Download Major Project Modeling of a disk type car horn

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Major Project
ME 492S
Modeling of a disk type car horn
Final Report
ass)
115
Under guidance of:
r..
Dr. S.P. Sin4h
(Mechanics Engineering Department)
Prof. B.C. Nakra
(Mechanical Engineering Department)
Submitted by:
41~~
ayv-
Arpit Tiwari (2001215)
Santosh Verma (2001252)
CERTIFICATE
This is to certify that Arpit Tiwari (2001215) and Santosh Verma (2001252), both
of them students of B.Tech Final year, Mechanical Engineering Department IIT Delhi
have completed the work required to be done in the current semester successfully.
Dr. .P. ingh
Mechanic
I Engineering Department
IIT Delhi
Prof. B.0 Nakra
Mechanical Engineering Department
IIT Delhi
ACKNOWLEGEMENT
We take, this opportunity to express our sincere and earnest gratitude to our guides
Dr. S.P. Singh and Professor B.C. Nakra (Indian Institute of Technology, Delhi) for their
ingenious and immaculate guidance and great persistence in our work. They have always
been a source of constant encouragement and support. We have always been benefited by
their sterling character and talent.
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ABSTRACT
The aim of this project is to analyze the sound produced by a disc type horn, used
in car. For this, the car horn is modeled by splitting it into four circuits namely electrical,
magnetic, mechanical and acoustic. The mechanical circuit was modeled using vibration
theory that is vibration of flat plates. The vibration response is Iater converted to acoustic
response. The response of diaphragm and mobile nucleus assembly to impact forces
produced when mobile nucleus is attracted by magnetic forces produced in the
electromagnetic coil is to be determined. For this an estimation of the value of this force
as well as the natural frequencies and mode shapes of diaphragm mobile nucleus
assembly. The electric circuit is first modeled to obtain the variation of electric current in
the coil as a function of time and then we modeled magnetic circuit and obtained the
variation of magnetic field both with respect to time and distance. Thus the variation of
force of magnetic attraction on mobile nucleus with time is calculated.
The first three natural frequencies and corresponding modes of the diaphragm
mobile nucleus assembly are calculated using Finite Element Method, Ritz Method and
Closed Form Solution involving Bessel Functions. Then we calculated response of the
magnetic force on the plate for the first natural frequency. The displacement due to the
magnetic force is plotted as a function of space coordinates and time. Fast Fourier
Transform of displacement was taken to verify the natural frequencies present in the
response.
Sound pressure and sound power levels produced by the diaphragm and resonator
is calculated using free average ' surface velocity and compared with experiment
evaluation.
Keywords:
Diaphragm, Mobile nucleus, Mode shapes, Bessel Functions, Modal Analysis, - Impulse
Response Function, Fast Fourier Transform (FFT), Sound level (dB).
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TABLE OF CONTENTS
Topics
Page number
Certificate...............................................................................1
Acknowledgement......................................................................2
Abstract............................................................... ....................3
List of figures/tables ...................................................................5
Nomenclature and abbreviations/Units of measurement ..........................7
Greek symbols and their meanings ...................................................8
1. Chapter 1: Introduction
1.1 Introduction ....................................................................9
1.2 Fundamentals of disc horn ....................................................9
1.3 Types of horn .....................................................................9
2. Chapter 2: Literature review and statement of problem
2.1 Literature review ..............................................................1 I
2.2 Problem formulation/steps involved in solving the problem............13
3. Chapter 3: Modeling
3.1 Current circuit .................................................................15
3.2 Magnetic circuit ...............................................................16
3.3 Mechanical circuit ............................................................ 17
3.4 Acoustic circuit ...............................................................24
4. Chapter 4: Results
4.1 Results for modeling of current circuit .....:..............................27
4.2 Results for modeling of magnetic circuit ..............................28
4.3 Results for modeling of mechanical circuit ..............................30
4.4 Results for modeling of acoustic circuit ............................ ... 36
5. Chapter 5: Conclusions/Scope for future work
5.1 Conclusions ..................................................................42
5.2 Scope for future work ......................................................43
References......................................................................44
Appendix .............................................................
...................... 45
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LIST OF FIGURES/TABLES
Figure Label
No.
Section Page
No.
No.
1.1
Schematic Diagram of a disk type car horn
1.3
10
3.1
Schematic of an LR circuit
3.1
15
3.2
Schematic Diagram of a solenoid
3.2
16
3.3
Dimensions and boundary condition of the diaphragm 3.3
18
mobile nucleus assembly
3.4
Values of ,%2 = araZ/ Dfor various mass ratios for 3.3
23
a clamped circular plate having a concentrated mass at
centre
3.5
Plot of 10 log10 o vs. frequency ratio for calculating the 3.4
25
value of geometric constant 6
3.6
Chart referred to for determination of type of radiation 3.4
26
field of the source
4.1
Plot of current in the coil vs. time
4.1
27
4.2
Plot of Magnetic Induction vs. Distance from the centre 4.2
28
of the coil.
4.3
Plot of Force on the mobile Nucleus vs. Time
4.2
29
4.4
First natural mode shape of diaphragm and mobile 4.3
30
nucleus assembly
4.5
Mode shape of vibration of diaphragm as obtained by 4.3
31
Bessel functions
4.6
Mode shape of vibration of diaphragm as obtained by 4.3
32
Ritz approximation
4.7
Plot of Force function in modal domain vs. time
4.3
33
4.8
Plot of Response function in modal domain vs. time 4.3
34
(damping considered)
4.9
Plot of Displacement of plate vs. radial distance and time
4.3
34
4.10
Plot of Velocity function at radius of 0.02 m vs. time
4.3
35
4.11
Velocity of [plate plotted as a function of radial distance 4.3
35
and time.
4.12
Fast Fourier Transform(FFT)of the displacement 4.3
function
36
in frequency domain.
4.13
Electrical circuit of the experimental setup.
4.4
37
4.14
Experimental setup for measuring the sound intensity at 4.4
37
required distances.
4.15
Angular locations of sound level meter around the horn 4.4
38
at a given distance.
4.16
Experimentalsetupfor determinationof Resonator 4.4.2
39
frequencies and approximate mode shapes
4.17
Plot of sound level as a function of distance from horn.
4.4.3
41
4.18
Comparisonof experimentalandtheoreticalsound 4.4.3
41
power.
Table
No.
Label
4.1
Natural frequencies of a plate clamped at edge and 4.3
Section Page
No.
No.
30
having concentrated mass at centre calculated using
different methods.
4.2
Sound level in decibels (dB) at various locations from 4.4
38
the horn
4.3
Comparison of theoretical and experimental values of 4.4.3
40
sound pressure level.
4.4-
Experimental measurement of sound power (dB)
4.4.3
41
NOMENCLATURE AND ABBREVIATIONS / UNITS OF
MEASUREMENTS
Quantities/Nomenclature
Units of Measurement
a: Radius of the plate
Meter
A: Area of mobile nucleus.
Sq. Meter (m2)
B: Magnetic induction
Tesla (T)
D: Directionality
Dimensionless
F: Force.
Newton (N)
I: current
Ampere (amp)
L: Inductance
Henry (H)
N: Number of turns in the coil.
Dimensionless
r1:Inner radius of coil.
Meter (m)
r2:Outer radius of coil.
Meter (m)
R: Resistance
Ohms (S1)
S: Surface area
Sq. Meter (m2)
t: time
Seconds (s)
<v2 >: Average Squared Surface velocity
sq. (m/s)
V: voltage
Volts (v)
x, : Distance from outer end of coil.
Meter (m)
x2 : Distance from inner end of coil.
Meter (m)
Abbreviations:
FEM/EEA: Finite element methods/analysis
FFT: Fast Fourier Transform.
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GREEK SYMBOLS AND THEIR MEANINGS
Quantities/Nomenclature
Units of Measurement
0: Magnetic Flux
Weber (Wb)
x: Permeability of mobile nucleus
Dimensionless
A:Time constant for LR circuit
Seconds (s)
}so; Permeability of free space.
Tesla.Amp. m12
pd.:
Dimensionless
Relative permeability of mobile nucleus.
dB: (Decibels) Sound Level
Dimensionless
a: Radiation Ratio
Dimensionless
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