Kuwait UniversityCollege of Engineering & Petroleum

Department of Mechanical Engineering

0630-475 Dynamics of Machines and Mechanical Vibration Laboratory

First semester, 2009/2010

Experiment No.3

Familiarization with and Performance

Check of, Vibration Testing &

Measuring Equipment

Omar Saleem - 205111466

Performed on: Wednesday Dec 2nd, 2006

Submitted on: Wednesday Dec 9th, 2006

Instructors:

Prof. Mohammed Al-ansaryEng. Tallaa Kamel

Table of ContentsList of Tables ………………………………………………………………………….3

List of Figures ……………………………………………………………………...…4

Introduction ………………………………………………………………………......5

Objectives …………………………………………………………………………….6

Safety Precautions ………………………………………………………………........6

Theory ……………………………………………………………………………...…7

Experimental Setup ………………………………………………………………….21

Experimental Procedure ……………………………………………………………..22

Tabulated Data ………………………………………………………………………23

Sample Calculations…………………………………………….……………………25

Figures ……………………………………………………………………………….27

Discussion ……………………………………...……………………………………30

Conclusions ……………………………………………………………………..…...31

Nomenclature ………………………………………………………………………..32

References …………………………………………………………………………...33

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List of Tables

Table (1) - Performance Check of Vibration Meters

Table (2) - Performance Check of Sine/Noise Generator and Exciter

Table (3) - Sensitivity Calibration of a Given Accelerometer

Table (4) - Dynamic Testing of a Given Structure (e.g. a beam)

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List of Figures:

Fig 1: Relation between the ratio X/F and omega to obtain natural frequency (ωn).

Fig 2: Measured response of a rotating disk with no imbalance.

Fig 3: history of responses recorded over a period of time.

Fig 4: Measured response of a rotating disk with no imbalance.

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Introduction

Vibration is a major factor in most failures in equipment and machinery. Vibration is

undesirable in equipments for this reason , but since almost every machinery or moving

part produces some amount of vibration so it is impossible to remove it from a system.

Therefore, it is important to measure and test this vibration so it remains within certain

safe limits.

The measurement of Vibration is done using specialized equipments some of which are

studied in the experiment. Different factors such as displacement, velocity and

acceleration are measured in order to have an idea about vibration in the machinery, Also

this analysis provides some idea about the general condition of the machinery. The

equipment use advanced approaches, such as the Fast Fourier Transform (FFT), to

analyze the data taken for study. One of the equipment also used is called the

accelerometer which measures the acceleration.

The equipment used for measurement need to be in satisfactory working condition to

ensure that proper results are produced using the equipment this is achieved by regular

calibration of the equipment to ensure high accuracy of the equipment. The condition of

machine can also be monitored using off-line machine health and condition monitoring

using a data collector and a PC-based software. In the experiment the Type 2526 collector

is used with a SENTINEL 7101M PC-based software.

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Objectives

(1) To be familiarized with both vibration measuring and testing equipment.

(2) To calibrate and make a performance check of vibration measuring equipment using

a Level Calibration Exciter.

(3) To check the charge sensitivity of a given accelerometer using a calibration exciter

with reference accelerometer and to compute the percentage drift in sensitivity with

respect to factory supplied value.

(4) To learn the off-line machine health and condition monitoring using a data collector

(Type 2526) and PC-based software SENTINEL 7107M.

(5) To perform the dynamic testing of a given structure using vibration exciter and

sine/noise generator.

Safety Precautions (i) Follow all electrical and electronic apparatus safety rules.

(ii) Check that the electrical equipment are set to match the available mains voltage and

correct fuse.

(iii) Do not perform any internal adjustments, maintenance or repair.

(iv) Accelerometer should be fixed with the exciters rigidly.

(v) All the connections of accelerometer to level recorder should carefully be made

straight using adhesive tape.

(vi) For the excitation of the accelerometer the calibration exciter frequency should be

swept slowly and carefully without increasing the gain too high. Be careful in increasing

the frequency and amplitude of excitation while using Sine/Noise Generator.

(v) Follow Laser Transducer Safety Rules posted with the apparatus.

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Theory

Origin of Vibration:

Vibration occurs because of the dynamic effects of manufacturing tolerances,

clearances, rolling and rubbing contact between machine parts and out-of-balance forces

in rotating and reciprocating members. Often, small insignificant vibrations can excite the

resonant frequencies of some other structural parts and be amplified into major vibration

and noise sources.

Sometimes, vibration is generated intentionally in component feeders, concrete

compactors, ultrasonic cleaning baths, rock drills and pile drivers as shown in figure

(1). Vibration testing machines are used extensively to impart a controlled level of

vibration energy to products and sub-assemblies where it is required to examine their

physical or functional response and ascertain their resistibility to vibration environment.

The vibration can consists of a single component occurring at a single frequency, as with

a tuning fork, or of several components occurring at different frequencies simultaneously,

as with the piston motion of an IC. Engine, as shown in figure (2).

Study of Vibration:

There are three major quantities of interest in vibration studies:

1. Vibratory displacement, 2. Velocity, and 3. Acceleration.

The measuring instruments take acceleration as input and other parameters are obtained

by an integrating process. Under steady state conditions if the phase relationships

between the three parameters are neglected, then the velocity at a given frequency can be

found by dividing the acceleration by a factor proportional to frequency, and the

displacement can be obtained by dividing the acceleration level by a factor proportional

to the frequency squared. A wider dynamic and frequency range is a prime requirement

of the vibration measuring equipment.

Displacement is often used as an indicator of unbalance in rotating machine parts because

relatively large displacements usually occur at the shaft rotating frequency which is the

frequency of primary interest for balancing purposes.

Velocity (RMS) measurements are widely used for vibration 'severity' measurements

because the vibration velocity is simply related to vibratory energy and is therefore a

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measure of the destructive effect of vibration. A given velocity level also signifies

constant stress for geometrically similar constructions vibrating at the same mode.

The acceleration is preferred where the frequency range of interest covers high

frequencies. Today, many vibration measurements are carried out upto 10 kHz and often

higher. The high frequency vibrations carry valuable information about the condition of

rotating element (ball, roller, needle) bearings, gear teeth, turbomachinery blading etc.

Measurement of random vibrations coming from fluid flow, jet noise, cavitation etc. are

often preferred alone or together with periodic vibration components. The acceleration is

measured by a transducer called accelerometer.

The Accelerometer:

It is an electromechanical transducer which produces at its output terminals, a voltage or

charge that is proportional to the acceleration to which it is subjected. Piezoelectric

accelerometers are universally used covering a wide frequency range. These piezoelectric

elements have the property of producing an electric charge which is directly proportional

to strain and thus the applied force when loaded either in tension, compression or shear.

The accelerometer configuration is shown in figure (3) in which the piezoelectric

elements are arranged so that they are loaded by a mass or masses and preloading spring

or ring. When subjected to vibration, the masses exert a varying force on the

piezoelectric elements which is directly proportional to the vibratory acceleration. For

frequencies below the resonant frequency of the assembly, the acceleration of the masses

will be the same as the acceleration of the base and the output signal level will be

proportional to the acceleration which the accelerometer is subjected to.

Sensitivity, Mass and Dynamic Range of the Accelerometer:

Ideally, the higher transverse sensitivity is preferred, but a compromise has to be made to

reduce the size of assembly. The sensitivity is not a critical factor as modern

preamplifiers are designed to accept these low-level signals.

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As a general rule, the accelerometer mass should be no greater than one-tenth of the

effective (dynamic) mass of the part of the structure to which the accelerometer is

mounted.

When it is required to measure abnormally low or high acceleration levels, the dynamic

range of the accelerometer should be considered. Theoretically, the output of a

piezoelectric accelerometer is linear down to zero acceleration but, in practice, the lower

dynamic limit is determined by the electrical noise from connecting cables and amplifiers

circuitry. This limit is normally below 0.01 ms-2 with general purpose instruments

measuring over a wide band. Significantly lower levels may be measured when using a

filter for frequency analysis. The upper dynamic limit is determined by the

accelerometer's structural strength. General purpose accelerometers are linear upto 50 to

100 kms-2 (5000 to 10,000g) which is well into the range of mechanical shocks.

Accelerometer Calibration and System Performance Check:

Factory provides a calibration chart for the sensitivity and response of each individual

accelerometer. There will be a minimal change in characteristics over a long time period.

Generally, the characteristics typically change less than 2% even over a period of several

years. However, in normal use, accelerometers are often subjected to quite violent

treatment which may result in a significant change in characteristics and sometimes in

permanent damage. It is therefore required to make a periodic check of the sensitivity

calibration and performance check. The sensitivity calibration of an accelerometer is

checked by fastening it to the small calibration exciter (B & K Type 4294) with back-to-

back connection to a reference accelerometer. The outputs of both accelerometers when

vibrated at 10 ms-2 and 159.2 Hz are recorded. The ratio of their respective outputs when

vibrated will be proportional to their sensitivities as given below.

where,

Sr(f) is the charge sensitivity of a known reference accelerometer,

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Hu(f) is the frequency response function of unknown accelerometer, and

Hr(f) is the frequency response function of the reference accelerometer.

The calibration accuracy is within ±2% when used carefully.

In order to check the frequency response of an accelerometer or measuring system the

calibration exciter Type 4290 is used with Sine/Noise Generator Type 1049 as shown in

figure (4). The frequency response is plotted from about 200 Hz upto 35 kHz. The

calibration exciter has a built-in control accelerometer which allows the vibration level at

the exciter table to be held constant over a frequency range which covers the resonant

frequency of many accelerometers. Calibration levels are rather low, i.e. of order of 1 ms-

2.

Mounting of Accelerometers:

The accelerometer is mounted with its main sensitivity axis aligned with the desired

measuring direction. The direction of minimum transverse sensitivity is indicated by a red

spot painted on many accelerometers. In this direction the transverse sensitive is virtually

zero. The method of attaching the accelerometer to the measuring point is one of the most

critical factors in obtaining accurate results for practical vibration measurements. The

ideal mounting is by a threaded stud onto a flat, smooth surface. A thin layer of grease

applied to the surface before tightening down the accelerometer will usually improve the

mounting stiffness. To prevent ground loops, a mica washer and isolated stud are used. A

permanent magnet is a simple attachment method where the measuring point is a flat

Ferro-magnetic surface. It also electrically isolates the accelerometer. Mounting methods

and examples of typical frequency responses are shown in figures (5a) to (5g).

Force Transducer:

Like the accelerometer, the force transducer also uses a piezoelectric element which,

when compressed, provides an electric output proportional to the force transmitted

through it. For dynamic force signals the same signal conditioning and measuring

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instruments as for accelerometer can be used. The force transducer is mounted in the

force transmission path so that it is subjected to the forces to be measured. It can measure

both tensile and compressive forces.

Vibration Measuring and Indicating Devices:

They can be classified into four categories:

Category(1): A Basic System

Vibration Level meter, Level Recorder and Integrating vibration meter are basic and

very accurate measurement devices. A block diagram shown in figure (6) illustrates how

a typical modern vibration meter is built-up. Rectified and unrectified vibration signals

can be fed to an oscilloscope, tape recorder, or level recorder.

Vibration Level Measurement Units:

The vibration amplitude can be quantified in several ways. Figure (7) shows the

relationship between the peak-to-peak level, the peak level, the average level and the

RMS level of a sine wave .

The Peak-to-Peak value indicates the maximum excursion of the wave, a useful quantity

where, for example, the vibrating displacement of a machine part is critical for maximum

stress or mechanical clearance consideration.

The Peak value is particularly valuable for indicating the level of short duration shocks

etc. But as can be seen from the figure (8), peak values only indicate what maximum

level has occurred, no account is taken of the time history of the wave.

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The Rectified Average value, on the other hand does take time history of the wave into

account, but is considered of limited practical interest because it has no direct relationship

with any useful physical quantity.

The RMS value is the most relevant measure of amplitude because it takes both the time

history of the wave into account and gives an amplitude value which is directly related to

the energy content, and therefore the destructive abilities of the vibration.

The Decibels: When measurements can not be conveniently presented on linear scales,

especially the accuracy of graph near zero axis becomes extremely difficult to interpret,

the data are presented in terms of logarithmic scales. One such logarithmic scale is the

DECIBEL (dB) scale. The dB is defined as:

where, X and X0 may be RMS displacement, velocity or an acceleration. The value X is

the measured quantity and X0 is the reference value.

Category(2): Analyzers for Fault detection and Diagnostics

These are the systems which perform frequency analysis and possess diagnostics

capabilities to perform on the spot frequency analysis and spectrum plot-out at each

monitoring port such as Vibration Analyzer (B & K Type 2515), Dual and Multi Channel

Analyzers (B & K Type 2032 and 2035) and Vibration meter (B & K Type 2511) with

Tunable Band Pass Filter (B & K Type 1621).

Frequency Analysis:

The vibration meter alone will give a single vibration level measured over a wide

frequency band. In order to reveal the individual frequency components making up the

wide-band signal a frequency analysis can be performed. A filter is used. It only passes

those parts of the vibration signal which are contained in a narrow frequency band. The

pass band of the filter is moved sequentially over the whole frequency range of interest so

that we obtain a separate vibration level reading for each band as shown in figure (9). The

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filter can consist of a number of individual, continuous, fixed-frequency filters which are

frequency scanned sequentially by switching or alternatively, continuous coverage of the

frequency range can be achieved with a single tunable filter. A constant percentage filter

bandwidth as narrow as 1% allows very fine resolution analyses to be made facilitating

the detailed examination of vibration phenomena. A narrow constant bandwidth analysis

is used with vibration problems associated with rotating machines such as gear boxes

where a fine constant bandwidth is needed to identify multiple harmonics and sidebands

due to modulation which occur at constant frequency intervals. Both linear and

logarithmic frequency sweeps may be selected. A portable vibration analyzer is shown in

figure (10).

FFT Analysis:

FFT stands for Fast Fourier Transform. The FFT algorithm is an extremely efficient way

of calculating the so-called Discrete Fourier Transform (DFT) which is a discrete, fine

approximation to the Fourier Transform.

Fourier Theorem: Any periodic function, no matter how complex it is, may be looked

upon as a combination of a number of pure sinusoidal functions with harmonically related

frequencies:

Fourier Transform: The Fourier Transform for the function g(t) is given by:

where f is the frequency. The actual equation for the forward transform is:

and for the inverse transform is:

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where G(k) represents the spectrum values at the N discrete frequencies k f, and g(n)

represents samples of the time function at the N discrete time points n t.

Category(3): FFT Analyzers and Computer-Based Systems:

To perform frequency analysis of vibration signals in the laboratory, two types of FFT

analyzers are available:

1. Dual-channel FFT Analyzer (B&K Type 2032) , and

2. Multi-channel FFT Analyzers (B&K Type 2035).

In addition to their analyzer functions, they are equipped with a signal generator which

can be tuned over the same frequency range as the analyzer. The analyzer side of the

instrument can be used at the same time to filter and measure dynamic response signals.

The FFT analyzers perform narrow band analysis and are therefore particularly suitable

for most vibration studies. They are also able to display the time function of the signal

being analyzed which is a particularly useful facility in the analysis of transient signals.

The FFT analyzers are equipped with memories to compare two spectra to be compared

with difference displayed. They allow to record much larger time signals so that larger

events may be examined in details, even in high frequency ranges where the normal

record length would be shorter than the cycle time. Data recorded by the analyzers can be

stored on floppy disks and transferred to PC-based software such as SMS-Star via the

built-in IEEE, IEC and RS232 interfaces as shown in figure (11). The interfacing of a

real-time analyzer to the PC facilitates the rapid automatic processing of analyzed data.

Category(4): Machine Condition and Machine Health Monitors:

The simplest system as described in category (1) utilizes a straight forward portable

vibration meter which measures the vibration level over a specific wide frequency range.

Measurement are compared with general standards or established reference values for

each machine. Machine condition is thus being evaluated in the field on a minimum of

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data. Fault detection at an earlier stage together worth diagnosis and break down

predictions become possible when using a system which can perform frequency analysis

as described in category (2). For many monitoring points, a PC based software is used.

Vibration samples from each machine are collected on a data collector (B&K Type 2526)

or vibration analyzer (B&K Type 2515) and are transferred to a PC. The resulting spectra

are compared with previously established reference spectra under automatic control from

a PC coupled to the analyzer. Narrow band frequency analysis on a linear frequency scale

gives an excellent display of harmonic and side band frequency components, a

particularly valuable feature for diagnostic purposes. Where the analyzer includes the

zoom facility, any part of the spectrum can be expanded to further enhance details of

individual component. The PC based software BK7616 and BK7107 enable routine

checking of large numbers of samples of machine vibration data. When any component in

new incoming spectra exceeds a preselected level in any of the lines of the reference

spectrum, this is automatically reported on the PC and can be printed out. The software

BK7107 includes programs for cepstrum analysis, trend predictions, harmonic and side

band cursor programs which enable harmonic and side band spacing to be accurately

measured. This is particularly valuable in gearbox fault detection.

Vibration Testing Equipment:

Vibration Testing:

The vibration testing is carried out to check whether the parts and structures, such as

sophisticated electronic and electromechanical instrumentation, control systems and

aircraft developed can withstand the severity of actual operational environment. Vibration

testing can be used for:

1. Production control,

2. Frequency Response and Dynamic Performance Testing, and

3. Environment Test.

The most common types of vibration testing are:

1. Sinusoidal Testing with fixed or sweeping frequency,

2. Random Testing with wide band or narrow band characteristics, and

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3. Force Testing using mechanical impedance or mobility concepts and

structural response measurements.

The Exciter:

It is an electrodynamic vibration generator. It works like a loudspeaker, where the

movement is produced by a current passing through a coil in a magnetic field. The force

used to accelerate the moving element is proportional to the drive current and the

magnetic flux. Therefore by controlling the current, the vibration level of the exciter can

be controlled. In small exciters (B&K Types 4294 and 4809) the magnetic field is

produced by a permanent magnet, whereas in the larger ones (B&K Types 4808 and

4814) electromagnets are used. The maximum current and the load determine the

acceleration level which can be obtained. At low frequencies, however, this acceleration

level will decrease due to displacement limitations of the moving element. Resonance in

the moving element will set the upper frequency limit. The performance and basic

construction of an exciter are shown in figure (12).

The Power Amplifier:

A Power Amplifier is used to drive exciters. Different Power Amplifiers are used for

different exciters depending upon their ratings. The Power Amplifier has a specified

frequency response and a specified power output capability. A balanced preamplifier and

the use of silicon transistors result in an instrument which can tolerate temperature

fluctuations and supply line variations, whilst maintaining good stability.

The frequency response for an exciter driven by a constant current will show three

regions of different natures. The first two regions represent the spring-mass system of the

moving element and its suspension with a resonance of typically 20 Hz. In the third

region, typically above 5 kHz for big exciters, axial resonance in the moving element will

occur, setting the upper operational frequency of the exciter as shown in figure (13). A

response curve for an exciter with a constant voltage input will show the same regions of

control, but the lower resonance is considerably damped, giving an easier control of the

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level. The voltage control, obtained by a low impedance amplifier is normally preferred.

In some cases, however, a current control will be advantageous, primarily when the

exciter is used as force generator or where non-feedback control is required using the mid

frequency range of the exciter. This demands a high impedance output and therefore

amplifiers will often have selectable impedance outputs.

The Exciter Control:

The use of a vibration exciter assumes a constant vibration level at the table. The

frequency response curve is not flat. It contains resonance, and other will be introduced

when a test object is mounted on the exciter. When used throughout a frequency range

the gain of the amplifier must consequently vary with frequency as shown in figure (14).

This gain is set by a controller, receiving feed-back information from the test object. The

main elements of an exciter control must therefore be a frequency generator, a vibration

meter and a level controlling circuit as shown in figure (15).

Vibration Response Investigation:

To perform vibration testing a vibration response investigation is made with the purpose

of checking the function of the test object and to examine the influence of resonance

throughout the frequency range. For all types of tests the resonance are found by a sine

sweep. The resonance frequencies are measured and the behavior of the structure can be

studied in detail by manually controlling the frequency. At the end of the test procedure, a

similar investigation is carried out for comparison.

The behavior of the structure is most easily studied by means of a digital stroboscope

(B&K Type 4913), triggered by the exciter control to follow the excitation frequency.

Better, however, is to use a trigger signal which differs slightly from the excitation

frequency, giving a slow-motion like image as shown in figure (16). This slow-motion

frequency, normally 3 - 5 Hz, can be set on the stroboscope to follow the excitation. A

further study of the behavior can be made manually delaying the trigger signal to move

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the image through one or more cycles or by using dual flashes to give a picture of the

extreme positions of the resonating part.

Mechanical Impedance and Mobility:

The mobility spectrum can be found from a sine sweep with a constant force applied to

the structure by an exciter. The force is transferred via a push rod and maintained

constant and the level is measured by a force transducer. The response is measured with

an accelerometer and plotted on a level recorder, synchronized to the generator

frequency.

Similarly the impedance spectrum can be found by maintaining a constant velocity and

measuring the force as shown in figure (17).

Often a plot of impedance or mobility as a function of frequency will give sufficient

information, whilst in other cases a further analysis of the response will be necessary to

give a complete picture of the dynamic properties.

Mode Studies:

The measurement of mobility or mechanical impedance gives the frequency response

function between the point of excitation and another point on the structure. However,

frequency response functions exist between all points of the structure, and if the structure

is to be described in this way, the result will be a very large number of functions. Data

reduction is therefore necessary and the technique used is to describe the modes of the

structure.

At particular frequencies, the natural frequencies, the structure will vibrate in a shape

called the mode shape as shown in figure (18). These frequencies are recognized as

resonance frequencies of the structure and correspond to minima on the mechanical

impedance curves and to maxima on the mobility curves.

Resonance Studies:

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At resonance the vibration amplitude is increased. The phase between force and response

is changed during frequency sweeping and passes through /2 at resonance. Higher

damping gives a lower and broader peak and phase change over a broader frequency

range. The damping is described by the quality factor Q, related to the band width of the

response curve at the half power points (3 dB from the maximum amplitude or 0.707´

maximum amplitude) as shown in figure (19).

An amplitude and phase curve will give adequate information of well separated

resonance, but for curves with resonance peaks strongly overlapping, the information is

difficult to interpret.

Plotting the response in a vectorial diagram, a Nyquist diagram has proved to be more

convenient. The axes in a Nyquist diagram are the real and imaginary parts of the

response. The numerical value of the vector is equal to the amplitude and the angle to the

real axis equals the phase angle between the excitation and the response. Thus each point

on the periphery corresponds to a certain frequency.

A resonance will be represented by a circle, where the intersection with an axis takes

place at the resonance frequency, the axis dependent on the phase-relationship between

force and response. The size of the circle depends on the damping, higher damping giving

a smaller circle.

Instead of being plotted against each other the real and imaginary parts of the response

can also be plotted against frequency as shown in figure (19)

Excitation Methods:

A vibration exciter is an excellent means of providing the force input to the structure to

be analyzed either by applying a sine or a broad band signal. In the latter case the input as

well as the output are measured and analyzed using Fast Fourier Techniques (FFT). The

frequency response is calculated from the input spectrum, measured with a force

transducer, and the output spectrum, normally measured with an accelerometer.

19

Instead of using an exciter a broad band excitation can be produced by an impact hammer

integrally mounted with a force transducer as shown in figure (20). The impact method is

fast: the impulse contains energy at all frequencies and will therefore excite all modes

simultaneously. The set-up time is minimal and requirements to the amount of equipment

are small. However, the signal to noise ratio is poor and for large, fragile structures with a

high degree of damping it can be very difficult to get a sufficiently large response without

damaging the test object. The vibration exciter has a high signal to noise ratio, an easy

control with choice of excitation wave forms and the possibility of exciting several points

at the same time.

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Experimental Setup

The experimental setup consists of the following:

(i) The vibration table (concrete beds),

(ii) Accelerometer with its accessories,

(iii) Impact hammer with cable,

(iv) Exciters (Type 4809, 4290 and 4294)

(v) Sine/Noise Generator with amplifier (Type 1049 & 2706)

(vi) Vibration meter(Type 2511) or Vibration analyzer (Type 2515) or FFT multichannel

analyzer (Type 2032/2035) with Level Recorder.

(vii) Digital Stroboscope.

(viii) Torsional Vibration Meter with Laser Transducer.

(ix) Integrated Vibration Meter.

(x) Tunable Band Pass Filter and Charge Amplifiers.

(xi) Machine Health & Condition Monitoring System.

(xii) Laser Velocity Transducer.

(xiii) Human Vibration Unit.

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Experimental Procedure

On completion of the familiarization part of the experiment, prepare an experimental

setup for the calibration of an accelerometer and record frequency response curve for the

accelerometer. Make sensitivity check as given in Theory & Background. Finally,

perform performance check using the calibrated accelerometer and calibration exciter for

vibration meter, tunable band-pass filter and sine/noise generator.

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Tabulated Data

Table 1: Performance Check of Vibration MetersMeasured Values For Set # 1 Measured Values For Set # 2

Frequency(Hz)

Acc. Level(m/s2 RMS)

Frequency(Hz)

Acc. Level(m/s2 RMS)

159.2 10 159.2 9140 6.5 150 2.4100 2.5 140 0.580 1.4 137.5 0.160 0.3 135 054 0 - -

Table 2: Performance Check of Sine/Noise Generator and ExciterGenerated Frequency (Hz) Measured Frequency (Hz)

2 23 34 45 5

5.5 5.55.75 5.75

6 66.25 6.256.5 6.56.75 6.75

7 77.25 7.257.5 7.58 8

8.25 8.258.5 8.59 910 10

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Table 3: Sensitivity Calibration of a Given Accelerometer

SerialNo.

Measurement usingAccelerometer # 1

Measuring usingAccelerometer # 2

Response Hr(f) (m/s2)

Response Hu(f) (m/s2)

Sensitivity Su1(f)

(pC/ m/s2)

Response Hr(f) (m/s2)

Response Hu(f) (m/s2)

Sensitivity Su2(f)

(pC/ m/s2)1 0.98 10 10.36 0.98 0.31 0.322 1.1 10 9.23 1.1 0.315 0.293 1.1 10 9.23 1.1 0.311 0.29- Average Su1(f) 9.60 Average Su2(f) 0.30- % drift 4.06 %drift 5.89

Table 4: Dynamic Testing of a Given Structure (e.g. a beam)

S. No.

Frequency of

Excitation (Hz)

Measured Response

(m/s2 RMS)

1 2 104*10-3 7.38 12.57 157.9 0.000659 0.0892 3 286*10-3 10.70 18.85 355.3 0.000805 0.0753 4 689*10-3 12.3 25.13 631.7 0.001091 0.0894 5 1.79 11.3 31.42 987.0 0.001814 0.1605 5.5 3.37 3.78 34.56 1194.2 0.002822 0.7476 5.75 5.12 9.58 36.13 1305.3 0.003923 0.4097 6 9.33 40.5 37.70 1421.2 0.006565 0.1628 6.25 31.7 227 39.27 1542.1 0.020556 0.0919 6.5 19.5 181 40.84 1668.0 0.011691 0.06510 6.75 7.84 90.5 42.41 1798.7 0.004359 0.04811 7 5.07 70.2 43.98 1934.4 0.002621 0.03712 7.25 4.41 71.1 45.55 2075.1 0.002125 0.03013 7.5 3.7 68 47.12 2220.7 0.001666 0.02514 8 2.91 66 50.27 2526.6 0.001152 0.01715 8.25 2.68 66.5 51.84 2687.0 0.000997 0.01516 8.5 3.79 102 53.41 2852.3 0.001329 0.01317 9 3.45 106 56.55 3197.8 0.001079 0.01018 10 3.12 118 62.83 3947.8 0.00079 0.007

Sample Calculations

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For table 3: Measurement using accelerometer # 1:Sfac=10.01SR = 1.015

Average Su1:

% of Draft:

For table 4:

Euler’s equation:

b= 30.5 mm = 0.0305 mh= 1 mm = 0.001mI=1/12(bh3)=2.54167*10-12

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l= 310 mm = 0.31

Comparing the natural frequency found experimentally and theoretically:From fig 1:ωn= 34.8 rad/sfrom Euler’s equation:ωn=48.95 rad/s

% difference =

Zeta from the figure 1:

Figure

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Fig 1: Relation between the ratio X/F and omega to obtain natural frequency (ωn)

27

Fig 2: Measured response of a rotating disk with no imbalance.

Fig 3: history of responses recorded over a period of time.

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Fig 4: Measured response of a rotating disk with no imbalance.

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Discussion

The experiment carried out to check the performance of the Vibration meters. It is can be

observed that the size or shape of the Vibration meter can affect the performance the

results displayed on table 1. It is seen that the vibration meter used to measure values for

set 1 had greater range of frequency to which it can measure vibration. Also while

checking the performance of sine/noise generator and exciter. During which an excitation

or disturbance of a certain magnitude was produced and the resulting signal is recorded,

as seen in table 2 the generated frequency and measured frequency are the same so it

show that the generator is performing satisfactorily.

The sensitivity of two unknown accelerometers were found by calibration using the

sensitivity provided by the factory. It is seen that the percentage drift for accelerometer

#1 is 4.06 % and for accelerometer #2 is 5.89%. Which is considerable high since an

accelerometer should have percentage drift below 2% for it to function effectively.

Figure 1 is plotted to show how the values of ratio of displacement and force changes

with the omega. The point of highest is where the displacement is the maximum and is

the natural frequency of the system found experimentally. The theoretical natural

frequency value is found by the Euler’s equation which uses the principle of

superposition. It is seen that the experimental and theoretical values differ from each

other with a percentage error of 28.9%.

The figures 2,3 and 4 shows the displayed results by PC- software SENTINEL 7107M

using a data collector (Type-2526). It can be seen that the program display different limits

in which a certain response can be judged to be either significant of negligible. In figure 2

the result of rotating disk without any imbalance is displayed, where the response is

below the alert level therefore in the safe range. Whereas in the figure 4 which shows the

response of a rotating disk with an imbalance, the response is within the alert areas so it

enables the operator to view the condition of the rotating disk. The figure 3 show the

history of result recorded over a period of time this help the operator to keep a track on

the equipment condition and how it varies with the passage of time.

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Conclusions

The following conclusion can be reached from the results obtained during the experiment.

Different Vibration meter may have different performance and the choice of the meter depends on the application.

Sensitivity calibration can be utilized to find sensitivity of the unknown accelerometer. Also the % Draft calculated show that the accelerometer need to be replaced.

The data collecting equipment combined with PC-based software can be used effectively to monitor vibration in machinery.

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Nomenclature

dB DECIBEL

f(t) function of time

F(f) the Fourier Transform

g(n) the inverse transform

G(k) the forward transform

Hu(f) the frequency response function of unknown accelerometer

Hr(f) the frequency response function of the reference accelerometer

N discrete frequencies k f and discrete time points n t

Su(f) the charge sensitivity of an unknown reference accelerometer

Sr(f) the charge sensitivity of a known reference accelerometer

X may be RMS displacement, velocity or an acceleration

X0 the reference value of displacement, velocity or an acceleration

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References

1. Bruel & Kjaer Publication, A world of Applications, BA0079-11.

2. Bruel & Kjaer Publication, Measuring Vibration, English DK BR0094-12.

3. Bruel & Kjaer Publication, Vibration Testing, BA0079-11

4. Bruel & Kjaer Publication, Structural Testing Part 1 & 2, English DK BR0458-12.

5. Bruel & Kjaer Publication, Machine Health Monitoring, English DK BR0287-12.

6. Bruel & Kjaer Publication, Machine Condition Monitoring, English BR0267-13.

7. Broch J. T., Mechanical Vibrations & Shock Measurement, 2nd edition Bruel & Kjaer, Denmark, April 1984

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