OPTIMISATION OF A CAR HORN USING MULTIPHYSICS
ANALYSIS
Marescotti Cristina, Bonfiglio Paolo, Pompoli Francesco
Mechlav, Tecnopolo dell’Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
Seco Jorge, Verzini Gerardo
FIAMM S.p.A - BU Horns, V.le Europa, 7,36075 Montecchio Maggiore (VI), Italy
A car horn is a safety device present on every type of vehicle as a warning system. In order
to be mounted on a vehicle standard CEE-ECE N° 70/388 gives the minimum performance
requirements in terms of sound emission that car horns must guarantee outside the vehicle.
At the same time the increase of noise treatments in engine compartment leads to necessity
to have higher performances of car horns themselves. Starting from such motivation collaboration between the University of Ferrara, and the FIAMM S.p.A. group aimed to optimize
and maximize the sound emission of its commercial car horns. In this paper two different
numerical models are presented and discussed. The first numerical model simulates the
crimped housing that generates the sound field in terms of its fundamental working frequency. The latter studies the complete system, that includes the crimped housing and the geometry of the spiral exponential horn shape (snail). Using an automatized procedure the geometry of the snail is modified according to an optimization scheme; the intent of the complete
procedure is to have an increase of sound pressure emitted and a set of cavity modes well
coupled with fundamental working frequency and its first harmonics. Several numerical
models will be presented and validated against experimental tests.
1. Introduction
A vehicle horn is a sound-making device used to alert people of a potential danger related to a
car and for this reason it must be assembled on every type of road vehicles. There are many kinds of
horns but electromagnetic devices are the most used on vehicles. The Directive 70/388/EEC [1]
establishes the minimum performances for car horn’s certification. Furthermore a horn must fulfil
another requirement related to the sound emission once it is mounted on a vehicle.
A very important issue for the certification of these devices is related the increased use of noise
control treatments in automotive applications. These treatments are utilized indeed to reduce the
noise inside and outside the vehicles and their presence in the engine compartment leads to significant reduction of the car horn sound emission.
The aim of this research is to define a fully numeric procedure for an optimization analysis of the
acoustic performance of the electromagnetic car horn devices, improving their sound emission.
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The research is composed of two different analyses. The former is focused on the electromagnetic
crimped housing, i.e. the element that generates sound field that will propagate and be amplified
inside horn’s cavity; the main properties describing the physics of sound generation are firstly estimated by several measurements and then used to build a numerical model that reproduces the mode
of operation on the horn. Finally the results of numerical simulations are compared to the experimental data for its validation. The latter analysis is dealing with snail geometry. which acts as s
waveguide and is able to amplify the acoustic field. A finite element model (FEM) is proposed to
optimize geometry of snails that will couple cavity modes and working frequency and its first harmonics.
2. Electromagnetic car horn devices
Electromagnetic vehicle horns are made by a flexible metal diaphragm, usually made of steel
sheet, that generates the sound field, a central armature attached to the diaphragm, a coil of wires
that forms an electromagnet (responsible for the electromagnetic force acting on diaphragm) and
finally a switch that control the current flux through the electric circuit. A spiral exponential horn,
here called snail, is used to better match the acoustical impedance of the diaphragm with open air,
and thus more effectively transfer the sound energy. The working principles of a car horn is represented in Figure 1 [2].
_f_
Figure 1. Working principles. a) Closed- circuit current, b) Open- circuit current, c) and d) generated
forces, e) acoustic field generated by the vibration of the diaphragm , f) section of the car horn.
When voltage (generally 12 V) is applied to the electromagnet, the armature moves down to its
mechanical limit, disengaging the contact and stopping the current flow. Diaphragm is released to
travel back past neutral position closing the switch again, and thereby pulling the diaphragm back,
setting up a new oscillation cycle [3]. This action is repeated about 400 times per second and the
vibration of the diaphragm, like a piston that generates a field of plane waves inside a cylinder, disturbs the air particles from their point of equilibrium . The number of times that the diaphragm
moves itself defines the main frequency of the device which sets the tone of the car horn. This tone
is also determined by the rigidity of the diaphragm, its physical size and constrains, the strength of
the electromagnet, the mass of the diaphragm, the mechanical arrangement of the switch contact,
the size and the shape of the horn.
In order to increase the emitted sound pressure, the cavity modes must be well coupled with the
fundamental working frequency and its first harmonics. Thus the working frequency of crimped
housing has to be controlled and, at the same time, the snail geometry has to be appropriate in order
to guarantee an optimal matching of the impedance between the diaphragm and open air.
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3. Material and methods
3.1 Multiphysics model for the estimation of the working frequency of the horn
Several measurements on the electromagnetic crimped housing have underlined that its working
frequency depends on many factors which could lead to a variation of such quantity up to 20 Hz for
same nominal systems. This is a very important issue to be faced, since as stated before working
frequencies and cavity modes of the snail need to be well coupled in order to ensure the maximum
sound emission outside the horn.
In the present paper an analytical model describing the electro-magnetic-mechanical behaviour
of crimped housing is proposed: in particular a lumped parameter model (RL circuit, electromagnetic force and displacement of the diaphragm) is coupled to a vibro-acoustic FEM model of the
diaphragm’s vibration that generates the acoustic field. The complete model is described by using
following equations:
(1)
di
i  R  R1  L1  e  0
dt
2
e
 i 
d 2w
dw
m 2  k1
 kw  C1 
  S p  dS  0
dt
dt
 w0  w 
where:
i is the current that flows through the coil [A];
e (=12 V) is the voltage at the coil end terminations;
R is the resistance of the coil [Ω];
R1 is an additional resistance due to arc discharge effect occurring all the times current suddenly
stops flowing through the coil [Ω];
L1 is the inductance of the coil [H];
w is the displacement of the diaphragm [m];
m is the mass of the diaphragm and of the armature connected to the diaphragm [kg];
k1 is the damping coefficient of the diaphragm [kg/s];
k is the spring constant of the diaphragm [N/m];
w0 is the start position of the mobile armature referred to the static pole [m];
C1 is the electromagnetic field constant [Nm2/A];
p is the acoustic pressure that operates on the diaphragm [Pa].
Parameters e, R, L1, m, k have been directly measured, while parameters R1, k1 and C1 are estimated from literature.
Set of differential equations (1) is numerically solved in order to calculate the current i(t) and the
displacement of the diaphragm w(t), as function of the time. At the same time the displacement w(t)
is used, as a boundary condition applied to the central point of the mobile armature, in the vibroacoustic FEM model of the diaphragm, allowing the calculation of the sound pressure outside and
inside the crimped housing. A 2D axial-symmetric vibro-acoustic model is depicted in Figure 2.
Finally the Fourier transform is applied to all signals in time domain (current, displacement and
sound pressure) in order to calculate the working frequencies of the crimped housing and values
from numerical models will be compared to the experimental ones in Section 4.
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4
1
5
3
2
Figure 2. Vibro-acoustic model of the diaphragm and air cavity. (1) diaphragm; (2) coil; (3) static
core; (4) air cavity outside the housing; (5) air cavity inside the housing.
3.2 Vibro-acoustic FEM model for the determination of the cavity modes of the
snail
The frequency domain vibro-acoustic FEM model used to determine the acoustic cavity modes
of snail is shown if Figure 3.
Figure 3. 3D Vibro-acoustic FEM model. (a) snail and diaphragm - (b) external air volume (c) complete model.
The boundary and domain conditions utilized in the model can be summarized as follows:
- the diaphragm and the snail (shown in 3(a)) are modelled as acoustic shells with linear
elastic mechanical properties (Young’s Modulus, Poisson’s ratio, damping loss factor
and the density);
- all the acoustic domains are modelled as air cavities with proper density (0) and sound
speed (c0).
- the external cavity (3(b) part 2) is modelled as an absorbing layer with wall impedance
equal to ρ0c0 and a complex density and sound speed calculated using Delany-Bazley
model with a flow resistivity of 4600 [Pa*s/m2]. Such domain is used to simulate a free
field condition outside the horn;
- a constant force [1 N] is applied to the diaphragm as depicted in figure 3(a);
- finally continuity boundary conditions are applied to the contact surfaces between housing, snail and air cavities. Such conditions guarantee the continuity of the sound pressure
and acceleration between the two different domains.
This analysis is carried out in a range of frequencies between 400 Hz and 2000 Hz in order to
calculated the cavity modes of the snail coupled with the diaphragm. These cavity modes are repreICSV22, Florence, Italy, 12-16 July 2015
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sented by the maximum values of the sound pressure emitted in the proximity of the snail’s mouth.
The same frequency response curves have been measured in a anechoic room and compared to the
FEM model results as discussed in Section 4.
4. Results
4.1 Determination of the working frequency of the vehicle horn
The i(t) current that flows through the electric circuit, the w(t) displacement of the diaphragm
and the sound pressure emitted p(t) have been measured in an anechoic room. The experimental
setup consists of:

POLYTEC OFV-3001: laser doppler vibrometer for differential measurements;

POLYTEC OFV-512: fiber optical sensor head for differential measurements;

PCB 377B20: 1/2" prepolarized condenser microphone 50 mV/;

NI USB-4431: a high-accuracy data acquisition (DAQ) module specifically designed for
high-channel-count sound and vibration applications (24-Bit Analog I/O, 102.4 kS/s, ±10
V);

NI-PCI-MIO-16E-4: uses E Series technology to deliver high performance and reliable
data acquisition capabilities to meet a wide range of application requirements. You get up
to 500 kS/s single-channel (250 kS/s multichannel), 12-bit performance on 16 singleended analog inputs. Used to record the current absorption of the housing.
Signals in time domain has been measured and post-processed using a software developed on
Labview platform. An example of test is depicted in Figure 4.
(a)
(b)
Figure 4. (a) Experimental measurement of current, displacement and sound pressure. (b) tests carried out
coupling the housing with plastic cylinders in order to evaluate the effect of acoustic load acting on the
diaphragm.
Figure 5 shows the comparison between the experimental and numerical current and displacement of the diaphragm time histories for the housing. From comparison in Figures 5 it is possible to
observe a satisfactory agreement between tests and numerical models. The signals also present a
similar working frequency after the Fourier transform has been applied, with a frequency of 418.1
Hz for the experimental measurements and 415 Hz for the numerical data.
As underlined in previous sections, the working frequency depends on different factors; among
them the acoustic load within the snail acting on diaphragm and the mass of the entire system play a
fundament rule; thus as additional tests and simulations, plastic cylinders have been coupled to the
housing (Figure 4(b)) in order to experimentally evaluate the variation of the main working frequency of the housing with the afore-mentioned acoustic load. Comparisons between numerical and
experimental values of main working frequency are summarized in Table 1.
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FEM Current
Experimental Current
FEM Displacement
Current [A]
Displacement [mm]
Experimental Displacement
Time [s]
Time [s]
Figure 5. Experimental and numerical comparison between current and displacement .
Table 1.Experimental and numerical working frequencies for housing coupled to cylinders.
Configuration
housing
housing + cylinder 5 cm length
housing + cylinder 10 cm length
Experimental frequency[Hz]
418.1
402.3
389.1
Numerical frequency [Hz]
415
420
430
From data summarized in Table 1 it is possible to observe that the effect of increase the acoustic
load on the diaphragm results in a growing of the working frequency of the entire system. On the
other hands the experimental values of the working frequencies decrease. The differences can be
explained in terms of added mass (not considered in the FEM model) due to the presence of cylinders themselves. In fact changing mass m in Eq. 1 leads to lower values of working frequencies. In
particular an added mass of 5 and 7 grams respectively are needed to match experimental values.
The physical meaning of such values will be investigated in the future. From an experimental point
of view these considerations are confirmed by some measurements carried out mounting the cylinder to increase the mass, with the same acoustic load and using cylinders of different size, in order
to have different acoustic loads, with the same mass.
Table 2. Effect of the acoustic load with the same total mass ( 1 a.m.= 21.0 grams).
Configuration
Total mass [kg]
housing+cylinder 5 cm+ 2 a.m.
housing+cylinder 10 cm
Length cylinder
[m]
0.05
0.10
0.0962
0.0974
Experimental frequency[Hz]
379.0
389.1
housing+cylinder 5 cm+ 3 a.m.
housing+cylinder 10 cm+ 1 a.m.
0.05
0.10
0.1172
0.1184
364.0
375.0
housing+cylinder 5 cm+ 4 a.m.
housing+cylinder 10 cm+ 2 a.m.
0.05
0.10
0.1382
0.1394
359.0
371.0
housing+cylinder 10 cm+ 4 a.m.
housing+cylinder 20 cm
0.10
0.20
0.1814
0.1852
354.0
368.0
As shown in Table 2, the experimental working frequency of the housing is changed by both the
variation of the acoustic load and of the added mass: configurations with the same added mass increase the working frequency with the growing of the length of the cylinder, thus with the increase
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of acoustic load. In fact, if the length is increased from 5 cm to 10 cm, the working frequency is
also increased by 10 Hz. In the last case, there is an increase of 14 Hz with a variation of the length
of the coupled cylinder that goes from 10 cm to 20 cm. On the other hands, configurations with the
same length (i.e. the same acoustic load that acts on the diaphragm) and an increased added masses
lead to a decrease of the experimental working frequency, as summarized in Table 3.
Table 3. Effect of the added mass (= a.m.) with the same acoustic load.
Configuration
Length cylinder
[m]
0.10
0.10
0.10
0.10
housing+cylinder 10 cm
housing+cylinder 10 cm+ 1 a.m.
housing+cylinder 10 cm+ 2 a.m.
housing+cylinder 10 cm+ 4 a.m.
Added mass [kg]
Experimental frequency[Hz]
389.1
375.0
371.0
354.0
0.0974
0.1184
0.1394
0.1814
Summarizing, the increase of the acoustic load and the increase of the total mass mounted on the
housing lead to an increase and a reduction of the working frequency, respectively.
4.2Determination of the cavity mode of the acoustic snail
The vibro-acoustic model of the snail presented in Section 3.2 is validated through some experimental measurements of acoustical cavity modes carried out for three different type of snails
(having different internal geometry as depicted in Figure 6) coupled with the same electromagnetic
housing.
Figure 6. Geometries of the tested snails.
In order to measure acoustical cavity modes, the housing has been excited by a low voltage (<
1V) logarithmic sweep sine from 400 Hz to 4000 Hz. Sound pressure levels are measured in the
proximity of the snail mouth and modes are evaluated from the peaks of the frequency response
function.
Table 2 shows the comparison between the experimental and the numerical cavity modes and
both experimental and numerical frequency response function are shown in Figure 8. Table 2.
shows that the model can predict the cavity modes of the snail with an error lower than 10 Hz.
Table 4. Experimental and numerical cavity modes.
Geometry
Mode 1
Mode 2
Mode 3
1
Fexp [Hz]
801
1220
1686
2
FFEM [Hz]
800
1220
1690
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Fexp [Hz]
747
1295
1676
3
FFEM [Hz]
740
1260
1665
Fexp [Hz]
815
1220
1642
FFEM [Hz]
810
1215
1650
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Experimental measurements
60,0
Geometry 1
Geometry 2
50,0
Geometry 3
Lp [dB]
40,0
30,0
20,0
10,0
0,0
400
600
800
1000
1200
1400
1600
1800
2000
1400
1600
1800
2000
Frequencies [Hz]
FEM model
Geometry 1
Geometry 2
60
Geometry 3
50
Lp [dB]
40
30
20
10
0
400
600
800
1000
1200
Frequencies [Hz]
Figure 7. Experimental and numerical cavity modes for the three geometry analysed.
It is worthy of mention that curves in figure 7 can be compared only in terms of peaks of the frequency spectrum since experimental and numerical input displacement are not the same.
5. Conclusions and future developments
In the present paper a fully numeric procedure for the analysis of electromagnetic horn has been
presented and discussed; In particular two different numerical model have been defined for the determination of the working frequency and cavity modes of the horn, respectively. Results from numerical models have been compared with experimental data and in all the case the agreement can be
considered satisfactory. Future work will be devoted to the definition of an automatized procedure
able to change the geometry of the snail in order to increase the sound emission of the horn.
REFERENCES
1 Directive 70/388/EEC (1970) – Audible warning devices for motor vehicles.
2 http://www.fiamm.com.
3 Bjørn Kolbrekh, Horn Theory: An Introduction, Part 1 and Part2, Article prepared for
www.audioXpress.com, 2008.
4 C. Marescotti, Multiphysics optimisation analysis of car horns (in italian), Tesi di Laurea
Specialistica A.A. 2013/2014.
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