Experience Gathered from the Use of ANSYS - TechNet Alliance

Summary
FEM Simulation of loudspeakers
and loudspeaker components
Leonhard Kreitmeier
Harman/Becker automotive systems
Straubing, Germany
The electrodynamic principle is widely used for Loudspeaker application due to the fact that the result
is a robust type of transducer.This Fact is especially useful in car application where there is massive
environmental testing done. FEM Simulations of these transducers helps defining the design of the
components without a large amount of samples. Also the components are defined and optimised with
respect to the sound pressure level frequency response SPL as the final target of the transducer.
In this Paper we want to show some of the special problems arising with FEM simulation of these
transducers. More specifically dealing with the problem of defining the material parameters.
Keywords
Loudspeaker, Material Parameter, Correlation, ANSYS MECHANICAL/EMAG,
20th CAD-FEM Users’ Meeting 2002 October 9-11, 2002
International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
on FEM Technology Friedrichshafen, Lake Constance, Germany
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2.4.3

1. Introduction
The investigation is done to an electrodynamic loudspeaker. (Fig. 1).
Figure 1:
electrodynamic loudspeaker
This speaker consists of the following main parts which are
• a vibrating mechanical structure (membrane, dust cup, voice coil, voice coil former, surround
and spider) which is clamped or glued to a basket (Fig. 2).
• a fixing structure (basket) (Fig. 3).
• a motor unit (Magnet structure) which is also fixed to the basket. (Fig. 4).
Figure 2: vibrat.structure
Figure 3: basket
Figure 4: motor unit
This structure is assembled that way that the voice coil, which is part of the vibrating structure, is
placed in the radial air gap of the permanent magnet structure.
The electrical signal is now transferred via Lorenzforces acting on the voice coil, due to the interaction
of the current in the voice coil and the Magnet field in the air gap of the magnet system. Thus an axial
movement (vibration) of the structure is created (electro dynamic interaction). The vibrating structure
(membrane) then creates air waves in the audio frequency range. (Fig. 1).
The FEM Simulation of this structure and of its parts has the target to create a constant sound
pressure level over the operating audio frequency range. Also the limitation of this vibration (motion) in
a defined manner and level is part of this simulations.
Denomination of certain parts of the vibrating structure (Fig. 5).
membran
surround
spider
Voice coil
Figure 5: vibrating structure
Dust cup
former
20th CAD-FEM Users’ Meeting 2002 October 9-11, 2002
International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
on FEM Technology Friedrichshafen, Lake Constance, Germany
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2. Simulation of electrodynamic Loudspeakers and their components
Some examples for this type of calculations are magnet calculations, none linear force excursion,
Force Factor Bl versus excursion calculation for magnet-voice coil configuration and frequency
response calculation for the complete loudspeaker.
• magnet simulation (optimisation) Fig. 6a,b
Flux Density B in the air gap
Created are Design spaces of geometric data versus the Flux Density B[T] in the air gap. The
variables to be optimised in this calculations, are iron part thicknesses, magnet material type
and dimension. Principle design space plots are
preferred versus single optimisation results (f.e.
random optimisation because of changing
optimisation target functions.
Figure 6a: magnet
• magnet simulation (large signal) Fig. 7a,b
Force Factor BL versus excursion x
Figure 6b: Design Space
The Designspace consists of the configuration type of magnet system and voice coil system. The
target is to design this excursion function of the
Force Factor Bl [ Tm] in a way that the distortion of
the transducer is minimised. Target function is
created by special large signal measurement
software.
Figure 7a:
• suspension simulation ( large signal )
Force versus excursion
Figure 7b: Bl vers. Excursion ( voice coil)
The Force – Excursion curve for the components (spider,surround) or the complete speaker, is
evaluated by a none linear calculation. The figure 8b show results for a spider and the variation of its
roll height. This allows geometric design
with respect to excursion limits. Fig. 8a,b
spider
Figure 8a:
Roll height
Figure 8b: Force-Excursion ( spider )
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
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• frequency response Topology Correlation
Sound Pressure Level (SPL) versus frequency
( dome tweeter ) Fig. 9a,b
The sound pressure frequency response is used two ways
- as a target function of an existing sample for material parameter definition
- optimisation for the geometric design data of the transducer.
In this example the frequency response curve for a dome tweeter is calculated from 8kHz up to 30kHz.
The results are used to determine the material parameters of the dome tweeter components by
correlation with the measured response.Sensitivity
analysis of the parameters allow to detect the
influence of the parameter on part of the response
curve and how it is typically changed.So certain
specifics of the frequency response should be
reproduced.
Figure 9a:
Figure 9b: Sound Pressure Level (SPL)
frequency response
3. Special requirements of an acoustic frequency response calculation
Now we want to look at certain specifics of calculating sound pressure level frequency response curve
by FEM simulation means with ANSYS/MECHANICAL.
What is of interest here are certain requirements concerning frequency calculation of the complete
loudspeaker over the audio frequency range.
3.1. Initial considerations
specifics on loudspeaker frequency response calculation should be considered here.
Initial considerations
• Axisymetric calculation in 2D
• Air space is reduced to 0.37 m
• Exact FEM modelling of geometry, wave guide, inner air spaces and glue is necessary
• sensitivity of the frequency response result is very high to geometric variations,
so the geometric data must be defined very exactly
• Results data of the FEM simulation ( Frequency resonse,basic resonance fo,excursion x ) are used
in different ways
to correlate with measured data of a sample to determine material parameters
to make design optimisation of geometric data in case the material parameters are defined.
The calculation is now performed as a harmonic calculation (Small Signal Domain)
20th CAD-FEM Users’ Meeting 2002 October 9-11, 2002
International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
on FEM Technology Friedrichshafen, Lake Constance, Germany
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3.2. special requirements of acoustic calculations
Specialities of a acoustic frequency response calculation
The specifics for such an acoustic calculations are
3.2.1 Frequency bandwidth is large
The frequency bandwidth for this transducers is very high . Fig. 10
• The frequency bandwidth covers the whole
audio bandwidth from 20 Hz to 20 kHz.
• Measured frequency range for the devices
is 0 Hz up to 30 kHz.
3.2.2 multi physic coupling
SPL
20 Hz
8 kHz
30 000 Hz
Figure 10: frequency response bandwidth
f [Hz]
There is a series of energy conversion from electrical signal to the final sound pressure wave in air.
Fig. 10
Sound Pressure Level SPL
• the fluid-structure coupling
the mechanical vibration creates an
acoustic pressure wave.
• the electrodynamic coupling
electrical signal is converted to
mechanical vibration of the structure.
3.2.3 number of DOF´s is extremely high
Figure 11: multi physic coupling
Lorenz Force F
the number of DOF´s becomes under certain conditions very high dependent on dimension and upper
frequency limit Fig.12a,b,c
• the main contribution due to air alements
• size of the elements is defined by upper bandwidth limit
Abbildung 12a:
structure
Elements : 906
DOF´s : 1812
Calc.time (25 frequ.) :
Figure 12b:
Structur+air space 0.375 m
Elements : 14040
DOF´s : 14946
Calc.time (25 frequ.) : 7 min
Figure 12c:
Structur+air space 0.375 m
Elements : 74646
DOF´s : 75552
Calc.time (25 frequ.) : -3 Std.
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
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3.2.4 difference of 2D and 3D calculation (radiating modes)
A 2D calculation is sufficient because only radial modes are contributing to the radiation. Only in
special cases a 3D calculation is necessary (Oval transducers,
asymmetric overlap of glued parts,etc,). High amount of elements
and thus an extended calculation time is achieved by solving a
3D Problem and keeping the resolution at the measurement point
the same as in the 2D axisymetric case. Fig. 13a,b,c
Figure 13a:
Structur+air space 0.375 m
Elements : 14040
DOF´s : 14946
Calc.time (25 frequ.) : 7 min
3.2.5 material parameters are frequency dependent
Figure 13b:
Structur+air space 0.375 m
Elements : 560.000
DOF´s : 560.000
Calc.time (25 frequ.) : -8 days
Figure 13c:
Structur+air space 0.375 m
Elements : 74646
DOF´s : 75552
Calc.time (25 frequ.) : -3 hours.
Material Parameters for most materials (paper,polymers, glues) are frequency dependent over this
extended frequency range.Measurements have been
done on this area and show a clear dependency on
E-Module
frequency and temperature over the audio frequency
range.
5 °C
• Measurements on Polyvinylchlorid results from
Becker and Oberst are shown in Fig. 14. [1] [2]
• The frequency range is from 10 Hz to 10 kHz
• The temperature range from 5 °C to 120 °C
• The Module is changing from 1.0e7 Pa to 5.0e9 Pa.
3.2.6 to measure frequency parameter
120 °C
Figure 14: E-Module of Polyvinylchlorid
Most available material parameter measurement tools are only for static measurements. The
consequence is for the determination of material parameters values at higher frequencies there is a
need to relay on correlation with result values ( frequency response, etc).
• measurement technique frequency range temperature range
• Push/Pull measurement 0Hz -40-300 °C
• Rotary-vibrating measurement 2Hz -40-300 °C
( Dreh/Schwingversuch )
• DMTA Dynamic Mechanical Thermal Analysis 1 - 200Hz -40-300 °C
• Modal Analysis measurement (by Laser) 1Hz - 5kHz -40-300 °C
Modal Correlation Software (LMS,IDEAS)
• Special Rotary-Vibration measurement 1Hz – 5 kHz -40-300 °C
( Mastering Technique ) 1Hz – 10 kHz -40-300 °C
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
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3.2.7 Material parameter correlation
For the entire frequency range correlation’s with result values like frequency response are the only
way to determine material parameter values. In the case of the frequency response the correlation is
done reproducing the special characteristics of the response curve. If there are none then samples are
created with different configuration (shapes, wave guide, etc ) or reduced amount of materials.
There are certain categories ( force-excursion, resonances, response curve) used for correlation
• correlation measurement component frequency range
• static force-excursion measurement surround/spider 0 Hz
• static force-3D deformation measurement cone 0 Hz
• Basic resonance measurement surround/spider 50 Hz – 2 kHz
• surround resonance Measurement surround 1 kHz
• cone resonance measurement cone 15 kHz
• Frequency response of SPL (Topology) loudspeaker 10 Hz – 30 kHz
• consistent multi response correlation loudspeaker 10 Hz – 30 kHz
• general sensitivity analysis
• special samples with reduced amount of materials
3.2.8 large amount of materials
The loudspeaker consists of a large amount of materials which are connected to each other. Mostly
These parts are glued but there is also the possibility of clamping. They all interact creating the
frequency response curve.
So only those parameter formulations (damping models) are available which can be assigned to a lot
of materials (material dependent damping ß i).
• minimum 2 materials
( membrane, glue)
• maximum up to 14 materials
3.2.9 restriction on material models to be used (due to large amount of materials)
Only those parameter formulations are available in ANSYS/MECHANICAL which can be assigned to a
lot of materials ( material dependent damping ß i )
• large amount of materials
• only certain damping mechanisms
can be used (material dependent
ß damping and element damping)
• parameter of the damping model
is used as adjustment parameter Figure 16: damping mechanisms in ANSYS
in an energetic view.
Global mass damping
element damping
3.2.10 MACRO in APDL
Global structural damping Global constant damping
Material depending structural damping
To incorporate these aspects into the calculation and using frequency dependent material parameters
an external Macro in APDL is created for these calculations.
This external Macro in APDL allows to formulate the material parameters as frequency dependent
functions as well as to use simply material dependent constant damping.
Iteration process of external macro (Ansys APDL language)
allows for
- application of material parameter functions (redefining and remeshing)
- constant damping ratio for different materials
- to choose linear or logarithmic frequency spacing
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
on FEM Technology Friedrichshafen, Lake Constance, Germany
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4. Examples
We want to go into details showing 2 examples of determining material parameters by correlation.
4.1. material parameter correlation of cone membrane
In this example the frequency dependent material parameter of different paper cones is determined by
use of correlation.
• Theoretical response curve known from
measurements. [1] [2]
( see point 4.1.1 )
• in the static case correlation with force-excursion
measurements are performed (3D deformation of
cone )
( see point 4.1.2 )
• In the upper frequency range 3kHz to 10 kHz
resonances of the cone are used for correlation.
( in this frequency range the cone does not vibrate
as a rigid poston – cone break up region )
( see point 4.1.3 )
4.1.1 theoretical response curve
Theoretic response curve from measurements
by Becker and Oberst on Polyvinylchlorid [1] [2]
Fig. 17
The absolute values of the E-module function depends
on the softening temperature of the material used.
In principle there is a continuos raising function with
temperature.
4.1.2 static case force-excursion correlation
2.
Cone res. 3.
1.
Force-excurs. theory
Figure 16: frequ.depending E of paper cone
Abbildung 17: E-Module Polyvinylchlorid
In the static case correlation with force-excursion measurements are performed.(3D deformation of
cone Fig. 18a,b,c,d
• in the static case the Youngs modulus E is determined by correlation with force-excursion
measurements
• this correlation is a replacement for static push/pull measurement done with special tailored, flat
samples.
• the advantage of the correlation is that the initial sample is used.
Figure 18a:
measurement
Figure 18b:
modelling
Figure 18c:
simulation
Figure 18d: correlation
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
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4.1.3 dynamic case cone resonance correlation
The definition of the cone material parameter in the dynamic case at higher frequencies ( 3 kHz to 10
kHz )is done by correlation with cone resonances. For this case a special sample is created with
removed surround and the dust cup replaced by a massive part. So the relevant materials remained
are the cone and the glue to the voice coil. In this upper frequency range the cone does not vibrate as
a rigid piston. So a multitude of resonances are created ( cone break up modes ). Fig. 19a,b
No surround.
Figure 19a:
special sample loudspeaker
(with no surround )
4.1.3 comparison with DMTA measurement
Figure 19b: cone resonances
Comparison of the correlation results(Fig. 20a) of two cone paper materials with DMTA measurements
Fig. 20b show a clear correspondence of the static values (0Hz or 1Hz) at a temperature of 27 °C.
Also the tendency of the frequency dependency towards higher frequency is represented in a
corresponding behaviour towards low temperatures in the DMTA measurement.
1.01 GPa
0.56 GPa
Figure 20a:
Determine E-Modulus by correlation
2.9 GPa 2.2 GPa
4.2. dome tweeter frequency response calculation
0.95 GPa
0.54 GPa
Figure 20b:
DMTA measurement of E-modulus at 1Hz
Dome Tweeter loudspeaker for high frequency reproduction require a very exact modelling due to the
fact that the sound pressure frequency response SPL shows high sensitivity concerning a variation of
geometric data.
Two procedures are possible either to use one frequency response and detect the frequency range
where the specific parameter acts upon or to use multiple sample type results using the same
materials (consistent set type of parameter).
4.1.3 Single frequency response topology
sensitivity analysis of material parameters
on the frequency response. Fig. 21a,b
Figure 11a: dome
Figure 21b: single frequency
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International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
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4.2.2 multi frequency response topology
Sensitivity analysis of material parameter on a multitude of frequency responses of different sample
types using the same materials. The changed geometry shapes of the dome membrane and the
changed acoustic wave guide in front of the transducer create a completely different frequency
response behaviour. The effects of the material parameters on those responses is also different.These
different target response curves allow to identify the correct set of parameters
Tweeter with wave guide 1. Fig. 22a,b
Tweeter with wave guide 2. Fig. 23a,b
Tweeter without wave guide. Fig. 24a,b
Conclusions
Figure 22a:
Figure 23a:
Figure 24a:
Figure 22b:
Figure 23b:
Figure 24b:
The Problems arising with the design of Loudspeakers can be solved with Ansys FEM simulations.
Also the specific formulations of frequency dependent material parameters can be implemented in
Ansys to adapt to the requirements of loudspeaker Simulations.
The definition and correlation of material parameters is the most time consuming part of the
simulations. Once these parameters are defined the performance of the loudspeaker, the geometric
design, the material choice, tolerance considerations, the weight and the related costs could be
optimised (minimised).
This is a much more time saving and cost optimised procedure of adoption to the required
performance than to build a huge amount of samples.
References
[1] Becker G.W., Oberst H..: "Frequency dependent material parameter of Polyvinylchlorid”,Kolloid
Zeitschrift 148, 1956, pp. 6
[2] Cremer L., Heckel M.: "Körperschall", Springer Verlag, 1996, pp 224
20th CAD-FEM Users’ Meeting 2002 October 9-11, 2002
International Congress Kultur- und Congress Centrum Graf-Zeppelin-Haus,
on FEM Technology Friedrichshafen, Lake Constance, Germany
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