually
employed. These exciters normally present very low damping and, below
resonance, their ascending frequency response can maximize the effect of the
upper harmonics of the driving frequency, contributing to signal distortion.
Strong signal distortions can also occur if a good impedance match is not
achieved between the power amplifier and the exciter (Jingfeng and Tianxiang,
2004). Stacked piezoelectric exciters that incorporate layers of damping
material present a better behavior since a flatter frequency response is obtained
(Jones et al, 1969).
Resonances are a design problem, which is very difficult to overcome duringthe
calibration stage. Therefore, it is better to avoid resonance frequencies at all.
Depending on the system, sometimes it is possible to change suspensions or
add some loading mass to avoid a specific resonance frequency. Since this is not
always feasible, there is a tendency in accelerometer calibration the use of
different types of exciters to cover specific sub-ranges of the frequency range of
interest.
7.FREQUENCY MEASURING INSTRUMENTS.
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