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

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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 76PART-B 76

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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 notexceed 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:

1.1Note 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 systemwill 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 excitation3. 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, motionsickness 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.

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and 1 Hz to 2 Hz for lateral motion. Also, for any dynamic system,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

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qualities of pieces of equipment of the same type 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

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Mounting MountingFle

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 ConditionBased Maintenance (CBM) are other terms used todescribe 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 doneautomatically 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

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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.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. Theyinclude piezoelectric accelerometers and velocity sensors and piezoelectric torque sensors and force sensors. It is also interesting to note that piezoelectric

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materials deform when subjected to a potential difference (or charge). Some delicate test equipment (e.g., in vibration testing) use piezoelectricactuating elements (reverse piezoelectric action) to create fine motions. Also, piezoelectric valves (e.g., flapper valves), directly actuated using voltage signals, are used in pneumatic and hydraulic control applications and in ink-jet printers. Miniature stepper motors based on the reverse piezoelectricaction 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

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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.

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 radiofrequencymagnetic 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.

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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 thedisplacement. 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 abranch 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.

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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

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4.2 VIBRATION ISOLATION WITH FLEXIBLE FOUNDATION

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4.3VIBRATION ISOLATION SYSTEM WITH PARTIALLY FLEXIBLE FOUNDATION

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4.4 SHOCK ISOLATION

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4.5 ISOLATION UNDER SHOCK

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 MODELFor 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 springK, 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 excitationoriginating in the machine, such as vane passing excitation in centrifugal pumps.

First, a few variables and dimensionless ratios must be introduced, since theresults 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 massratios, 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.

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DERIVATION

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PROBLEMS:-

1.

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2.

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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 reciprocatingmachines.

• 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

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of wheels and tuned vibration dampers.

• 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 ofcentrifugal 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

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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. 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 dampingconstant ba and the excitation frequency ω. Hence, the transfer function of the damped system is

From 1 we get 2

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1. & 2. By solving above 2 eqns we get

12.108

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Fig shows

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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 beingin use Such irregularities may rise due to the inhomogeneous distribution of material within the part, bending and deflection of rotating shafts, andeccentricity 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.

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STATIC BALANCING

• Static Balancing simply means the insurance of mass distribution about the axis of rotation of the rotating mechanical part in the radial directions, withoutconsideration 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 oneof 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 (miei2) and moments (aimiei2), 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

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examples given above. The basic steps are: (1) determine the magnitude and the phase angle of accelerometer signals at the bearings with and without trial masses at the bearing planes; (2) using this data, compute the necessarybalancing 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.

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In determining an unbalance load, the accelerator readings must be taken with respect to a body reference on the rotating object. Since this 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:

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1. Amplitude of each accelerometer signal2. Phase lead of the accelerometer signal with respect to the synchronized and referencefixedstrobe 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

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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 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. 48

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? 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 BALANCING49

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10 FIELD BALANCING

Field balancing is a technique used to balance a rotating part in place without removing the part from the machine. The advantages of field balancingare 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 correctionweights.

A B C D

Fig A Shows the access requirements for field balancing eliminate many machinesFig B depicts an end view of a rotorFig 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 viewof 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 trialweight, 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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DESIGN CONSIDERATIONS

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The basic design steps for a vibration isolator, in force isolation, areas follows:

1. The required level of isolation (1 – T) and the lowest frequency ofoperation (ω0) are specified. The mass of the vibration source (m) isknown.

2. Use equation (12.11) with ω = ω0 to compute the required stiffness k ofthe isolator.

3. If the resulting component k is not satisfactory, increase m by69

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 thedesign cycle.

12. ACTIVE VIBRATION CONTROL

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ELECTRO-MECHANICAL SYSTEM

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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 methods5. 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 monitoring11.Active vibration control.

PART-B1. Explain specification of vibration limits. (8M)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)

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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 TECHNIQUESCondition monitoring

Next we summarize vibration analysis and describe five other technologies that can be utilized to determine thehealth of rotating machinery, and other key assets such as switchgear, insulators, compressed air systems, andothers. These topics are summarized in order to give the attendee a working knowledge of each technology.

Acoustic emission (ultrasound): What is acoustic emission?

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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 effectof 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? What other test types tell you about the condition of the rotor, stator, and insulation

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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 PART-A 150PART-B 150

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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–damper models. The mass–spring–damper model is an example of a simple harmonic oscillator.

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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 INSTRUMENTS86

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 thedisplacement, velocity and acceleration components of a system:

Spring force ∞ displacementDamping force ∞ velocityInertia 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 TRANSDUCER88

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 gageO/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,

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the LDV makes the vibration measurement without mass-loading the target, which is especially important for MEMS devices.

  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.

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LDVs are used in a wide variety of scientific, industrial, and medical applications. Some examples are provided below:

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

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acoustics (eg operating vibration analysis ) has become in many of these areas has become an important goal of product development, because the dynamic 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

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that measure gravity, wherein an accelerometer is specifically configured for use in gravimetry, are called gravimeters.

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.

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Building and structural monitoring

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.

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In Belgium, accelerometer-based step counters are promoted by the government to encourage people to walk a few thousand steps each day.

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

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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.

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

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17.Seat pad accelerometers

18.Shear mode accelerometer

19.Strain gauge

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.

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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)

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.

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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 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 utilizingsleeve/journal bearings. They have excellent frequency response with no lower frequency limit and can also be used to provide a trigger input for phase-relatedmeasurements.

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 frequencyinstability 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 togenerate 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 ingas 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 commonlyreferred 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 sensorin 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

Following are the top features required of a quality vibration sensorin the food and beverage industry, along with the reasons why:• Low frequency response ≤ 1,0 Hz– For low rotational speed of machines• Small physical size

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– Small bearing and access restrictions• 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)Following are the top features required of a quality vibration sensorin 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.METALWORKINGFollowing are the top features required of a quality vibration sensorin the metalworking industry, along with the reasons why:• Low frequency response ≤ 1,0 Hz– 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.

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5. ACCELEROMETER MOUNTINGS

An accelerometer is an instrument that senses the motion of a surface to whichit is attached, producing an electrical output signal precisely analogous to thatmotion. The ability to couple motion, (in the form of vibration or shock), tothe accelerometer with high fidelity, is highly dependent upon the method ofmounting the instrument to the test surface. For best accuracy, it is importantthat the mounting surface of the accelerometer be tightly coupled to the testsurface to ensure the duplication of motion, especially at higher frequencies.Since various mounting methods may adversely affect accuracy, it is importantto understand the mechanics of mounting the accelerometer for best results.

Figure a illustrates the accelerometer. Its spring-mass analogy is Figure band Figure c is a typical frequency response plot for such a system. The plot isobtained by graphing accelerometer output vs. frequency with input vibrationlevel held constant at each frequency setting. Every such system has a mountedresonant (or natural) frequency, fn characterized by a very high peak of outputat resonance. The solution for the differential equation of motion yields thedefinitive expression for the resonant frequency as follows: fn = 1/2π√KMwhere: 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

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in which s is the displacement amplitude (or stroke). The corresponding velocity and acceleration are

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 = ωsa = 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 performancecurve 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,

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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 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

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6B HYDRAULIC EXCITERS

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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 whichthe 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 offlexible support an other corresp. To nat. freq. ofmoving 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

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the reference surface is on the top of the transducer and the piezoelectric 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 theaccelerometer. 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 heatingon accelerometers specifications. Lower acceleration levels or increasing the air flow around the driving coil of electrodynamic exciters can minimizethis 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 itsmaximum 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 sensitivitydetermination.

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 opposedpoints 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 aflat 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 vibrationmeasurements.

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 minimizethis 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 theinfluence 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.

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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). 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 thesuspension 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 usuallyemployed. 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 oradd 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 ofinterest.

7.FREQUENCY MEASURING INSTRUMENTS.

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Advantages

1.No contact with vibrating body. 2. Measure lowest freq.

8. SYSTEM IDENTIFICATION FROM FREQUENCY RESPONSE Frequency response is the quantitative measure of the

output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency,

SIGNAL ANALYSIS

•To det the freq response of system under known excitation•Signal analysis is done by

-Spectrum analyzer-Octave and 1/3rd octave filters-Bandpass filter (for sequential analysis)-Real time analysis (for transient signal analysis )

SPECTRUM ANALYZERS

• Device that analyzes a signal in the frequency domain by separating the energy of the signal into various frequency bands• Separation is done by filters

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• In recent days digital analyzers are popular• Used for machine condition monitoring

OCTAVE &1/3RD OCATVE FILTER

•Vibratory signal of a m/c under steady state condition in time domain is called as signature•Used to obtain the vibration levels for all discrete freq. components in m/c sign. over wide range•Fig shows response character of octave filter•Desired no of filters-to cover given range of freq.

Example: Octave filter with freq. 31.5, 63, 125, 250 & 500Hz- to obtain vibration levels over 5bands.

•To improve analysis 1/3rd octave-with freq. 20, 25,31.5,40,50,63,80,100,125,160,200,250Hz etc.

RESPONSE CHARACT. OF ACTAVE BAND FILTER

BAND PASS FILTER (TUNABLE FILTER)

RESPONSE OF A FILTER

Permits the passage of frequency components of a signal over a frequency band and rejects all other freq. components of the signal

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• Graph shows the response character of a filter whose lower and upper cut off freq are fl and fu.• Practical filter will have a response character deviating from ideal rectangle fc-Centre frequency• In Constant percent bandwidth filter,band width (fu-fl)/fc is constant• In Constant bandwidth filter,(fu-fl) is independent of fc.

REAL TIME ANALYSIS

• If vibr. signal is transient RTA is useful•O/P is presented in TV type of tube to facilitate to observe the spectrum continuously and capture whichever portion of the signal is desired andrecorded. Magnetic tape is used for recording so that the signature can be stored for playback.

9. TESTING FOR RESONANCE AND MODE SHAPES

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IMPORTANT UNIVERSITY QUESTIONS 2 MARKS

1. Name 2 frequency measuring instruments ?2. What is meant by frequency response?3. What is resonance?significance of resonance?How to avoid resonance?4. Enlist vibration measuring instruments?5. List any 2 materials used as vibration absorbers?6. What is meant by Lumped mass system?7. List out any 2 different sensors used in vibration applications.8. List some significance of vibration analysis?9.What is the use of vibration excitors?

PART- B

1.Explain the construction & working of various types of vibration excitors? (16M)

2.Explain (4X4=16M) (i) Accelerometer mountings(ii) Selection of sensors(iii) Measurement of frequency(iv) System identification

3. Procedures involved in selection of sensors ? (8M)4. Constuction & working of Electrodynamic & Hydraulic excitors? (8M)5. What is Gaussian random process ? Why it is frquently used in vibration analysis? (8M)6. Different tpes of accelerometer mounting? With neat sketch. (8M)7. Brief notes on (8X2=16M)

(i) Free vibration test(ii) Frequency measuring instruments

8. Describe different types of sensors used for vibration measurement (8M)9. Constuction & working principle & sketch of Mechanical vibration exciter?

(8M)6. Lumped mass system (2M)

A lumped mass system is a load in a system which that can be applied to a node in a static stress, natural frequency (modal) or modal superposition analysis.

A lumped mass can be used to resist the translation or rotation of a node.

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