Devendra Vibration

Rotor Dynamics and Vibration of Machinery

ASSIGNMENT

Centre Name: Mechanical and Manufacturing

Course Name: M.Sc (Engg) in Rotating Machinery Design

Name of the Student : Devendra Singh Bhati

Student Registration No : BSB0909001

Module Leader at MSRSAS : Dr. B. V. Vijay

FULL TIME 2009 BATCH

M. S. Ramaiah School of Advanced Studies New BEL Road, Gnanagangothri Campus, MSR Nagar, Bangalore-560 054

Tel: 23605539 / 23601983 / 2360 4759. Fax: 2360 1923 website: http://www.msrsas.org

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M.S Ramaiah School of Advanced Studies –Postgraduate Engineering and Management Programme (PEMP)


ii

Declaration Sheet

Student Name Devendra Singh Bhati

Reg. No BSB0909001

Course Rotating Machinery Design Batch FT-2009

Module Code RMD 507

Module Title Rotor Dynamics and Vibration of Machinery

Module Start Date 22/11/2010 Submission Date 07/12/2010

Module Leader Dr. B. V. Vijay

Submission Arrangements

This assignment must be submitted to Academic Records Office (ARO) by the submission date before 1730

hours for both Full-Time and Part-Time students.

Extension requests

Extensions can only be granted by the Head of the Department / Course Manager. Extensions granted by any

other person will not be accepted and hence the assignment will incur a penalty. A copy of the extension

approval must be attached to the assignment submitted.

Late submission Penalties

Unless you have submitted proof of Mitigating Circumstances or have been granted an extension, the penalties

for a late submission of an assignment shall be as follows:

Up to one week late: Penalty of one grade (5 marks)

One-Two weeks late: Penalty of two grades (10 marks)

More than Two weeks late: Fail - 0% recorded (F2)

All late assignments must be submitted to Academic Records Office (ARO). It is your responsibility to

ensure that the receipt of a late assignment is recorded in the ARO. If an extension was agreed, the

authorization should be submitted to ARO during the submission of assignment.

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assignment questions. Each participant is required to retain a copy of the assignment in his or her record in

case of any loss.

Declaration

The assignment submitted herewith is a result of my own investigations and that I have conformed to the

guidelines against plagiarism as laid out in the PEMP Student Handbook. All sections of the text and results,

which have been obtained from other sources, are fully referenced. I understand that cheating and plagiarism

constitute a breach of University regulations and will be dealt with accordingly.

Signature of

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iii

M. S. Ramaiah School of Advanced Studies Postgraduate Engineering and Management Programme- Coventry University (UK)

Assessment Sheet

Department Mechanical and Manufacturing Engineering

Course Rotating Machinery Design Batch Full-Time 2009

Module Code RMD 508 Module Title Rotor Dynamics and Vibration of Machinery

Module Leader Dr. B. V. Vijay Module Completion

Date 07/12/2010

Student Name Devendra Singh Bhati ID Number BSB0909001

Attendance Details Theory Laboratory Fine Paid (if any for shortage of attendance)

Remarks

Written Examination – Marks – Sheet (Assessor to Fill)

Q. No a b c D Total Remarks

1

2

3

4

5

6

Marks Scored for 100 Marks Scored out of 50

Result PASS FAIL

Assignment – Marks-Sheet (Assessor to Fill)

Part a b c d Total Remarks

A

B

C

Marks Scored for 100 Marks Scored out of 50

Result PASS FAIL

PMAR- form completed for student feedback (Assessor has to mark) Yes No

Overall-Result

Components Assessor Reviewer

Written Examination (Max 50) Pass / Fail

Assignment (Max 50) Pass / Fail

Total Marks (Max 100) (Before Late Penalty) Grade

Total Marks (Max 100) (After Late Penalty) Grade

IMPORTANT

1. The assignment and examination marks have to be rounded off to the nearest integer and entered in the respective fields

2. A minimum of 40% required for a pass in both assignment and written test individually

3. A student cannot fail on application of late penalty (i.e. on application of late penalty if the marks are below 40, cap at 40 marks)

Signature of Reviewer with date Signature of Module Leader with date

Abstract

This assignment deals with the Rotor Dynamics and Vibration of Machinery.

Generally Vibration is an oscillatory motion-a movement first in one direction and then back

again in the opposite direction. Part A focused on the optimization need in industry cases.

Given argument “Optimization must be initiated early in the design cycles of rotating

machinery, rather than when design cycles are nearly done” is debated in this part”.

Important cases which leads to vibration problems are briefly and suitable suggestion are

mention to enhance the argument for scope of optimization in design of rotating machinery.

Part B is deals with the experimental testing. The Finite Element Analysis is carried

out on a bar for modal characterization and response estimation by using ANSYS tool. This

part case of spring is stiffness is chosen and solve for the modal characteristics of the bar, that

is, modal frequencies and associated mode shapes. Proper Justification is enclosed and

suitable comments are given for the different number of modes, with FRF.

Part C of the assignment work is the continuation of Part B. In this section, the

validation for the analyses is carried out. The test setup consisted of 4 accelerometers,

impulse hammer and real time spectral analyser. Comments on the accelerometer placement

position are given. A plot of the test modal frequencies and the solution from the FE analyses

is plotted. A plot of FRF from the test and FE solution is also plotted with same scale as the

earlier plot. The results of both the above plots are discussed. The correlations obtained from

the comparison of the test and FE solution are summarised.



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Table of Contents

Abstract ...................................................................................................................................... 1

Table of Contents ....................................................................................................................... 2

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

List of Table ............................................................................................................................... 5

Nomenclature ............................................................................................................................. 6

CHAPTER 1 .............................................................................................................................. 7

1.1 Introduction ................................................................................................................................... 7

1.2 Vibration criteria „drive‟ design .................................................................................................... 7

1.3 Industry cases syntheses ................................................................................................................ 8

1.4 Arguments ..................................................................................................................................... 9

CHAPTER 2 ............................................................................................................................ 10

2. Introduction ................................................................................................................................... 10

2.1 Given problem statement ............................................................................................................ 11

2.2 FE model and element selection ................................................................................................. 11

2.3 Case 1: Modal analysis as per the given condition ..................................................................... 13

2.3.1 Harmonic analysis .................................................................................................................... 15

2.3.2 Case 2: common case ............................................................................................................... 16

2.4 Frequnecy Response Function (FRF) ......................................................................................... 18

2.5 Summary ..................................................................................................................................... 19

CHAPTER 3 ............................................................................................................................ 20

3.1 Experimental set up and testing .................................................................................................. 20

3.2 Accelerometer placement location .............................................................................................. 21

3.3 Modal tests and Correlations....................................................................................................... 21

3.4 FRF tests and Correlations .......................................................................................................... 22

3.5 Summary ..................................................................................................................................... 24

CHAPTER 4 ............................................................................................................................ 25

4.1 Comments on Learning Outcome ............................................................................................... 25



3

REFERENCES ........................................................................................................................ 26

BIBILIOGRAPHY .................................................................................................................. 27



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List of Figures

Figure 1. 1 Optimization driven design process..................................................................................... 7

Figure 2. 1 Experimental setup of the vibration apparatus ................................................................... 10

Figure 2. 2 Dimensions of the mass and spring and bar ....................................................................... 11

Figure 2. 3 FE model of the bar ............................................................................................................ 11

Figure 2. 4 Selection of element type ................................................................................................... 12

Figure 2. 5 Solid 8 brick element .......................................................................................................... 12

Figure 2. 6 Real constant for bar and given weight ............................................................................. 13

Figure 2. 7 Frequency contour for mode shape 1.................................................................................. 13

Figure 2. 8 Frequency contour for mode shape 2.................................................................................. 14

Figure 2. 9 Displacement contours for mode shape 10 ......................................................................... 15

Figure 2. 10 Frequency contour for mode shape 1................................................................................ 16

Figure 2. 11 Frequency contour for mode shape 2................................................................................ 16

Figure 2. 12 Displacement contour (Harmonic) for mode shape 2 ....................................................... 17

Figure 2. 13 Displacement contour (Harmonic) for mode shape 100 ................................................... 17

Figure 2. 14 Frequency response (given condition) ............................................................................ 18

Figure 2. 15 Frequency response (common case) ................................................................................ 18

Figure 3. 1 Universal vibration apparatus ............................................................................................. 20

Figure 3. 2 spring and motor location on the bar .................................................................................. 20

Figure 3. 3 The modal frequency at 225rpm for 1 kg mass at spring .................................................. 22

Figure 3. 4 The modal frequency at 305rpm for 1 kg mass at spring .................................................. 22

Figure 3. 5 The FRF plot for case 1 obtained by experiment .............................................................. 23

Figure 3. 6 The FRF plot for case 1 by FE analysis ............................................................................. 23

Figure 3. 7 The FRF plot for case 2 obtained by experiment ............................................................... 23

Figure 3. 8 The FRF plot for case 2 obtained by experiment ............................................................... 24



5

List of Table

Table 2. 1 Eigen frequencies and mode shapes .................................................................................... 14



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Nomenclature

List of Symbols

A Area m2

ρ Density Kg/m3

γ Poisson‟s ratio --

f Frequency Hz

E Young‟s Modulus GPa

Acronyms

MDO Multi Disciplinary Optimization

3 –D 3 Dimensional

GPa Giga Pascal

Hz Hertz

FRF Frequency Response Function



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CHAPTER 1

1.1 Introduction

Optimisation is process that seeks best design which is distinctly different from the

traditional specification based processes and which aims at achieving efficient performance.

This process involves comparison of processes and invariably defining attributes for the

design of the component. The new techniques “Multidisciplinary Optimization” or MDO are

recently used in the aerospace as well as automotive industries. MDO permits optimization of

a number of design variables affecting disparate functional disciplines, using system-level

measures of merit, and in the presence of multiple system design constraints. A design step

can be broken into three major phases, namely Conceptual Design, Preliminary Design, and

Detail Design. Each of these has different tasks and objectives, and the design process in each

phase is quite unique from other phases. Thus, the tools to be employed differ, and even the

people involved are usually different. Optimization methods during conceptual design focus

on the overall design characteristics rather than finer details of the concept. Typical

parameters being included while optimization techniques [1].

Figure 1. 1 Optimization driven design process [1]

1.2 Vibration criteria ‘drive’ design

It is very important that turbomachinery be designed in a way to assure trouble-free

operation. Turbomachinery components, especially blades, are exposed to loads that can

cause failure, designing reliable components requires in-depth vibration and stress analysis.

Turbomachinery design faces inherently multidisciplinary optimization problem with many

conflicting design objectives and constraints.



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Major decisions for the Multi disciplinary Optimization design concept have to be made

in the early design phases when very little knowledge exists about the design. Only small

design changes are possible in later design phases due to time limit. Parameters used for

optimization methods allow to improve the product performance (e.g. by weight reduction)

and simultaneously to reduce time and cost in all design phases. Consideration of various

Multi disciplinary Design Criteria like strength, stability, vibration, dynamics, aero elastics,

structures, control, manufacturing, testing can be perform in this design concept. So we see

that t vibration drives the design process in deciding on the time of final product. Optimizing

the overall design with interaction of one or more disciplines gives rise to multidisciplinary

optimization. If these optimizations are brought in at preliminary design stages then are called

preliminary multi disciplinary design optimization. Performance improvement and weight

reduction for cost reduction are conducted in designing rotating machines, a danger of fault

occurrence is accompanied by because of a shortage of design strength; therefore, the design

optimization technology is widely used. [2]

1.3 Industry cases syntheses

The first industry case is an optimization of gas turbine blades has been done. This

optimization was conducted to improve the advanced cooling systems of high pressure

turbine blades by employing multi-objective generic algorithm. Due to high gas temperature

of the orders of 2000 K at 40 bar at the turbine entry for most of aero-engines, it is very

essential to maintain the material temperature below the melting temperature of the metal.

The tip of the blade region is has very complex 3D flow field which makes it very difficult to

optimize the cooling system using the standard design methodologies considering the fact

that minimizing the hot leakage air from pressure to suction side has a negative impact on

turbine aerodynamic efficiency. First a parametric CFD model is run under the optimization

algorithm by linking it to 3-D CFD code to get the optimum values of geometric parameters.

The 3D code is then substituted into mathematical functions reducing the computational time.

The final design is obtained from the optimization techniques is proved that same heat

transfer performance with a reduction of approximated 16% of the cooling air required [3].

Second case study is chosen form the current propellers are selected because of their very

high efficiency together with peculiar characteristics, such as: high trust generation under

different conditions, long lifetime, and low cost, high mechanical integrity. The purpose of

the present effort is to optimize the low noise production. Recent advances in computing

capabilities have made such multidisciplinary optimization an affordable option. Two



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separate tracks of the optimization procedure have been investigated. First, the aero acoustic

has been developed and validated through conform to data. The results are in close with

experimental measurements and numerical results obtained with other codes for propellers

with subsonic, sonic or supersonic tip speeds. The second track focused on the best choice for

airfoil parameterization. Indeed, the performance of a blade is strongly dependant on the

airfoil shape so it is desirable to use the parameterization that yields the most promising

airfoils. Additionally, two optimizers one based on a binary coded Genetic Algorithm and the

other relying on Multi-Objective Differential Evolution. With the help of optimization tool

Comparison of the predicted Acoustic Pressure (Pa) with the one obtained from a reference

code for an advanced propeller is done and the reduction is noise level is drop down to 4 %

with the help of early stage of design process [4].

1.4 Arguments

The optimization is cost affective and time saving. As discussed in industrial cases it

is clear that optimization when done early in design cycles proves to be beneficial efficiency

wise and performance wise too, because once the design cycles are nearly complete, it

becomes difficult and may be necessary to change the design of the system. Also the

modification goes up resulting in financial waste. Many a times by bringing in the

optimization at the final stages, the efficiency and performance may not improve to the

expected level making way for redesigning. Also when optimization is taken at the last stage,

it is sometimes not easy to modify the design of components easily as the design of one

component may depend on the design of other component, which results in constraining the

optimization process with such obstacles. Preliminary design with multi disciplinary

optimization effects of interaction of multiple disciplines in conceptual phase which

decreases the time spent in detailed design phase.



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CHAPTER 2

2. Introduction

The test setup for the experiment is shown below, which includes a exciter in a form

of a motor with eccentric mass. The speed variator helps the motor to run at different rpm

which helps to understand the resonances at different speed. In the universal vibration

apparatus, the rectangular bar is hinged at one end and supported by a spring at the other,

which is chosen as stiff. Over some part of the bar‟s span, an imbalanced rotor is coupled

dynamically, thereby causing excitation of the bar. The bar is made of steel with Young‟s

modulus E = 200 GPa, Poisson‟s ratio = 0.29, and mass density = 7800 kg/m3. The spring is

placed at the end of the bar at a distance of 810 mm and motor is at a distance of 165 mm

respectively over the bar.

Figure 2. 1 Experimental setup of the vibration apparatus

Using universal vibration machine set up the frequency response functions are found out.

These will help in vibration and modal analysis. Modal analysis is carried out to find the

natural frequencies, damping ratios, and mode shapes of a structure.



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2.1 Given problem statement

First we have to create a finite element model of the bar under its support conditions.

The bar is measured as 860 mm in length and 20 mm width and 10 mm thickness. The bar is

fixed at one end and other end is fixed with the support in which the spring is placed. Motor

is placed at 165 mm from the mass is selected 1.9 kg and where spring is placed at the end.

From all this parameter we have to keep in mind and design a simple bar which should be in

3-D in nature because thickness is mentioned as 10 mm for the bar.

Figure 2. 2 Dimensions of the mass and spring and bar

2.2 FE model and element selection

ANSYS is one of the leading commercial finite element programs in the worldwide

and can be applied to a large number of applications in engineering. A finite element

solution can be validated in several aspects of modelling to obtain a good finite element

solution for problems in structural mechanics.The given problem is deal with structural

analysis so we have chosen the structural option in the tool [5].

Figure 2. 3 FE model of the bar



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The h-method is selected here; h method is used to refine the mesh automatically in

regions where certain results are of interest.

Figure 2. 4 Selection of element type

For the rectangular bar, 3D SOLID with 8 node BRICK type of element is selected.

This element is selected as it has three degrees of freedom with 8 nodes for each element. 8

brick node exhibits less resistant to other deformation modes, also these elements consume

less potential energy. The two MASS 21 elements considered while modeling the rectangular

bar. One mass element represents the mass of the motor and the mass refers to the mass

applied at the spring. The mass element is a point element having 6 degrees of freedom

defined by a single node. Next is spring element is chosen as COMBINATION14. This

longitudinal spring/damper system has uni-axial tension compression elements with 3 degrees

of freedom at the nodes. The rectangular bar is hinged at one end and free at the other end.

Since it is Hinged it can only rotate in Z axis, so the other degrees of freedom are constrained

(constrained in X and Y axis (translation and rotation). The spring is only free to rotate in Y

axis i.e axis perpendicular to the axis of the bar; rest degrees of freedom are constrained. Next

we had selected the real constant for mass of the bar and the spring cases. For both the cases

the Mass is selected and the bar and spring is 6.75 and 1.9 kg respectively.

Figure 2. 5 Solid 8 brick element



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Figure 2. 6 Real constant for bar and given weight

The exciter motor is run at three different speeds, as we increase the speed the

deflection in spring and the bar is more and cause resonance. At each speed similar modal

characteristics is expected. The eccentric mass is kept constant.

2.3 Case 1: Modal analysis as per the given condition

A modal analysis is typically used to determine the vibration characteristics (natural

frequencies and mode shapes) of a structure or a machine component while it is being

designed. It can also serve as a starting point for another, more detailed, dynamic analysis,

such as a harmonic response or full transient dynamic analysis. Block Lanczos method –

typically used for large symmetric eigenvalue problems, this method utilizes a sparse matrix

solver. This method is suitable for finding few modes in a small/ large DOF model.

Figure 2. 7 Frequency contour for mode shape 1



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In the mode shape 1 the frequency is obtained as 1.939 Hz. The maximum deflection

is obtained nearer to the tip of the bar and it will decreases along the length. The minimum

deflection is shown here is at hinge.


The next mode shape obtained and the frequency is obtained as 11.024 Hz. The

maximum deflection is shown here is middle of the bar. At the tip it is nearer to zero and the

supportive hinge has a positive deflection as compare to tip of the bar.

Using PCG Lanczos method we can able to extract few modes shape only. Also this

method gives the Eigen values starting from lowest Eigen frequencies. Since the maximum

speed that the exciter could excite was around 2000 rpm, only frequencies which were around

50-100 Hz were capture in the solution. Hence only first two mode shapes are shown in the

Fig.2.7-2.8 which is within the range of frequencies.

Table 2. 1 Eigen frequencies and mode shapes

Mode shape Frequencies (Hz)

1 1.939

2 11.024

3 41.835



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2.3.1 Harmonic analysis

Harmonic Analysis is used to determine the response of a structure to harmonically

time-varying loads. Any sustained cyclic load will produce a sustained cyclic response (a

harmonic response) in a structural system. Harmonic response analysis gives the ability to

predict the sustained dynamic behavior of structures. A harmonic analysis, by definition,

assumes that any applied load varies harmonically (sinusoidally) with time. To completely

specify a harmonic load, three pieces of information are usually required: the amplitude, the

phase angle, and the forcing frequency range.

Figure 2. 9 Displacement contours for mode shape 10

For the harmonic response the frequency range is nearly about to say is 401.86 Hz.

The mode shape is shown here for 10th

subset. The displacement is higher at tip of the bar

where the spring is attached. The spring is 50 mm away from the tip of the bar. The hinge

side we observe that there is no deflection because the hinge is fixed element at the end of the

bar.



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2.3.2 Case 2: common case



For the common case the frequency for subset 1 and 2 are 3.159 and 9.361 are Hz are

shown in the contour. The mode 1 have maximum deflection at tip of the bar whereas in

mode 2 the maximum deflection is nearly in the middle of the bar. The tip have nil deflection

but the supportive hinge have a middle range of the deflection range.



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Figure 2. 12 Displacement contour (Harmonic) for mode shape 2

Figure 2. 13 Displacement contour (Harmonic) for mode shape 100

Figure 2.18 and 2.19 showing the dispalcement contours for the harmonic analysis.

The frequency range is in between 0.4 and 20 Hz for the subset 1 and 100 respectively. The

harmonic modal analysis for subset 1 is showing the lesser dispalcement at tip of the bar but

in subset 100 it is maximum at mid of the bar the hinge have less displacement as comapre to

the modal analysis.



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2.4 Frequnecy Response Function (FRF)

The idea of FRF is to calculate the structure's response at several frequencies and

obtain a graph of some response quantity (usually displacements or amplitude) versus

frequency. The "Peak" responses are identified on the graph for both the cases. This analysis

technique calculates only the steady-state, forced vibrations of a structure. The general

procedure for harmonic analysis is as follows

Harmonic type of analysis is selected from a range of analysis types. Once the

harmonic type of analysis is selected the, the sub-steps value and the frequency valued in

range of 0 to 10 and the sub step of 100 is substituted. The loading and boundary conditions

on the structure is specified by selecting the displacements/force from the load option in

ansys tool.

Figure 2. 14 Frequency response (given condition)

Figure 2. 15 Frequency response (common case)



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2.5 Summary

A FE model was built using appropriate methods to get the modal characteristics of

the bar. The mode shapes are obtained occurring at high speeds. The frequency response for

appropriate modes were calculated at higher speeds spring has a greater tendency to get

excited towards the fundamental frequency as shown in Fig.2.14 and 2.15. The FRF gives an

idea as to how the system behaves to the dynamic loading.

Figure 2.14 and 2.15 shown for common and given condition cases. In the case of

given condition the frequency range is obtained as 1.93 and after that resonance occurs. The

next plot shown for the common cases in which the frequency is nearly about 3.1 Hz. as we

increase in mass which is going to decrease the frequency values as which is clearly

understood by the both the cases. The given condition have a mass of 1.9 Kg, so the

frequency range is about 1.93 Hz , and also in common case the mass is taken as 1 Kg so the

range is nearly about 3.14 Hz. The resonance level shown for the both the cases, higher the

mass value will have less resonance level in the system. The resonance level should cross the

limit to make system stable and lesser vibrate. The next resonance occur at 11.02 Hz but the

level is less, the lesser resonance level which help the system to cross it limit and make it

stable. Also there is difference in all the modes of both the cases. This difference can be

attributed to the change in mass at the spring and the change in motor position. In case 1 the

motor in mounted at a distance of 165mm from the hinged end with 1 kg mass at spring, in

case 2 the motor is mounted at 430mm form the hinged end with 1.9 kg mass at the spring.



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CHAPTER 3

3.1 Experimental set up and testing

Figure 3. 1 Universal vibration apparatus

The test setup is shown in Fig.3.1 where two accelerometers are used, one near the

exciter and the other near the spring; both the accelerometers are connected to a data

acquisition system. In the universal vibration apparatus, the rectangular bar is hinged at one

end and supported by a spring at the other, which is chosen as stiff. Over some part of the

bar‟s span, an imbalanced rotor is coupled dynamically, thereby causing excitation of the bar.

Figure 3. 2 spring and motor location on the bar



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3.2 Accelerometer placement location

Accelerometers are devices that measure the acceleration of the vibrating body. Since

they have higher natural frequency than the frequency which it measures, they are generally

lighter and can be placed with ease without affecting the characteristic of the actual system.

Uni-axial accelerometers were used in our experiments hence they were placed in the

direction of motion of the bar i.e. where it can capture/ measure most (maximum) of

acceleration. The accelerometer is attached without regard to end results in order to facilitate

data collection speed.

In this case we have placed the accelerometer nearer to the spring and one is near to the

motor. The location is set because to obtained the minimum deflection in bar. The mode 1

have only single node but whereas in mode 2 we have a single node. By keeping this in mind

we adjusted the accelerometer nearer to the spring. The position of accelerometer is to tracing

the higher frequency range within its limit of operation. The placement can be varying by

user defined to obtain different modes by excitation of the bar. The accelerometer is placed at

a distance of 750 mm form the bar tip and another is placed nearer to motor. Here in the

given condition is it nearly about 3.14 Hz. By analogue result it is nearly 3.75 Hz.

3.3 Modal tests and Correlations

Form the modal testing the frequency is 3.14 and 9.61 Hz for the mode shape 1 and 2

respectively. The plot shown in figure 3.6 and 3.7 are shown the frequency range of 3.75 Hz.

The difference in the frequency varies because of the addition vibration in the apparatus.

Mainly the frame and the hinge connector are also affecting and vary the frequency range.

The rpm indicator which placed on the top and the changes in rpm may also lead to vary the

range of the frequency. Below figure 3.3 and 3.4 showing the major component which may

cause the addition vibration in the system and may increase the resonance level too.



22

Figure 3. 3 The modal frequency at 225rpm for 1 kg mass at spring

Figure 3. 4 The modal frequency at 305rpm for 1 kg mass at spring

Figure 3.3 and 3.4 showing the frequency range of 3.75 Hz. The right hand side are continues

lines are related to disturbance in the apparatus. As per the compare form the modal analysis

from the given case it is showing the higher frequency range because of higher excitation in

the bar. The FE analysis recorded 3.14 Hz respectively for the given condition. The excitation

in the experimental set up is much nearer to the FE analysis as we observed in the figure 3.4.

3.4 FRF tests and Correlations

Next we have to relate it with the FRF data. The hammer excitation also response for the

frequency ranges. As we continuously impacting on the bar for the different response in the

system. The range is nearly about 3.75 Hz is obtained. The frequency range for the common

case is also nearly about 3.14 and for the given condition is it 1.93 Hz. The hammer impact is

not the same at a time and not also on the different location of the bar, so the frequency is



23

randomly selected. By changing the impact location on the bar can also gives changes in the

frequency response. Here the frequency is nearly about 3.75 Hz.

Figure 3. 5 The FRF plot for case 1 obtained by experiment

Figure 3. 6 The FRF plot for case 1 by FE analysis




24


3.5 Summary

It is clear from above discussion that the frequency response from a FE model and the

experimental results are relating with one another. Also it gives a clear picture of responses of

relative elements in a system at different frequencies and dynamic conditions. Thus the

experiment helps validate our FE model. From the above figure it is clear that near the motor

at 305 rpm, region is susceptible to both the first resonance frequency 3.75Hz and the second

frequency at 11.39 Hz. However the acceleration is almost same when compared to response

at 225 rpm and less compared to 305 rpm. Lots of noises/ unwanted responses felt in the

experiment also reflects in the frequency response measured using a data acquisition analyzer

due to multitude of facts.



25

CHAPTER 4

4.1 Comments on Learning Outcome

By undergoing this module we were able to:

Understand the role and importance that vibration in any design scenario of a rotating

machinery and in various industries.

Optimization techniques design, its initiation early in the design cycle.

vibration testing with validating the FE model

Use a commercial software/tool and understand how it is used in synergy with the test

apparatus and the algorithms being used to simulate the results.

The learning outcomes were met which were addressed directly/ indirectly in our

assignments. Form this module I got knowledgeable with the tools and lab class the idea are

much clear and the problem are easy to understand which was explained in the classes. The

basic knowledge to the Rotor dynamics and vibration is covered and the tool like MATLAB

is much more important to solve a real time problems.



26

REFERENCES

[1] Unknown,http://www.altairhtc.com/europe/presentations/Keynotes1/Keynote_Eads_S

chuhmacher.pdf, retrieved on 24th

Nov 2010.

[2] Unknown, http://www.ozeninc.com/downloads/ch_turbineblades_optimization.pdf

, Retrieved on 24th

Nov 2010.

[3] Unknown, http://www.vki.ac.be/download/phdthesis/phdsum_marinus.pdf, Retrieved

on 24th

Nov 2010.

[4] Unknown,http://books.google.co.in/books?id=9N7sQjcFaDwC&dq=turbomachinery+d

esign+and+theory&printsec=frontcover&source=bn&hl=en&ei=gNooTIjEM8i3rAfjk6i

EBQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCIQ6AEwAw#v=onepag

e&q&f=false, Retrieved on 25th

Nov 2010.

[5] ANSYS Inc., ANSYS Help manual v 12.0, Mechanical APDL, 2009.

http://books.google.co.in/books?id=9N7sQjcFaDwC&dq=turbomachinery+design+and+theory&printsec=frontcover&source=bn&hl=en&ei=gNooTIjEM8i3rAfjk6iEBQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCIQ6AEwAw#v=onepage&q&f=false






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BIBILIOGRAPHY

[1] Dr.Vijay B.V., Rotor Dynamics and Vibration of Machinery, Course Notes, M.S.

Ramaiah School of Advanced Studies, Bangalore, June 2010.

[2] P. Srinivasan, Nonlinear Mechanical Vibration, 1st Edition, New Age International

Publishers, 2002.

[3] Singiresu S. Rao, Mechanical Vibration, 2nd

Edition, Pearson Education (Singapore) Pvt.

Ltd., 2004.

[4] Nitin S. Gokhale, Practical Finite Element Analysis, 1st Edition, Finite to Finite, 2008.

[5] W.T. Thomson, Vibration, Prentice Hall, 5th

ed., 1997.

[6] Leonard Meirovitch, Elements of Vibration Analysis, McGraw Hill, 1986.

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Devendra Vibration