Design of Multifunctional Body Panels in Automotive Applications CHRISTOPHER J. CAMERON Licentiate Thesis

Design of Multifunctional Body Panels in Automotive Applications CHRISTOPHER J. CAMERON Licentiate Thesis
Design of Multifunctional Body Panels in
Automotive Applications
Reducing the Ecological and Economical footprint of the vehicle industry
CHRISTOPHER J. CAMERON
Licentiate Thesis
Stockholm, Sweden 2009
TRITA-AVE2009-30
ISSN 1651-7660
ISBN 978-91-7415-362-0
KTH School of Engineering Sciences
SE-100 44 Stockholm
SWEDEN
Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till
offentlig granskning för avläggande av teknologie licentiatssexamen i lättkonstruktioner
Måndagen den 8 juni 2009, klockan 13.15 i sal D3, Kungliga Tekniska Högskolan, Lindstedtsvägen 5, Stockholm.
c Christopher J. Cameron, May 2009
Tryck: Universitetsservice US-AB
iii
Abstract
Over the past century, the automobile has become an integral part of modern industrialized society. Consumer demands, regulatory legislation, and the corporate need to
generate a profit, have been the most influential factors in driving forward the evolution of the automobile. As the comfort, safety, and reliability of the automobile have
increased, so has its complexity, and most definitely its mass.
The work within this thesis addresses the twofold problem of economy and ecology
with respect to sustainable development of automobiles. Specifically, the conflicting problems of reducing weight, and maintaining or improving noise, vibration, and
harshness behaviour are addressed. Potential solutions to these problems must also be
executable at the same, or preferably lower production costs. The hypothesis is that by
replacing acoustic treatments, aesthetic details, and complex systems of structural components both on the interior and exterior of the vehicle with a single multi-functional
body panel, functionality can be retained at a reduced mass (i.e. reduced consumption
of raw materials) and reduced fiscal cost.
A case study is performed focusing on the roof structure of a production vehicle. Full
vehicle and component level acoustic testing is performed to acquire acoustic functional requirements. Vibro-mechanical testing at the component level is performed
to acquire structural functional requirements complimentary to those in the vehicles
design specifications. Finite element modelling and analysis is employed to create
a model representative of the as-tested component and evaluate its acoustic and mechanical behaviour numerically. Results of numerical simulations are compared with
the measured results for both acoustic and mechanical response in order to verify the
model and firmly establish a set of acoustic and mechanical constraints for future work.
A new, multi-layered, multi-functional sandwich panel concept is proposed which replaces the outer sheet metal, damping treatments, transverse beams, and interior trim
of the existing structure. The new panel is weight optimized to a set of structural constraints and its acoustic properties are evaluated. Results show a significant reduction
in mass compared to the existing system with no degradation of the acoustic environment.
A discussion of the results is presented, as is a suggestion for future research.
v
Acknowledgements
The work presented in this thesis has been carried out within the centre for ECO2 Vehicle
Design at the Department of Aeronautical and Vehicle Engineering, KTH.
Funding is provided via Vinnova and industrial partners Saab Automobile AB, Bombardier
Transportation, and A2 Acoustics. The financial support of all parties is gratefully acknowledged.
I would like to thank Dr. Per Wennhage and Professor Peter Göransson, firstly for giving
me a chance at being a researcher, and secondly for all their help and advice thus far.
This project would of course not have been possible without the help of Saab Automobile
AB and more specifically, Mr. Sven Rahmqvist; thank you for your assistance an input. I
am also grateful for the assistance of Eva-Lotta Saloniemi Modin for helping with nastran
problems both large and small.
To Associate Professor Leping Feng for his assistance in performing measurements both
at Saab and MWL and in his assistance in post processing some of the results, I extend my
gratitude.
I cannot forget thank Professor Zenkert, the other senior members, my colleagues and our
lab engineers within the division of lightweight structures. Everyone there has at some
point helped me along the way. I have enjoyed working with all of you and look forward
to continuing to do so. To Mr. Kaufmann, thanks for, among other things, interesting
lunch box discussions and your knowledge of fine cheese. To Mr. Stig, a special thanks for
R
balancing out the office. What would the world be like without telemark skis and Apple
computers?
To my family, thank you for lending your support from all the way across the pond.
Last, but not least, to my biggest source of love, strength, and inspiration; Camilla. Without
you I never would have made it this far. Thank you.
Stockholm, May 2009
vi
As this thesis may be read outside of Sweden an explanation of the Swedish Licentiate degree may be necessary. An intermediate academic degree called Licentiate of Technology
can be obtained half-way between an MSc and a PhD. While less formal than a Doctoral
Dissertation, examination for the degree includes writing a thesis and a public thesis defence.
vii
Dissertation
This licentiate thesis is based on an introduction to the area of research and the following
appended papers:
Paper A
Christopher J. Cameron, Per Wennhage, and Peter Görannson. Prediction and Measurement of Noise and Vibration Behaviour of Trimmed Body Components at Mid-Frequencies,
Manuscript submitted for publication to Applied Acoustic, March 2009.
Paper B
Christopher J. Cameron, Per Wennhage, Peter Görannson and Sven Rahmqvist. StructuralAcoustic Design of a Multi-functional Sandwich Panel in an Automotive Application,
Manuscript submitted for publication to Journal of Sandwich Structures and Materials,
May 2009.
Contents
I Introduction
1
1
Background
3
2
Automotive Noise Vibration and Harshness
7
3
Sandwich Structures
14
4
Optimization
18
5
Summary of Work Performed and Discussion of Results
22
6
Future Work
35
Bibliography
36
II Appended papers
43
ix
Part I
Introduction
1
Introduction
3
1 Background
sustainable development noun (a) Economics: economic development which
can be sustained in the long term; (b) Ecology: utilization and development
of natural resources in ways which are compatible with the maintenance of
these resources, and with the conservation of the environment, for future generations.
The above definitions are taken from the Oxford English Dictionary, second addition [1]
Automotive History
The first production Model T, built by the Ford Motor company, was available to for sale to
the public on October 1st, 1908. The model T was a car that changed automotive history,
selling over 15 million vehicles over 22 years of production [2]. The model T was significant not because it was fast, quiet, or particularly comfortable, but because it was cheaper
than its competitors, mass produced, and could be repaired and maintained relatively easily.
Figure 1: The 1915 Ford Model T
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Christopher J. Cameron
One hundred years after the first Model T, the automobile has become a method of transportation completely integrated into the infrastructure of developed countries and of increasing importance to the worlds developing economies [3]. Two significant influences
on the development of the automobile have been the consumer and the regulating bodies.
The automotive consumer has come to expect, among other things, improvements in performance, reliability, comfort, and fuel economy with each new vehicle. Governmental
bodies around the world enforce safety and emission regulations like those of the UNECE
in Europe, and the FMVSS and CMVSS in North America. Vehicle manufacturers must
also generate a profit to both fund their research and development work as well as fulfil
responsibilities to their shareholders. In order to meet all the demands of the consumer,
fulfil the requirements of the regulatory bodies, and at the same time produce a net profit,
the automotive industry is in a constant state of change.
Modern Vehicles
Over the years, consumer demand for options such as power windows, power steering,
heated seats, and in recent years complex information and entertainment systems has lead
to a steadily increasing number of components, and thus mass. The increasing electrification of vehicle systems leads to more wiring in vehicles, and increased demands on
power systems, in turn making them heavier. Safety improvements also lead to increases
in curb weight. Airbags and similar systems add mass directly while the contribution of
energy absorbing deformation zones is less obvious. As you increase the amount of mass
Figure 2: A SAAB 93 Sport Combi (image courtesy of SAAB Automobile)
in a vehicle, the basic laws of physics dictate that you must increase the amount of energy
necessary to move the vehicle. While modern combustion engines are much more efficient
than their predecessors, if the mass of the vehicle consistently increases, the efficiency and
power output of the engine must follow suit to obtain the same performance for the same
amount of fuel.
Looking at some unofficial data [4, 5] as presented in table 1, it is rather obvious that an
upward trend in vehicle mass exists. It should be stressed, that while data from vehicles
Introduction
5
Table 1: Unofficial Vehicle Curb Weights of Saab cars 1950-2008
Model Year
Model Name
1950-52
0956-58
0959-66
1966
1969-84
1976
1979-93
1984
1986
1985-98
1988
1999
2001
2004
2008
Saab 93
Saab 93
Saab 95
Saab 96v4
Saab 99
Saab 99EMS
Saab 900
Saab 900Turbo
Saab 9000i
Saab 9000
Saab 900i
Saab 9-3
Saab 9-3Viggen
Saab 9-3 1.8i
Saab 9-3
Curb Weight
805 kg
810 kg
905 kg
946 kg
955 kg
1161 kg
1174 kg
1340 kg
1280 kg
1302 kg
1285 kg
1305 kg
1438 kg
1440 kg
1400-1600 kg
produced by Saab has been used, it is by no means the only vehicle manufacturer where
this trend can be seen and it is rather doubtful that any vehicle manufacturer could produce figures showing the contrary. While advances in combustion engine technology have
been significant through the decades, the fact remains that emissions are still produced in
amounts directly related to the mass of the vehicle in question.
The ECO2 Factor
In the past decade, an increase in world wide media coverage of climate issues has lead to
an increased global awareness of the environment. International agreements like the Kyoto
Protocol, adopted in 1997, place binding targets on pollution emissions of industrialized
countries [6]. In October 2007, former United States vice-president Al Gore and the Intergovernmental Panel on Climate Change were awarded the Nobel Peace Prize for their
work with man-made climate change [7]. The magnitude of these occurrences emphasize
the increasing focus on the environment in recent years among governments of the world,
the scientific community and the general public. These issues effect the automotive industry both directly and indirectly; directly via regulatory bodies that create and enforce
more stringent environmental requirements, and indirectly via the very real demands of the
automotive consumer.
Within the automotive industry, there is a great interest to meet and exceed the demands
of the consumer and the governmental bodies in regards to all of their requirements. The
6
Christopher J. Cameron
complicating factor is however that this cannot be done at a fiscal loss to the company or at
a tremendous cost to the consumer, or the company (and possibly the consumer) will end
up bankrupt.
Methods of producing what the consumer wants at a price they are willing to pay which
fulfils or exceeds regulatory requirements are what the automotive industry is constantly
searching for. Taking into account the desires of both the consumer and the vehicle producer to eliminate excessive waste, avoid depletion of natural resources, and minimize the
impact of the vehicle on the environment and the resulting need becomes clear: methods
of sustainable development are required.
Sustainable development, with respect to both economics and ecology within the automotive industry are the core elements of the work within this thesis. Specifically, methods
of reducing weight, production cost, and production time of a passenger car whilst maintaining or exceeding engineering and consumer requirements and improving assembly ergonomics are examined. The methods proposed should have advantageous effects not only
on the immediate factors (such as weight) but on secondary factors (such as fuel economy,
styling, etc).
Specifically, noise vibration and harshness (NVH) criteria are investigated due to their
importance to the consumer and their sensitivity to reduced weight and increased stiffness
seen as necessary to achieve lighter, safer vehicles in the future.
Case Study
The work in this thesis examines the possibilities in reducing both ecological and economical footprints in vehicle production by combining the functionality of several traditionally
separate components into a single multi-functional part. In this particular case, the roof
system of a passenger car, from the interior trim to the exterior surface, is replaced by a
single multi-layer, multi-functional sandwich construction. The methodologies developed
attempt to fuse knowledge from several traditionally separate automotive disciplines into a
singular toolbox for use with generic automotive design problems.
Introduction
7
2 Automotive Noise Vibration and
Harshness
Noise Vibration and Harshness
Noise, Vibration and Harshness, more commonly known as NVH, is an all encompassing
engineering discipline that deals with the objective and subjective structural dynamic and
acoustic aspects of automobile design. The NVH engineer is interested in the structural
dynamic response of the vehicle from the complete assembled system down to the normal
modes of the individual components. As a vehicle is a moving dynamic system, its response to stochastic, time varying inputs is important for safety, quality, and comfort of the
passengers.
One specific area of study within NVH is vehicle acoustics. Sound plays an important part
in the development of a motor vehicle. Certain aspects of noise produced by a vehicle
are controlled by governmental regulations, for example pass-by sound levels or exhaust
sound emission[8]. Other aspects of sound are controlled specifically within the individual
company as a method of quality control. Meeting the constantly increasing, and complex
needs of the consumer is also a key concern of the NVH program for any vehicle and
deserves some specific attention.
Psychoacoustics in NVH
When a customer is deciding which vehicle to purchase, the overall quality of the vehicle
is an important factor. This applies not only to the fit and finish of the bodywork, or the
upholstery in the interior, but also to the sound and vibration behaviour of the car. Whether
on an active or more subconscious level, customers pay attention to the sound quality
of a vehicle, and it is an important by-product of design. Noise and vibration can have
both positive and negative attributes; an irritating sound may cause the driver to become
distracted, but engine noise and drivetrain vibration provide feedback on the operation of
the vehicle. In addition the image of the brand can be effectively transmitted by the sound
produced by the powertrain.
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Christopher J. Cameron
For a vehicle model to sell well, it is highly desirable to maximize the positive response
and minimize the negative response to a given acoustic stimulus for a population of potential customers. The interpretation of what is positive and negative sounding to a customer
is however a complex relationship. Studies have shown that the two similar sounding
statements "This sound is annoying." and "I am annoyed by this sound." can have vastly
different effects on the customers emotional state [9]. Objective NVH evaluation is difficult, if not impossible due to the unpredictability of the human senses. Genuit and Fiebig
[10] showed that in a laboratory environment, visual stimulus can affect a persons interpretation of a vibrational or auditory stimulus. Terminology such as loudness, sharpness,
roughness, fluctuation, strength and tonality are required within NVH to describe the quality of sound within a vehicle. The fact that perception and interpretation of a given noise
varies between individuals and that a great deal of training is necessary to be a consistent
and accurate at assessing noise, i.e. linking terminology to perception, is an ongoing problem within automotive NVH [11]. A great deal of work has been done attempting to link
objective tests and subjective evaluations of sound and vibration. Attempts have been made
to create standardized acoustic comfort scales using automated recording and evaluation
methods [12], however at the present, it seems that the state of the art is not capable of
emulating the human factor in the NVH equation.
The Physical Phenomena of NVH
NVH in passenger cars can be divided into two categories of interest [13].
• Noise: Audible sound in the frequency range 30-4000 Hz
• Vibration: Tactile vibration in the frequency range 30-200Hz
The three main contributors to interior noise are the engine and accessories, tyre/road interaction, and airflow over the external bodywork (wind noise) [14].
In a typical welded metallic body in white (BIW), noise transmission into the interior can
occur along two distinctly different transfer paths; via airborne waves, or structure borne
vibration.
Airborne Sound
Airborne sound often originates from external sources and propagates into the vehicle interior via holes in the bodywork, door seals, weld seams, etc [13]. Airborne sound propagation is predominantly in the higher frequency ranges. 80% of noise above 1000Hz is
airborne in nature [15].
Controlling airborne sound can be done by eliminating the source of the sound (if possible), or eliminating the transfer paths into the vehicle. Increased sound pressure follows
Introduction
9
the path of least resistance, and commonplace solutions such as acoustic baffles, urethane
filler foams, rubber plugs and grommets, and adhesive seam sealants are used to impede an
airborne sound propagating into the passenger compartment [15]. The implementation of
these sorts of solutions rely heavily on testing, and experience of the engineers involved.
For sound inside the compartment the absorption provided by soft, open structured materials can also be used to control high frequency airborne sound, this mechanism will be
discussed in more detail in the section entitled "Porous Materials in acoustics".
Structure Borne Sound
Within a vehicles interior, 85% of noise under 500 Hz can be classified as structure borne
sound [14]. Simply stated, structure borne sound is the result of mechanical vibrations
causing localized displacements of air. Sound levels due to vibration can be directly related
to the volume of air which is displaced. A 1 cm3 volume displacement, which could be
achieved by a 1 m2 area of roof vibrating with a displacement amplitude of 1 µm, can
cause a sound pressure of 75 dB in a vehicle interior [16]. Much of the noise in the
frequency range up to 500 Hz is caused by cavity resonances which may be excited by
vibrations of the body in white (BIW) caused by suspension or drivetrain inputs. The term
booming noise is often used to describe acoustic phenomena in the frequency range below
250 Hz [17]. Body vibration levels are directly related to the road roughness, vehicle speed,
suspension design etc. For a more complete explanation of the phenomena of structure
borne noise in general, the interested reader is directed to [18].
Control of structure borne sound is primarily done by altering stiffness and damping characteristics of the vehicle structure or isolating a source from a receiving point. Structural
stiffening may be applicable if vibrations are forced, damping when resonant vibration is
the dominant issue, and isolation is useful where strong transmission paths exist and both
source and receivers are stiff [19]. Stiffness is controlled by sheet metal thicknesses, geometry, weld points, etc. Damping, while also greatly affected by the joining method used,
is primarily achieved using viscoelastic damping treatments. Constrained layer, free layer,
and tuned viscoelastic dampers are often used on large panel surfaces, such as roofs, floors,
doors, etc, to reduce vibration levels. The use of viscoelastic damping materials in the automotive industry is well documented [20] and experimental work to determine their size
and placement, such as performed in [19, 21], is commonplace. Isolation is often used in
motor and suspension mount design.
Computational Methods in Acoustics
Historically, NVH has been a manpower intensive process of "test-analyze-fix" [22]. Vehicle refinement often takes place in the final stages of production when designs are fixed and
solutions to acoustic problems are far from ideal. In recent times, NVH has been making a
progressive transition to computational methods and is taking a more preventative role in
vehicle design.
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Christopher J. Cameron
Over the past 40 years, much work has been done attempting to predict internal noise in
vehicles, primarily focussing on the frequency range 50-200Hz. This is the range where
structure borne noise is dominant within the vehicle. A summary of this work can be found
in [14]. Finite element analysis is the predominant method of choice within this frequency
range. This is also the method primarily used within the work in this thesis. Other methods,
such as statistical energy analysis (SEA) will not be discussed here.
One of the primary limiting factors in implementing FE in NVH analysis, has been the
modelling of the interior treatments. Structural models are considered reliable and can be
used, for example, to locate possible locations for surface damping treatments [23]. Capturing the frequency and temperature dependant damping properties of viscoelastic materials such as anti-flutter adhesives is however a more complicated matter which requires a
rigorous testing program to evaluate the material [24]. While some tools and methods exist
to simplify the validation of FE models with experimental results, the process is costly and
time consuming and generally involves a lot of adjusting of the model to fit the test results
[25].
A confounding factor in NVH analysis is the presence and influence of air. Unless testing is performed in the absence of air (i.e. in vacuum), the fluid surrounding a vibrating
component will provide a certain amount of vibrational damping. The fluids effect on the
global structural behaviour is often considered minimal, however in the case of resonant
modes within the fluid cavity, this is not necessarily true. Accurate detailed modelling
of the fluid cavity in the passenger compartment is not always performed, and for a large
number of NVH calculations, the fluid is excluded from the calculations to limit calculation
time. While computational methods like automated multi-level substructuring (AMLS) can
greatly reduce the calculation time [26], achieving sufficient model fidelity to represent the
phenomena at hand at the frequency at hand is always a problem. References [16, 27] give
a rather detailed discussion of the subject matter which can be recommended to the interested reader. In linking the structural model to the acoustic media, the current state of the
art utilities automated search algorithms to link structural elements to surround fluid elements [28, 29]. The control of these algorithms is not always simple and straightforward,
and a degree of user skill is required in order to achieve the desired coupling and avoid
unwanted coupling.
In a coupled fluid-structure problem, not only is the frequency of a resonant mode important, but also the phase. While a BIW may be capable of exceeding a given requirement,
say the frequency of the first global bending mode, it is also necessary that mode shapes
and phase of components of the BIW are of a certain nature. If for example, the roof
and floor vibrate in a first panel mode out of phase (i.e. the "breathing" mode), there will
likely be a problem with booming noise due to the compression of the fluid cavity. If
the same vibration mode occurred in phase, the air compression may be minimal and no
booming noise would occur. This sort of behaviour makes it important to understand the
entire system, however the limitation in computational efficacy has meant that while full
BIW analysis is possible, and in fact performed, full vehicle NVH analysis is still under
development.
Introduction
11
NVH engineering is very much a refinement process, and physical testing relies on the
production of prototypes which can be very expensive. While computational methods
can be used at any time in the design process, they often rely on a complete model being
available for analysis. This is often due to the fact that global NVH behavior is significantly
difficult to downward cascade to the component level [22]. While computer models are
typically less expensive to produce than prototypes, waiting for a complete model of the
vehicle until the final stages of pre-production means that a large number of the designs
are fixed, and numerical analysis is implemented as a tool for "virtual firefighting" rather
than for prediction and problem avoidance. The advantages of being able to use numerical
methods from the beginning of the product cycle have been observed by many researchers
and NVH engineers [30], restrictions in hardware, software, and a lack of methodology are
the major restrictions at the moment.
Vibration and Acoustics in production vehicles
Often, NVH engineers strive to find an ideal solution for an acoustic or vibrational problem
within a vehicle. Whether that solution is obtained by an intensive test scheme utilizing
prototypes, or production vehicles, or whether the use of numerical methods is highly integrated, a common difficulty remains; namely the stochastic nature of NVH in production
vehicles.
In recent years, several studies of large populations of production vehicles have been performed [31, 32, 33]. Results for these studies show the significant impact of minor differences in production on structural and acoustic NVH behaviour. Fluctuations in structural
and acoustic frequency response functions may vary from 1 or 2 dB, up to 15-20dB, even
for vehicles which should be identical [31]. These variations are not likely to be caused
by some fault in the assembly process, i.e "lemon" examples, as few vehicles will deviate
consistently from the mean population across the full frequency spectrum of measurement
[32]. Instead, the variation in sound and vibration behaviour is attributed to a chain of
very minor deviations within the assembly process whose sum is greater than the parts.
Changes in such items as trim details, seat fabric, or carpeting will have a direct effect on
the interior sound quality. For this reason, it remains a problem that any ideal solution
arrived at with the help of physical or numerical experiments, will in fact be adjusted to fit
exactly the prototype or model in question, and may be over, under, or poorly designed for
the remaining vehicles within the population. While some effort has been made into developing a more statistical based approach to predicting NVH behaviour [33], their exists
no complete solution at the current point in time.
Balancing Computation with Experiment
In the previous two sections, a description of the current limitations regarding computational methods of evaluating vehicle NVH experimentally have been given.
12
Christopher J. Cameron
Difficulties in modelling the exact phenomena which occur in reality have been described.
Finite element analysis is, in essence, solving a system of equations and so for the vast
majority of finite element problems (exceptions such as buckling phenomena occur) there
exists only one solution; i.e. it is a deterministic method. Arguably, it is not possible to
recreate an exact replica of a phenomena observed in reality using a mathematical model
as it will always include some sort of limiting simplification.
Regarding the experimental evaluation of NVH, it has been shown in the literature, and
is a rather well known fact in industry, that the measurement of acoustic and vibrational
characteristics of a vehicle can vary significantly even among vehicles which are identically
constructed. Variation depends on manufacturing tolerances and environmental conditions,
among a great many other things, but even the engineer performing the measurement is a
variable. It has been argued that the exact same measurement performed under the exact
same conditions by two different engineers would be different, if only subtly so.
This brings up the questions of what is it that FE should be used for in an NVH perspective? This is an interesting topic which has been discussed by, among others, Gartmeier
[34, 34]. If the population of vehicles being produced can vary significantly in their NVH
characteristics, what then is the purpose in attempting to duplicate the exact response of
a single arbitrary example from the population? Finite element models, especially in the
early stages of development, are capable of quickly establishing global characteristics for
a new design, however while vast quantities of time and money might be spent on model
refinement to mimic a given sample, the capabilities of that model in predicting the behaviour for the majority of the population may or may not be improved. The suitability of
an experimentally obtained solution on a single vehicle may also be questionable for the
other vehicles in production. Finite element analysis is an effective tool in NVH analysis,
however the question of resource investment on refining and improving a model to represent an experimental "reality", which is in fact only one member in a statistically varying
population should be asked. While the validation of mathematical models is essential, in an
area such as vehicle NVH which involves a great deal of uncertainty, especially involving
the human perception factor, perhaps "close" should be considered "good enough".
Porous Materials in Acoustics
Porous materials such as polymer foams, or fibre insulation, are capable of absorbing sound
by converting the energy present in a sound wave into heat energy. The exact mechanism
of the conversion process depends upon the geometry of the porous material as well as the
frequency in question. The exact mechanisms of this absorption will not be discussed in
detail within this work, and instead the reader is directed to [35].
Porous materials can be classified as a passive means of noise control. The efficacy of
passive noise control is greatest at higher frequencies, perhaps in the region of 1000 3000 Hz [36], however they are still capable of providing significant noise reduction(i.e.
greater than 10dB) above 125 Hz. Many modern cellular foams are created from polymeric
Introduction
13
materials by the use of chemical blowing agents [37] and it is possible to vary the size and
geometry of their cellular construction. Altering the size and cell type of foams affects
their acoustic properties [38], as well as combining layers of different kinds. Historically,
the effectiveness of a given foam or combination of foams at absorbing sound energy has
been measured experimentally, as for example in [39].
Within the work in this thesis, numerical methods are used to model the elasto-acoustic
properties of porous solids in an NVH application. Calculations are performed using commercially available numerical codes [40] in addition to in-house hierarchical finite element
solvers. The exact models used are explained in [41, 42, 43, 44] and are not included here.
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Christopher J. Cameron
3 Sandwich Structures
The Basic Sandwich Structure
A structural sandwich, in its most basic form consists of two stiff, strong and thin sheets
bonded to either side of a relatively thick, weaker, lightweight core material. Figure 3
shows a schematic drawing of a basic sandwich structure.
Figure 3: A basic sandwich construction
The most common face sheet materials in structural sandwich components are metals or
fibre reinforced plastics. Common core materials are expanded foams of PVC, PET, or
other plastics, honeycombs of aluminium or resin infused paper (Nomex), or balsa wood.
The face sheet layers in a sandwich structure carry applied bending loads and moments as
tensile and compressive stresses while the core material carries transverse loading predominantly as shear [45].
A monolithic construction of unit width and thickness t, as depicted by the uppermost
beam in figure 4, will have a certain stiffness in bending which can be normalized as 1.
In sandwich terminology, this bending stiffness is also called flexural rigidity. By splitting
thickness t and separating the two halves with a lightweight core material, the bending
stiffness can be increased without greatly increasing the weight. By the same method that
the stiffness is increased, so is the bending strength of the sandwich, i.e. the loading level
at which failure in bending will occur. The relative increase of flexural rigidity and bending
Sandwich Structures
Introduction
15
The Sandwich Effect
Weight Flex.Rigidity
Bending Strength
1
1
1
~1
12
6
~1
1
48
12
t
t/2
2t
t/2
4t
Figure 4: The sandwich effect (courtesy of Zenkert)[45]
strength is shown for a two fold and four fold increase of sandwich thickness for the same
thickness of face sheet material t in figure 4. Core material is assumed to be of a much
lower density than face sheet, and thus the additional mass does not contribute significantly
to the mass of the construction.
The deformation of sandwich structures is not only controlled by the bending stiffness, but
also by the shear effects. As face sheets are usually quite thin, they present little resistance
to bending moments; at the same time core materials are relatively weak and can relatively
easily be deformed by in-plane and out-of-plane stresses due to the applied loads. Shear
stresses and deformations, usually ignored in problems where monolithic structures are
subjected to bending loads, contribute considerable to the response of a sandwich structure
subject to the same loading scenario. In the bending of sandwich beams, the contribution
of both pure bending and shear deformation must be accounted for. As mentioned in
[45], the effects of these shear deformations are not always obvious, and may surprise the
inexperienced analyst.
Applications of Sandwich Structures
Stiffness in bending is only one aspect of what a sandwich panel can provide. By varying
the face sheet material and the core material properties, characteristics such as sound absorbance, damping , corrosion resistance, recycle-ability, density, and sensitivity to out-ofplane loading, to name a few, can be altered to suit the desired application. The sandwich
construction offers a great deal of flexibility in design for a minimized weight penalty.
Despite their many advantages, sandwich constructions are not infallible, and not necessarily always the correct choice for certain applications. Sandwich structures in general are
poorly suited to concentrated out of plane loading which can lead to core or face material
failure and failure of the structure. To an engineer working with sandwich construction,
phenomena such as face sheet buckling, global buckling, core shear failure, face sheet delamination, and adhesive layer failure must be understood to construct a robust structure.
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Christopher J. Cameron
Special design consideration must be taken when introducing loads into a sandwich structure or when creating a joint between two sandwich panels due to stress concentrations an
other effects [46].
The aforementioned points need not prohibit the use of a sandwich structure in a given
design, but are given to emphasize the necessity of detailed knowledge of the subject matter
by the design engineer. For further explanation, the interested reader is directed to [45],
the primary resource for sandwich information used within this work (and for a great many
sandwich structure engineers!).
Sandwich Structures in the Automotive Industry
While a great deal of literature on sandwich structures describes the potential for their use
within vehicles and development of tools to ease their implementation has been ongoing
since at least the mid 1980’s [47], the use of pressed and spot/laser welded steel structures is
still the praxis within the automotive industry. Very little published work exists describing
full scale mass production of automobiles which use sandwich structures as load bearing
or structural components. The primary reason for this, according to the literature, is cost;
should a new material be used to replace an old, its entire cost including raw material,
manufacture, design, and development must be less than that of the material is should
replace [48]. While the raw material costs of sandwich structures are generally higher
than their steel equivalents, this is not the major cost which has prevented the full scale
implementation of sandwich structures in automotive production.
Computational simulation is heavily relied upon to predict and optimize high and low speed
impact behaviour of vehicles to meet stringent government safety requirements on frontal
and side impact, and rollover (among other things) [49, 50, 51]. Modelling techniques
and material models for use with metallic construction have been developed over decades
and are tested and reliable. The same cannot be said of the modelling methods of typical
sandwich structures in crash. Even the simplest sandwich construction using a metallic
face sheet and a polymer foam core becomes a very complex problem when attempting to
predict face-core de-bonding, or buckling phenomena, particularly when dynamic loading
is involved. Experimental methods are often necessary to asses the crashworthiness of
sandwich structures [52]. As the current state of the art in finite element analysis is not
capable of consistently predicting the crash behaviour of sandwich structures, increased
use of sandwich structures in the automotive industry would necessitate an increase in
prototype based crash tests for development and validation. While in the long term, this
would no doubt lead to a better understanding of the behaviour of sandwich structures in
impact, and much improved modelling techniques, in the near term it would be a substantial
cost.
Manufacturing costs are also of interest. Existing methods for sandwich construction usually involve much lower rates of production and are significantly less automated than those
used in the automotive industry. On the other hand, the cost of high quality tooling for a
Introduction
17
composite based sandwich structures is a fraction of that for high quality steel stamping
tools. The lowered cost of tooling offers added benefit with respect to styling; as tooling costs less, it may be switched out more often and changes in design can be achieved
quickly. Using conventional methods of production, the only possible way to achieve the
production rates necessary would be to introduce more production stations. Determining at
which point the balance between production rate, tooling/material/personnel cost, and production area requirements/costs exist is beyond the scope of this thesis, but is an interesting
area of speculation. New methods of production are being developed which show promise
[53], and it is likely only a question of time and resources before satisfactory production
rates and levels of automation sufficient for the automotive industry are achievable. Sandwich constructions also have the potential to eliminate problems of corrosion and increase
the lifetime of components, provided they are designed and manufactured correctly. While
this may be of questionable interest to the vehicle manufacturer, as they wish to sell more
vehicles, the interest of the consumer in a product that is more durable and has a longer
lifetime may be worth more so as to compensate for the reduced sale in new vehicles; this
is however purely speculation at this point in time. In 1995, when the use of aluminium
and magnesium was becoming increasingly popular for automotive applications, a cost per
kilogram weight reduction of less than $2 U.S. was required for a new material to have a
good chance of being implemented in a new design [48]. While it is unknown at the moment how that figure has changed since, the influence of environmental costs has no doubt
contributed to its increase. Already we are seeing that the significant use of composite
materials and sandwich structures is possible in automotive applications, even if they are
somewhat extreme in nature [54]. The question remains as to how long it will take until
this technology becomes accepted, or even encouraged in more mainstream automotive
engineering. The potential for the technology to yield solutions for the industry is perhaps
only limited by the possibilities of the industry to provide solutions for the technology.
Time, and money it seems, will determine what happens next.
18
Christopher J. Cameron
4 Optimization
Basic Optimization Theory
Optimization,within the context of this thesis, refers to an iterative process in which an
equation or set of equations is solved to minimize a certain quantity most often with a set
of mathematical constraints placed on the unknown variables. The basis for successfully
solving an optimization problem is a well described mathematical expression of the quantity to be optimized, commonly known as the objective function. One or more unknowns,
called design variables, must be given which are allowed to be altered by the optimization algorithm to achieve a best possible value of the objective function. Constraints are
envelopes within which certain parameters are valid, such as the values of the design variables or a result from a calculation. Equation 4 shows a basic optimization problem where
f (x) is the objective function, x1 and x2 are the design variables, and the inequalities for
G(x) represent the constraints.
minimize
f (x) = x1 + x2
subject to:
G(x1 ) ≥ a
G(x2 ) ≥ b
(1)
Each iterative loop in an optimization should yield an improved value of the objective
function, and valid values of the parameters on which constraints are placed. For a detailed
explanation in optimization theory, the interested reader is directed to [55].
Computational Structural Optimization
Structural optimization can, generally speaking, be broken into three separate categories:
size optimization, shape optimization , and topology optimization [56]. In size optimization, dimensions of the various components are used as design variables, for example sheet
metal thickness. Shape optimization alters the geometric boundaries of the structure to
Introduction
19
achieve an optimized solution. Topology optimization uses the presence or absence of
material at a given point as the design variable to achieve an optimized configuration.
The case study in the work performed in this thesis can be classified as a shape optimization
with several design variables and a single objective function. A component of sandwich
construction is to be designed which shall be as light as possible but must uphold a certain
level of performance. The objective function for this problem is the weight of the panel.
Thickness of the individual layers of the panel are the design variables. Constraints are
placed on the optimization by limiting deformation under load and the frequencies of the
normal modes of vibrations. The problem is a twofold numerical problem, finite element
analysis calculations provide input to the numerical algorithm for the iterative optimization
loop.
The first step in solving a given optimization problem is to select a suitable algorithm. The
choice of algorithm will depend on the type of problem at hand, the number of design
variables, the nature of the objective function, and the computational cost involved with
each. For a single variable objective function with a continuous derivative, gradient based
methods may be the most optimal. If the objective function is highly stochastic, has discontinuous derivatives, or is a multi-objective function, different algorithms may be necessary
or prudent for computational efficiency. In 2008, Duddeck [57] performed an evaluation of
a number of optimization algorithms for multi-objective design optimization within the automotive industry. Conclusions of this evaluation were rather simple; for linear problems,
like basic NVH global stiffness and normal mode problems, gradient based methods are
effective. More complex problems, especially those with multi-criteria objective functions
require optimization schemes more capable of finding a global, rather than local optima.
While algorithm efficiency is important, the single largest problem in numerical optimization is the computational time required to evaluate a single loop in the optimization cycle
[58]. Improvements in CPU speed, memory capacity, and software capabilities have reduced the total cost of computer based optimization roughly one billion (1 000 000 000
000) times since computer based optimization began in 1971 [59]. Despite this fact, over
the past decades, the time required for performing a specific type of calculation has not
drastically improved and remains around the region of 12-20 hours. This can be attributed
to two different factors of complexity; modelling and analysis.
The problem with analysis is rather simple. In many cases, there exist problems where
the most well developed implementations of mathematical models are not capable of explaining or modelling the observed phenomena. As new models are developed, or existing
models adapted to solve these problems, the computational time generally increases to
solve the problem. It may even be that in order to gain a better understanding of a problem,
an analyst may change to a more accurate, and usually more complex form of analysis; for
example from linear to non-linear solution sequences within FE [59].
Demands on model fidelity increase according to the demands of the analyst and the capacity of the computational arrays available. Currently, a characteristic element length of
approximately 10 mm is considered sufficient for many applications. Smaller element size
20
Christopher J. Cameron
often yields increased accuracy, especially in regions of stress concentrations. Element
size also is a controlling factor in the frequency limit of a dynamic analysis; a finer mesh
will provide reasonable results to higher frequencies. No intelligent computational analyst
would refuse a more refined FE model if it were capable of being computed in the same
or less amount of time. This amount of time is however directly related to the computer
hardware available.
Kodiyalam et al describe a state of the art computational array in 2004 having 128 CPU’s,
each 400 MHz, with a total of 131 GB of RAM [60]. Numerical calculations within this
thesis were performed on a single workstation using 4 processors, each 3.14 GHz using 16
GB of memory. While the number of processors and amount of memory used in this thesis
are dwarfed by the array used in [60], the speed at which a single binary calculation can be
made has increased by a factor of eight. The ongoing conflict between Moore’s law1 and
Parkinson’s Law2 however likely means that while technology and software improve, time
will always be the governing constraint on optimization problems.
Assuming then that the total amount of time used for optimization is somehow held constant, it is perhaps interesting to look at the current method for dividing up calculation time
between different areas of study. Crash and impact simulation is, without question, the single most computationally expensive area in vehicle design; this is an opinion unanimously
agreed upon by all sources found in the literature [56, 57, 59, 60, 61]. Crash optimization
using modern, efficient algorithms, such as latin hypercube sampling, requires 3 to 4 calculations for each design variable [61]. Given that each calculation can take between 12-20
hours, it can easily be seen that several weeks may be required for even a moderately simple optimization problem. It is a general default that NVH optimization is included simply
as a constraint on global bending stiffness of the BIW and a restriction on the frequency
for a resonant mode of vibration. In none of the literature on multi-objective optimization was an NVH analysis performed using a full cavity FE model. Given the number of
constraints on crash behaviour, it is perhaps not an unexpected trend, however, it can be
expected that as with all other areas of numerical computation, the level of intricacy of
NVH optimization will increase as hardware and software allow.
The problem of long computational times is hardly a new issue, and different approaches
at minimizing its effect on the design process have been developed. In large FE problems substructuring-i.e. breaking a single large model into several interconnected small
models- is often used. A very well known and effective method called automated multilevel substructuring (AMLS) is used a great deal within the automotive industry and has
been proven to both speed up calculation times and enable accurate results up to higher
frequency ranges within a given length of time [62]. For the optimization of a single component within a body in white, the use of super-elements has also been explored [63, 64].
1 In 1965, Gordon Moore, founder of Intel, stated that the number of devices on a silicon chip would double
every 18 months. This is commonly known as "Moore’s Law" [59]
2 In 1959, Cyril Northcote Parkinson published an essay in "The Economist", the opening line of which was:
"It is a commonplace observation that the work expands so as to fill the time available for its completion". This
statement has become more commonly referred to as "Parkinson’s Law"- C.Northcote Parkinson, The Economist,
November 1955
Introduction
21
So far, within the literature, limited work has been done on full scale optimization of coupled fluid structure systems, especially those with acoustic objective functions, except for
rather geometrically simple problems [65]. This is largely due to the increased number of
degrees of freedom due to the fluid cavity in addition to the added computational difficulty
in solving a coupled fluid-structure problem. While new methods of dealing with this problem are being developed [27], the current state of the art in coupled fluid structure analysis
lacks the number or refinement in numerical tools compared with structural analysis by
itself.
Within an industrial context, in addition to all of the absolute time constraints caused by
model size, and computational issues, there exist a great many practical points of interest
that are perhaps relevant to discuss. Regardless of the efficiency of the models and computers, engineers must be involved in the process to achieve results that are meaningful [66].
There also exists the problem of transposing a global design objective which is of interest,
to a more localized design requirement which can be optimized [67]. As an optimization
problem seeks to include more areas of interest, it requires the input of more groups of
experts which are often located at least at different areas within the company if not at different locations around the world. While a single analyst may be capable of carrying out
a simple multi-disciplinary problem, complex refined problems will require more than a
single individual [58]. These sorts of organizational problems can also be costly, but the
cross-competency interactions can also help to develop new areas of study; for example
including fiscal or environmental impact factors in the structural design process [68]. In
the end, it must also be remembered that in an industrial context, the exact optimal solution
is not of interest, it is instead a sufficiently good solution that can be reached in a minimal
amount of time which is the goal.
Optimization within this work
The method of moving asymptotes (MMA) [69] was chosen to solve the optimization
problem assesed in this work. MMA was chosen for the following reasons:
• MMA is well suited for solving structural optimization problems.
• Experience and Competence in using MMA exists within the research group.
• MMA was available in an easily implemented software package available within the
division of lightweight structures.
Specifically, the program Xopt developed and provided by Alfgam Optimering AB3 was
used.
3 www.alfgam.se
22
Christopher J. Cameron
5 Summary of Work Performed and
Discussion of Results
The previous chapters within this thesis have given a background in the areas of vehicle
NVH, sandwich structures, and optimization. This chapter will position and explain some
details of the work performed and its contribution to the body of scientific knowledge in
the field.
The research work leading to this thesis forms a synthesis between design of a structurally
viable component and its acoustic performance. The paradigm used is multifunctionality,
i.e. designing an integrated component with desired acoustic and structural performance at
a low weight.
To establish a datum baseline, an initial campaign involving testing and simulation of a
state-of-the-art vehicle component (in this case, the roof system of a passenger car) was
performed. The results from this work formed the starting point for the actual design optimization, leading to the new, integrated concept derived having lower weight, comparable
performance, and lower level of complexity.
Baseline Characterization
The testing and simulation work to establish the current state-of-the-art involved several
steps. Initially, full-vehicle acoustic measurement of a production Saab 9-3 SportCombi
was performed. Following this, the roof structure of the same production vehicle was
removed and sent to KTH where laboratory measurement of acoustic and vibro-acoustic
properties could be performed. Sound transmission loss (STL) testing was performed for
both the full vehicle, and for the component according to international standards.
Comparison between the results of STL testing for full vehicle and component testing
showed extremely good agreement as can be seen in figure 5. Two significant conclusions
which can be drawn from the acoustic testing results are as follows:
• With regards to sound transmission loss testing, for the roof panel at least, and most
certainly for other body panels, in-situ testing yields sufficiently accurate results as
Introduction
23
to eliminate the need to disassemble a vehicle to measure individual components.
• In frequencies above approximately 1000 Hz, sound transmission through glass surfaces contributes significantly to the total sound transmission into the passenger
compartment.
Sound Reduction Index
Full Vehicle with Headliner
Full Vehicle without Headliner
Component with Headliner
100
500
1000
5000
10000
Frequency [Hz]
Figure 5: Sound transmission loss comparison
In addition to sound transmission loss testing,vibro acoustic testing on the roof component
was done to measure structural frequency response for a forced excitation. An inertia
shaker was attached to the drivers side A-pillar and excited using a white noise signal. A
laser vibrometer was used to measure the vibrational velocity of a set of grid points on the
inner headliner and outer roof. Figure 6 shows the shaker setup and measurement points.
Figure 6: Inertia shaker attachment and measurement grid points
24
Christopher J. Cameron
Table 2: Mechanical properties of headliner components
Young’s Modulus[MPa]
Component
Outer Membrane
Inner Membrane
Foam Layer
Testing
9100
4800
8.80
Literature
4500-7500
4500-7500
3.45
For the baseline configuration, tensile testing of the material in the vehicles headliner was
performed in order to fully characterize its properties. Testing was performed according to
international standards [70] using equipment available in the lightweight structures laboratory at KTH. The headliner, as illustrated in figure 7, was composed of three structural
components; two fibre reinforced plastic membranes, and a cellular foam core assumed
to be polyurethane based. A total of ten samples of each structural layer were tested to
obtain Young’s modulus. Tensile testing of the structural foam, while not ideal, was the
only method available given the limited amount of material and its geometry. The values of
stiffness for the various layers were compared with values within the literature and found to
be reasonable, if somewhat above expectations. Table 2 shows the results of tensile testing
compared to values within the literature.
Upper Membrane
Structural
Foam
Lower
Membrane
Acoustic Foam
Aesthetic Treatment
Figure 7: Closeup of headliner cross-section
Complimentary to the testing, numerical simulations were performed. The intention of the
numerical simulations were to develop and verify a methodology which could be later used
in the design optimization process. This was achieved through two fundamentally different
modelling approaches, one focused on realism, i.e. true geometry, and one focused on
accuracy and computational effort, i.e. simplified geometry. In the baseline configuration,
the headliner was of specific interest.
Introduction
25
The headliner is in itself, a multi-layer component, however as the focus of the work was
on a more global structural-acoustic level, a simplified method of modelling the headliners
properties was developed. This was achieved using the results in table 2 together with basic
sandwich theory.
For a sandwich structure, the Young’s modulus through the thickness varies depending
on the material layer. Figure 8 shows the cross-section for an arbitrary sandwich with
dissimilar faces, as was the case for the headliner.
t1
E1
tc
Ec
z
e
E2
t2
Figure 8: Arbitrary sandwich cross-section (redrawn from [45])
Flexural rigidity (denoted as D ), which describes a sandwich beams stiffness in bending,
can for a unit width sandwich beam of arbitrary cross section (see figure 8) be expressed
in the following manner [45]:
D=
Z
Ez 2 dz =
E1 t31
E2 t32
Ec t3c
+
+
+
12
12
12
tc + t2
E1 t1 (d − e) + E2 t2 (e) + Ec tc (
− e)2
2
2
Where:
e=
E1 t1 d
E1 t1 + E2 t2
d−e=
d=
E2 t2 d
E1 t1 + E2 t2
t2
t1
+ tc +
2
2
2
(2)
26
Christopher J. Cameron
Lower case t denotes a thickness, and E is the Young’s modulus. Subscripts 1 and 2 denote
the upper and lower face sheets. Subscript c denotes the core material. In this case, the
face materials are the two fibre reinforced membranes and the core the polyurethane foam
layer. Lower case z denotes the vertical coordinate of the sandwich cross-section where
z = 0 is the neutral axis of the sandwich structure. By inserting values of t and E into
Equation ( 2), a value can be obtained for the flexural rigidity.
The thickness of each of the components comprising the headliner were measured at a number of locations, and average values for each layer were inserted into equation 2. Thickness
variations were primarily within the urethane foam core, most likely an effect of the manufacturing process which often involves press forming [71].
Using a total nominal thickness for the entire headliner of 6.0 mm , an equivalent Young’s
modulus was obtained for use in the FE model according to equation 3. Density of the
model was based on measured mass of the headliner.
Eequiv = R
D
=
z 2 dz
D
(6.0)3
3
[M P a]
(3)
These methods enabled the entire headliner to be modelled without detailed modelling of
the individual layers which was of sufficient accuracy for the work performed within this
thesis.
Using a hierarchical finite element code developed in house (and explained in detail in [41,
42] ), sound transmission loss calculations for the roof structure with equivalent headliner
properties were made through the frequency range of 100 Hz to 1000 Hz and compared
to the aforementioned testing. Results can be seen in figure 9. The conclusions of this
comparison is as follows:
• Hierarchical FE modelling using the equivalent solid methodology is accurate in
predicting sound transmission loss up to approximately 500 Hz.
• Above 500 Hz, the simplicity of the model prevents the accurate prediction of sound
transmission loss; this is mainly related to the excitation method.
In addition to hierarchical FE analysis, coupled fluid-structure analysis using Nastran was
performed. A model of the headliner was created using the equivalent mechanical properties. Damping properties of the headliner were calculated based on material properties of
the acoustic foam layer and on theories for acoustical wave propagation within porous media which can be found in the literature [35]. A structural model of the component tested
in the laboratory was created as was an acoustic cavity model accounting for the headliner.
A cross-sectional view of the FE model can be seen in figure 10.
The model was excited in the same manner as in laboratory test, i.e. a harmonic excitation was applied to the drivers side A-pillar, and vibration velocity levels of the headliner
Introduction
27
Full Vehicle with Headliner
Full Vehicle without Headliner
Component with Headliner
Sound Reduction Index
Heirarchical FE Solution
100
200
300
400
Frequency [Hz]
500
600
800
1000
Figure 9: Measured and numerical sound transmission loss in 1/3octave bands
Existing
Structure
Headliner
Roof Air
Cavity
Passenger
Air Cavity
Figure 10: Cross-section of FE model
and outer roof were calculated. A basic parameter study was also performed using the FE
model to evaluate the effects of headliner stiffness and boundary condition variations on
the vibration levels of both the headliner and the outer roof. In comparing results from
vibroacoustic testing with calculations using the Nastran model good agreement was obtained. Figure 11 shows one such example of comparison between measurement and finite
element calculations.
Christopher J. Cameron
Velocity
28
Measured Mean
Nominal Stiffness
No BC at Edges
No RBE Coupling
100
150
200
250
300
350
400
450
500
Frequency
Figure 11: A comparison of FE and vibroacoustic testing results
In comparing the FE results to testing results, the following conclusions were made:
• The mechanical coupling between the roof structure and the headliner has the largest
impact on the vibration level of the headliner among the parameters investigated.
• Stiffness properties of the headliner have relatively little effect on its vibrational
behaviour
As the headliner in a vehicle interior is a large surface in direct contact with the air surrounding the vehicle occupants, its vibrational behaviour is significant to the level of sound
within the cabin. Should such a design be used, from an acoustic standpoint, a better understanding of the nature of the attachment mechanism would aid in NVH development.
While the above points are important, the single largest contribution to vehicle NVH analysis is as follows :
The method of modelling, using equivalent properties, while simple, proved
to be accurate from a vibro-acoustic standpoint. Modelling of interior trim
components using three dimensional finite element models is still in its infancy
for both academic and industrial applications. This observation is based on
a thorough literature survey and discussions with experienced individuals in
Introduction
29
industry. Accounting for the acoustic and vibrational aspects of interior trim
by modelling the actual components is the next frontier within vehicle NVH
and offers a powerful tool for prediction during design.
In addition to being quite accurate, in particular concerning the higher frequency range,
the modelling methodology developed was simplistic enough that implementation for other
trim panels of interest should not be exceedingly difficult. In addition , the work within this
paper has contributed to extend the understanding of coupled structure-acoustic analysis
using finite elements in the mid-frequency range.
Introduction of Multifunctional Sandwich Concept
In the second part of the work, a new concept for a roof system was proposed in which all
components from the outer sheet metal to the interior trim were replaced by a single multifunctional sandwich panel. Figure 12 gives a graphical representation of the concept.
Acoustic Absorbent
Outer Sheet Metal
Headliner
Anti-Flutter Adhesive
Anti-Flutter Adhesive
Rear Header
Beam
Panel Damping Treatment
Front Transverse Beam
Rear Transverse Beam
Front Header
Beam
External Face
Sheet
Interior Aesthetic/Structural
Treatment
Structural Foam Layer
Acoustic Foam Layer
Figure 12: A schematic of traditional and sandwich panel design
Two configurations of the concept were proposed, each consisting of four components; external face sheets of isotropic material, a structural foam layer of typical polymeric sandwich core foam, a single layer of lightweight, open–celled acoustic foam , and an interior
face sheet which provides both structural and aesthetic functionality (see Figure 12). In
one panel configuration, the interior face sheet was perforated to allow fluid interaction
30
Christopher J. Cameron
Table 3: Material properties in FE model for sandwich panels. In cases where properties
differ, perforated values are shown inside square brackets
Material
E (MPa)
G (MPa)
ρ (kg/m3 )
ν
Outer Sheet
Struct. Foam
Ac. Foam
Inner Sheet
Aluminium
70 000
26 000
2710
0.3
Closed Cell Foam
135
35.0
100
0.4
Open Cell Foam
0.10
–
30
0.1
Aluminium
70 000 [46 460]
26000 [–]
2710 [2170]
0.3 [0.27]
between the passenger cavity and the acoustic foam, thus providing sound absorption in
the interior of the panel. A fixed rectangular hole pattern was assumed with holes 2.0
mm in diameter and 4.0 mm centre to centre spacing. For numerical purposes, a method
was derived from the literature [72, 73] to model the perforated plate with equivalent solid
properties. Table 3 shows the values of material data used in the optimization.
Both configurations of the panel were optimized to a set of structural constraints obtained
via engineering specifications and finite element analysis of the existing design. Results
for the objective function, design variables, and active constraint can be seen in table 4.
Table 4: Optimization results for perforated and non-perforated panels
Optimized Mass(% of Conventional)
t Outer Sheet [mm]
t Structural Foam [mm]
t Inner Sheet [mm]
Active Constraint
Perforated Panel
Non-Perforated Panel
17.643
0.200
5.088
0.200
Local static disp.
18.215
0.200
4.6004
0.200
Local static disp.
The structural optimization performed was, in itself, not entirely remarkable; established
optimization algorithms were used, as were somewhat standard forms of static and structural dynamic constraints. In establishing the requirements, the difficulty in translating
global requirements to component level requirements was emphasized, as was the need for
improved understanding in this area. Two interesting points that were established from the
results are the following:
• For the examined structural constraints, the existing construction is tremendously
mass-inefficient due to compromises between requirements of design and production
• Robustness required for everyday use may in fact be the limiting factor for minimum
weight when replacing a steel structure with a sandwich structure
Introduction
31
After structural optimization, the two configurations of the sandwich component were
evaluated using advanced finite element analysis software for poro-elastic acoustic calculations. The software CDH\EXEL4 in conjunction with NXNastran 6.0 was utilized
to perform coupled fluid-structure analysis. Frequency response analysis was performed
using a single fluid cavity of identical exterior shape as that used for the conventional solution. Both the conventional and sandwich panel models were excited in the same manor,
namely a single node inside the fluid cavity located approximately at the drivers head was
excited and the average fluid pressure within the cavity was calculated for the frequency
region 100-500 Hz. Results of the calculation can be seen in figure 13.
Conventional Roof
Sound Pressure [dB]
Perforated Sandwich
Non-Perforated Sandwich
100
150
200
250
300
350
Frequency [Hz]
400
450
500
Figure 13: Average sound pressure in cavity vs excitation frequency (Y-Axis 5 dB steps)
The results in Figure 13 showed that the general behaviour of all three configurations was
quite similar. This result was, from an acoustic standpoint, very significant; despite the fact
that mass of the system has been reduced by approximately 80%, no noticeable degradation
of the acoustic environment has taken place.
Figure 14 shows the same results as obtained in Figure 13, however levels have been averaged over 10 Hz intervals. Here, the differences between the conventional and sandwich
configurations is much clearer. It can be seen without doubt that no degradation of the
4 http://www.cdh-ag.com/de/exel.html
32
Christopher J. Cameron
Conventional Roof
Sound Pressure [dB]
Perforated Sandwich
Non-Perforated Sandwich
100
150
200
250
300
350
Frequency [Hz]
400
450
500
Figure 14: Average sound pressure in cavity vs excitation frequency [Averaged over 10Hz]
(Y-Axis 5 dB steps)
acoustic performance has taken place in spite of the significant reduction of mass. It would
also appear, that in the frequency range above 300Hz, the sandwich constructions in fact
may perform better than the conventional design. Differentiating between the perforated
and non-perforated configuration is somewhat more difficult. At some frequencies the perforated panel appears to perform better, and at others the non-perforated. This observation
brings up an interesting point of discussion; while the non-perforated panel represents a
minima in acoustic absorption, the perforated configuration, which was rather arbitrarily
chosen, offers potential for improvement in absorption characteristic.
The final results of the work in this thesis yield a component that meets the structural
targets without degrading acoustical performance, but is of questionable robustness and
which proved impossible to produce with conventional methods. While this result is in
itself uninteresting, being merely an academic proof of concept, the major contribution to
vehicle NVH from the work in can be described as follows:
The proposed concept offers a new idea within the area of sound and vibration control within an automobile. Heavy and inefficient visco-elastic damping treatments, insulation, and aesthetic treatments have all been replaced by
Introduction
33
the use of a more intelligently designed structure offering integrated damping
via the use of structural and acoustic foam elements. Utilizing the sandwich
concept to obtain maximum stiffness for minimum weight results in large reductions in mass while still meeting the same structural criteria, and without
degradation of the acoustical environment.
While the final panel is not suitable for production, this work provides a proof of concept
and a strong argument for further investigation and optimization.
Further Implications
Using some creative thinking, it is quite possible to create a long list of potential areas of
improvement a modular sandwich based construction could achieve for the case studied
in this thesis. The potential for a significant reduction in the mass of the roof system is
obvious. An improvement in the acoustic properties of the interior should also be achievable. While it is explicitly within these two areas that improvements can be quantified with
exact numbers and numerical results at present, a number of other areas would however be
affected directly as a result of the switch to a modular sandwich construction.
Among other things, it is reasonable to presume that improvements within the following
areas should be attainable:
• Reduced assembly line time
• Improved assembly ergonomics
• Improved fuel economy via reduced weight
• Improved aerodynamic drag via reduced frontal profile OR
• Improved interior headroom for the same frontal profile
• Increased styling flexibility (assuming use of composites materials)
There of course exist disadvantages with a switch to new methods of construction and
materials. While it has not been addressed within the current work thus far, one cannot
discuss sandwich constructions without discussing composite materials such as fibre reinforced plastics. The discussion surrounding the advantages of composite materials in
the automotive industry, especially with structural application in mind, has existed at least
since the mid 1980’s. With the exception of extreme applications such as supercars, there
exist few current examples of composite sandwich structures making a significant contribution to a series production automobile. Previously, engineers have reduced vehicle
weight by changing from standard grades of carbon steel to aluminium, magnesium, or
high-strength stainless steel alloys. While this has been effective to a degree, vehicle curb
34
Christopher J. Cameron
weights continue to rise and the choice of light weight metallic materials is dwindling if
not already exhausted.
Presumably, the two greatest hinders to engineered materials in the automotive industry
are cost and crash safety. Sandwich structures, especially those using fibre reinforced
plastics are significantly more expensive to produce than their stamped steel equivalents
using current methods of construction. It is however a fact that tooling required to produce
a stamped steel structure is incredibly expensive, and production of such components must
continue for several years to achieve a return on investment. Tooling required for composite
based sandwich structures is a fraction of the cost, which would allow increased flexibility
in design changes under a vehicle models lifetime; this must of course be balanced with the
need for increased numbers of production stations to obtain the production rates necessary
to maintain the existing assembly line speed. Certain methods of construction, for example
the use of thermoplastics as face sheets and core material show promise, and increase
both the speed at which components can be produced as well as the recycleability of the
components.
With regard to crash safety, it is most certainly possible to create a vehicle using composite materials and sandwich construction that is as safe or safer than a stamped steel
construction. The problem is of course not making the vehicle safe, but making it safe for
a reasonable cost. Computational crash calculations take up the majority of CPU time in
modern vehicle design and are the foundation of the vehicle design process. The current
state of the art regarding the capacity to model, predict, and optimize the collapse of sandwich structures is vastly inferior to the level of understanding regarding metallic structures.
Research in this are is ongoing and while it is likely only a question of time until the same
level of reliability is reached in predicting crash behaviour of sandwich structures and composite materials as exists for metallic structures today, the question of how long it will take
remains open. Unfortunately, the intermittent period between now and then would rely
significantly on prototype crash tests, which are both expensive and time consuming, and
at present reserved mostly for validation of numerical results.
One interesting aspect to the entire problem is the capacity of the automotive industry to
find solutions for new and difficult problems. If the automotive industry as a whole should
decide to embrace the technology and put its collective resources behind finding solutions,
it will, without a doubt, shorten the process considerably. This however would require an
investment in both time and financial resources that might not be favourably looked upon
by the industry without significantly more stringent regulatory legislation.
One might be prone to think that, given the current focus on environmental issues and
exhaust emissions as well as the more recent economic problems facing the global automotive industry, that a switch to methods which will could potentially save resources
both economically and ecologically is lying "right around the corner". As the viewpoint
of "right around the corner" has been re-iterated for nearly twenty five years, the question
of how long the corner is, or if perhaps the corner is actually a roundabout remains to be
answered.
Introduction
35
6 Future Work
The work within this thesis has focused on the mass optimization of a sandwich panel
to a given set of structural constraints. Acoustic properties have been assessed, but have
been a passive component in the calculations. In future work, it is the intention of the
author to implement a more complex multi-objective optimization problem where acoustic
aspects as well as structural aspects will be active parts of the optimization. Additional
design variables which will affect both the acoustic and structural properties of the structure
shall be included such as material properties of the structural and acoustic foams, and
mechanical properties of the face sheet materials.
Within the remaining time in this project, it is also hoped that the ecological and economical aspects of the optimization process can be assessed by more direct methods, such as
perhaps life cycle analysis, or some kind of environmental impact factor.
36
Christopher J. Cameron
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Introduction
41
Division of work between authors
Paper A
Measurements were performed by Cameron with assistance from Saab and MWL Personnel. Post Processing of results was performed by Cameron. Nastran modelling was
performed by Cameron and Hierarchical modelling by Göransson. Analysis and interpretation of results was jointly performed by Cameron and Göransson. Cameron wrote the
paper with support from both Görransson and Wennhage.
Paper B
Modelling and analysis in Nastran was performed by Cameron. Cameron and Wennhage
developed the optimization scheme together and Cameron executed it. Göransson provided
the basis for the poro-elastic modelling. Cameron and Göransson implemented the acoustic
analysis together. Cameron wrote the paper with support from Göransson , Wennhage and
Rahmqvist.
Part II
Appended papers
43
Introduction
Paper A
45
PREDICTION AND MEASUREMENT OF NOISE AND
VIBRATION BEHAVIOR OF TRIMMED BODY
COMPONENTS AT MID-FREQUENCIES
Christopher J. Cameron ∗, Per Wennhage, Peter Göransson
Centre for ECO2 Vehicle Design
KTH Aeronautical and Vehicle Engineering,
Kungliga Tekniska Högskolan (KTH)
SE-100 44 STOCKHOLM, SWEDEN
http://www. eco2vehicledesign. kth. se
Abstract
The work within this paper focuses on the application and validation of numerical methods
for predicting the acoustic and structural NVH behaviour of trimmed body components in an
automotive context.
Specifically, the roof structure of a passenger car was investigated from various performance
aspects, using both structural and acoustic excitation. The roof was initially tested in situ, with
and without interior lining, to provide a reference for subsequent component tests. It was then
detached from the car, mounted in a rigid frame and tested in a transmission window using both
acoustic and structural excitation.
A finite element model of the detached component was developed using shell and solid elements for the structure and solid elements for the interior lining. Predictions were carried out to
evaluate the sound transmission loss as well as the vibrational frequency response due to a force
applied to the structure. Special attention was given to the modelling of the headliner as well as
the air gap separating the headliner from the outer sheet metal.
The main objective of the current work has been to establish a datum reference for alternative
designs. From this aspect, the validation of the numerical modeling methodology used was a
crucial step. It was found that the predictions agreed very well with the measured data. As an
additional, very interesting result, it was also found that the in-situ testing correlated well with
the transmission suite testing.
Key words: acoustics, structural, equivalent, transmission, structure borne, interior trim,
numerical modelling, measurement
1. Introduction
The importance of the noise and vibration (NVH) function requirements of modern vehicles
are of ever increasing importance for vehicle manufacturers, perhaps even more emphasised with
∗ Corresponding
Author
Email address: [email protected] (Christopher J. Cameron )
Preprint submitted to Elsevier
May 11, 2009
the current trend towards environmentally compatible hybrid-electric power train concepts.
While the structural design of an automobile body during the last decades have come to rely
heavily on finite element analysis, the NVH design traditionally has been based on the use of
experimental prototypes and the skills of experienced engineers to adjust the acoustic properties
of the full vehicle. For this purpose body treatments and interior trim components are added to
provide aesthetics, thermal insulation and to control transmission of noise and vibration in order
to improve the acoustic environment.
The vehicles acoustic interior trim has rarely been modelled in detail, if at all in industrial
practice, and its effects are often accounted for by the use of global fluid damping constants and
additional masses etc. The reason for these simplifications are several, both related to a fundamental lack of proper modeling methodology but also to computational efficacy, e.g. performing
coupled fluid-structure analysis, including the effects of damping provided by the car interior, has
in any given commercial code been computationally expensive, and furthermore usually limited
to the frequency domain below 200Hz.
Thus there has been a need for improved simulation and modeling techniques, in order to
allow better control of the early stages of the acoustic design of the full vehicle. Much research
has been spent on this aspect during the last decades and different methods for predicting the
acoustic properties of the full vehicle have been developed[1]. With the increase in computer
power seen during the last decades, and the advancement in CAE/CAD tools, modelling of interior trim using finite element models has reached a level of maturity sufficient for industrial
application.
The influence of the interior trimming is a crucial aspect of a full vehicle NVH simulation
model, in particular concerning the often discussed medium frequency range, here somewhat
arbitrarily defined as the frequency range between 100 and 500 Hz. As a vast majority of vehicle
development work is done using computational methods, any new tools developed should be
complementary to finite element analysis.
The work within this paper focusses on such methods for prediction of NVH behavior of
trimmed body panels subjected to structural and fluid borne acoustic excitation. It is demonstrated that modelling of interior components, both for airborne and structure borne transmission
can be used to investigate the effects of interior trim on the interior response. In particular, this
study aims at investigating the interaction between the roof structure and the interior headliner
trim component, and the sensitivity of this system to variations in roof liner properties and attachment conditions.
Measurements were made using a complete vehicle provided by Saab Automobile AB(SAAB).
After removing the roof system, component tests were performed at the Markus Wallenberg Laboratory for sound and vibration research (MWL) at KTH to gain a better understanding of the
roof components. Finally, a finite element model of the roof system including the acoustic trim
was developed which can be used to study the interaction between the roof trim and the air
cavities of the passenger compartment and the roof.
2. Method
Full vehicle acoustic measurements were performed in a semi-anechoic chamber at SAAB.
Sound Transmission loss was measured according to international standardised methods [2, 3]
both with and without the inner headliner installed.
The roof structure was removed from the vehicle and measured at MWL. Sound transmission
loss testing was performed in addition to vibro-mechanical testing.
2
Tensile testing was performed to obtain the mechanical properties of the constituent components of the headliner. An equivalent solid representation was developed for the headliner to
simplify the modelling using basic sandwich theory [4] and measured mechanical data.
Two different FE codes were used to simulate the acoustic behavior of the roof structure with
the headliner as measured at MWL. Both codes use the equivalent solid representation of the
headliner component. In house hierarchical FE code was used to calculate the sound transmission loss of the system using a geometrically simplified model. Vibro-mechanical analysis was
performed using NX nastran 6.0. A model of the roof structure was created from an existing full
vehicle model provided by SAAB. The interior headliner was modelled as a three dimensional
solid, impervious to fluid flow. Acoustic damping within the Nastran model was achieved by the
use of a surface impedance calculated according to the methods described in [5] and applied on
the interior side of the headliner.
A direct comparison of the sound transmission loss for the full vehicle, component, and
computational model across the mid-frequency range was performed.
A comparison of average vibrational velocities of measurement points in the laboratory and
the numerical model was performed for both the outer roof sheet metal and the inner headliner. A
parameter study was performed varying headliner stiffness, headliner fixation, surface impedance
at the headliner, and the acoustic properties of the passenger cavity.
2.0.1. Full Vehicle Testing
Full vehicle testing was performed in the NVH laboratory at SAAB, in Trollhättan, Sweden.
A semi-anechoic room with absorbent walls and ceiling and a hard floor was used for measurement. A standard production SAAB 9-3 Sport combi was supplied for the testing.
The vehicle was parked in the middle of the anechoic room and a 100W sound source was
placed inside the vehicles passenger compartment. The source was supplied with a signal from a
Brüel & Kjær Type 1405 white noise generator in the frequency range 250Hz -10kHz. A Brüel
& Kjær Type 2706 power amplifier was used between the noise generator and the sound source.
Sound pressure within the vehicle was measured using 3 randomly placed pressure microphones moved to 24 different locations during the course of testing. Microphones were isolated
from structural vibration by means of elastic cording.
Sound transmission loss for the roof system was measured by scanning the roof using a Brüel
& Kjær Type 4135 two microphone sound intensity probe according to international standards[2].
Size constraints prohibited scanning of the entire roof in a single pass, and so it was broken
up into 9 subsections. Subsections 1–7 were drawn out based on the location of cross-beams and
additional structure under the outer sheet metal. Subsections 8 & 9 are the central and perimeter
sections of the roof panel. Each subsection was scanned individually. Figure 1 shows a schematic
of the subsection layout for scanning.
In total, the entire roof was scanned four times. The first complete scan consisted of sections
1–7. The second complete scan consisted of sections 8 & 9. This redundant scanning was
done in order to see the effect of sound leakage through door and window seals–i. e. flanking
transmission. The same measurements were performed after removing the inner headliner. This
was done to measure the acoustic contribution of the headliner on the full vehicle scale.
Sound intensity for each subsection was measured and the Sound Reduction Index(SRI) for
each section was calculated according to international standards [3]. SRI for the entire roof
was calculated using the area weighted average of the subsection values. Values of the sound
reduction index were plotted across the frequency spectrum and can be seen in the results section.
3
Figure 1: Area layout for sound intensity scanning measurement
2.0.2. Component Transmission Testing
After full vehicle testing, the roof section was removed from the car and attached to a rigid
steel frame. All windows were removed and the openings were closed with MDF (fibre-board)
panels and a layer of mineral wool, see figure 2. Silicone glue was used around the perimeter
of the MDF panels to effectively seal the holes in an effort to eliminate any potential flanking
transmission.
Figure 2: Roof Structure attached to steel frame with mdf closures
The structure was mounted between the reverberant and anechoic rooms at MWL. Due to the
size of the roof and attached framework, the exterior surface of the roof faced the reverberant
room and the headliner the anechoic room. A Brüel & Kjær Type 1405 signal generator was
used to produce a white noise signal between 100Hz-5khz fed through an NAD C370 stereo
integrated amplifier to a sound source in the reverberant room. Average sound pressure levels
in the reverberant room were measured using a microphone mounted on a rotating boom. The
measurement areas on the outside of the roof were re-drawn on the interior side of the headliner
as accurately as possible. Sound intensity scanning was performed on the headliner side of the
roof structure according to international standards [3]. It should be emphasised that the source
and measurement sides of the roof as mounted in MWL are switched compared to the setup at
SAAB. Figure 3 shows the roof as mounted in MWL for testing.
For the experimental setup at MWL, it was possible to measure the entire inner roof at once in
4
Figure 3: Roof Structure mounted in MWL
addition to the individual subsections. This enables SRI to be measured directly rather calculated
as a sum of weighted averages. Results for SRI were plotted against the frequency interval and
can be found in the results section.
2.1. Vibro-Mechanical Testing
In addition to the sound absorption capabilities of the roof structure, it was decided to characterise the structures response to mechanical vibration. Such a test provides both an important
picture of the vibroacoustic properties of the component as well as a part of the experimental
correlation. A Brüel & Kjær Type 1405 signal generator and Type 2706 power amplifier were
used to excite a Brüel & Kjær Type 4809 inertia shaker attached to the structure at the midpoint
of the driver’s side A-Pillar. A threaded washer was glued to the A-pillar and a force transducer was screwed into to the washer. The shaker was suspended from a steel frame with rubber
straps. A small diameter stinger was used to attach the shaker to the force transducer. Using a
small diameter stringer ensured that the force applied to the structure was as close as possible to
perpendicular to the sheet metal at the point of excitation.
A Brüel & Kjær Type 2635 charge amplifier was used to amplify the signal from the force
transducer. A laser vibrometer consisting of a Polytec OFV 303 Sensor Head and Polytec OFV
3001 Controller was used to measure the vibration levels of the outer roof and the headliner.
Reflective tape was used to mark the measurement points and enhance the reflected signal to the
laser. Analysis of the signals was performed using siglab on a PC. The inertia shaker setup and
the inner and outer roof measurement points can be seen in figure 4.
Vibrational velocity was recorded for 180 points on the exterior of the roof and 21 points on
the interior side of the headliner. Matlab was used to post-process the data. Average vibrational
velocity for the measured surface was calculated using the individual measurement points for the
respective surface.
2.2. Tensile Testing of Headliner Components
The inner headliner is a sandwich construction consisting of two stiff fibre reinforced membranes separated by a foam core. On the interior side of the sandwich is a second layer of
relatively soft open celled foam and a final layer of perforated fabric are used to provide sound
absorption and an aesthetically appealing surface. Materials such as glass fibre reinforced plastics
5
Figure 4: Inertia Shaker Attachment and Measurement Grid Points
and polyurethane foam are often used in headliner applications [10, 11] and while representative
values can be obtained from the literature [7, 8] experimental testing was deemed necessary to
obtain actual mechanical properties. Figure 5 shows a cross-section of the measured headliner.
Figure 5: Cross-section of Headliner Construction
A square approximately 35cm by 35cm was removed from the centre section of the headliner.
This area corresponds to the thickest and most uniform thickness part of the headliner. The upper
membrane and lower membrane were peeled from the urethane foam core. Additionally, the soft
inner foam layer was peeled from the inner membrane. Each layer was trimmed to a square 25cm
x25cm. The urethane foam was weighed and its density calculated assuming a uniform thickness
of 6.0 mm.
6
Tensile testing was performed according to ASTM standards [6]. This test method was used
because the inner and outer membranes were of a glass fibre reinforced construction. Tabs for
clamping, as described in the testing standard were not used as they were not deemed necessary
to gain basic stiffness information. The same testing method was used for testing the foam
samples. While the choice of this test method for the foam samples was not optimal, it was
deemed accurate enough to gain an estimate of the foams properties.
Ten samples measuring 25mm by 250mm were cut from the outer membrane, urethane foam,
and inner membrane respectively. Samples were placed in pneumatic clamps fitted to an Instron
screw driven Universal Testing Machine. An extensometer and a 30kN load cell were used to
record the load v/s displacement behavior of the samples. The extensometer was attached to
the sample using rubber bands. A picture of the sample in the test rig can be seen in figure 6.
Displacement control was used to regulate the rate of loading of the specimens.
Figure 6: Tensile testing of headliner components
Stress v/s Strain plots were obtained by post processing the test results using Matlab( TM ).
Within the initial elastic region of the deformation, a first order polynomial curve was fitted to
the data to achieve a value for the Young’s modulus. This was repeated for each of the test
specimens, and average values for all the samples of a given component were calculated. For the
fibre reinforced layers, a tensile Young’s modulus of 9.1 GPa for the outer membrane and 4.8
GPa for the inner membrane was obtained. A tensile modulus of 8.8 MPa was obtained in the
same manner for the urethane foam.
According to the literature, for a glass fibre reinforced phenolic composite, values of Young’s
modulus range from 4.5 - 7.5 GPa, depending upon whether the fibres are continuous or chopped
[7]. This agrees well with test data for the inner and outer membranes, however it implies that
some additional form of reinforcement is likely present in the outer membrane.
For the urethane foam, a density of 55.7 kg/m 3 was obtained. According to [8] the relationship between the polymeric solid and its corresponding open celled foam can be described as in
Equation (1).
7
Ef oam
≈
Esolid
ρf oam
ρsolid
2
(1)
Using the relationship in Equation (1) for the density calculated from the sample and using
properties for solid polyurethane found in [8], yields a Young’s modulus for the foam of 3.45
MPa. A compressive modulus of 10MPa is listed in [7] for a polyurethane foam of slightly lower
density (30kg/m 3). This data would seem to indicate a somewhat exaggerated estimate of the
urethane foams properties achieved by tensile testing.
2.3. Numerical Simulation
While some work has been done in analysing the effects of the roof cavity-headliner interaction [9] its effect is not well understood and seldom modelled numerically. The majority of
information available regarding the acoustic or structural properties of headliners comes from the
headliner manufacturers themselves [10, 11]. A method for numerically analysing the acoustic
properties of the acoustic trim would be an interesting step towards an independent in-situ design
methodology.
2.3.1. Modelling of the Headliner
Accurate modelling of each individual layers of the headliner as shown in figure 5 would be
computationally quite expensive due to the small thicknesses and necessity for a great number
of elements. A modelling approach more suitable to an industrial environment was desired,
and so another method of modelling the headliner was developed where a homogeneous three
dimensional element with isotropic properties could be used instead.
The upper three layers within the headliner make up a classical sandwich structure. The
stiffness contribution of the aesthetic fabric treatment and the soft, porous acoustic foam to the
overall stiffness of the headliner can be ignored. For a sandwich structure, the Young’s modulus
through the thickness varies depending on the material layer. Figure 7 shows the cross-section
for an arbitrary sandwich with dissimilar faces.
Figure 7: Arbitrary sandwich cross-section (Redrawn from [4]
The flexural rigidity of a sandwich beam describes the structures stiffness in bending. Flexural rigidity for a unit width sandwich beam, denoted as D, of arbitrary cross section as shown in
figure 7 can be expressed in the following manner [4]:
8
D=
Ez 2 dz =
E1 t31
tc + t2
E2 t32
Ec t3c
+
+
+ E1 t1 (d − e)2 + E2 t2 (e)2 + Ec tc (
− e)2 (2)
12
12
12
2
Where:
E1 t1 d
E1 t1 + E2 t2
E2 t2 d
d−e=
E1 t1 + E2 t2
t2
t1
+ tc +
d=
2
2
e=
(3)
(4)
(5)
Lower case t denotes a thickness, and E is the Young’s modulus. Subscripts 1 and 2 denote
the upper and lower face sheets. Subscript c denotes the core material. In this case, the face
materials are the two fibre reinforced membranes and the core the polyurethane foam layer.
Lower case z denotes the vertical coordinate of the sandwich cross-section where z = 0 is the
neutral axis of the sandwich structure. By inserting values of t and E into Equation ( 2), a value
can be obtained for the flexural rigidity.
21 square samples were cut from the headliner at the measurement points of the inner roof
and the thickness for each of the layers were measured. A range of thicknesses was found to
exist within the upper structural foam layer, most likely due to the manufacturing process which
often involves pressing[10]. Thicknesses of the membranes, inner foam layer, and porous fabric
layer were constant. The thickness of the urethane foam varied from 1.5 mm to 6.0 mm. A
nominal thickness of 4.0 mm was chosen to use in the FE model. The inner foam/fabric layer
was constant at 2.0 mm.
A total nominal thickness for the entire headliner in the model was chosen as 6.0 mm. Two
layers of hexagonal solid elements were used to model the headliner following the geometry of
the inner surface. Holes for attachment of lighting, etc., were ignored.
Using the calculated values of flexural rigidity, together with the fixed mesh thickness of
6.0 mm, an equivalent value of Young’s modulus for the solid can be obtained by manipulating
Equation (2) so that E equiv can be calculated as follows:
Eequivalent = D
=
z 2 dz
D
(6.0)3
3
[M P a]
(6)
Using this method, a range of values for E equiv was obtained. A minimum equivalent stiffness of 101.0 MPa and a maximum equivalent stiffness of 1358.8 MPa were obtained. A nominal
value of Eequiv for an estimated average core thickness of 4.0 mm and measured stiffness for
each of the various layers was calculated to 622.0 MPa.
Due to the constantly changing cross-section thickness and uncertainty in exact material
properties, it was not deemed sufficiently accurate to calculate the equivalent density based on
the material properties and geometry. Instead, an equivalent density was calculated by using the
actual mass of the headliner and the volume of the headliner model according to:
ρequivalent =
M assactual
V olumemodel
9
(7)
In the vehicle, the headliner is equipped with wiring and lighting systems. This mass is
accounted for within the equivalent density calculation. The local stiffness effects of these components were however ignored.
2.3.2. Numerical Sound Transmission Loss
Sound transmission loss was calculated using in-house hierarchical FE for poroelastic materials [12, 13, 14]. For these calculations, a geometrically simplified model was used. The model
consisted of layers of simple rectangular boxes of representative size and thickness. The bottom
layer was a fluid cavity of an equivalent size to that in the vehicle. This fluid cavity was attached
to a layer representing the headliner. The headliner was in turn attached to a second much smaller
air cavity representing the gap between the headliner and the roof sheet metal. Following this
was a layer representing the sheet metal and finally a third layer of air.
Higher order polynomials (5th order up to 500 Hz and 8th order up to 1000 Hz) were used
in order to permit accurate calculations without unnecessarily increasing the number of elements
within the model.
Normal incident acoustic waves were used as an acoustic load through the frequency range
of 100-500Hz. The simulation model was described in detail in [15] and will not be repeated
here.
Sound transmission loss was then calculated in the same manner as performed with experimental measurements, but here using values from the numerical model. Incident and transmitted
wave amplitudes were taken from the computed results and the transmission loss calculated.
2.3.3. Numerical Vibro-Mechanical Response and Parameter Study
Vibro-mechanical simulation was carried out using the commercial FE code NXNastran 6.0.
A full vehicle FE model was provided by SAAB and modified to contain only the components
in the structure seen in figure 2. The tubular steel frame which the roof structure was welded to,
and shown in figure 2, was not included. The steel plates which the pillars were welded to were
included in the model and used to apply boundary conditions. The edges nodes for the plates
were restricted in all translational and rotational degrees of freedom. By applying such boundary
conditions, it was assumed that the stiffness contributed of the tubular steel frame to the entire
structure could be ignored.
Based on the assumption that the headliner is of such construction that fluid may not pass
through, it becomes necessary to separates the passenger compartment into two fluid cavities.
These two air volumes are herein referred to as the roof cavity and the passenger cavity respectively. The roof cavity is the air space between the inner headliner and the exterior sheet metal.
The passenger cavity is the remaining fluid in the passenger compartment including the volumes
within the doors. Within the vehicle, while fluid may not pass through the headliner, no airtight seal exists around its perimeter. To account for this the two fluid cavities within the model
are connected via the enclosed airspace within the A, B, C, and D pillars. Figure 8 shows a
cross-section of the complete FE model as implemented in Nastran.
2.3.4. Headliner Boundary Conditions
Attachment of the headliner to the structure of the vehicle is usually achieved by the use of
plastic and metallic clips. The exact stiffness of these attachments was unclear in the present
vehicle, and their actual influence on the performance of the trim component unknown, and so it
was decided to investigate several scenarios numerically.
10
Figure 8: Cross-Section of FE Model
In the first configuration the clips are replaced by rigid elements between the attachment
points on the headliner and the corresponding point on the structure. Nodes along the front
and rear edge of the headliner are restricted in translational degrees of freedom as in the actual
vehicle, the headliner is held in place using other trim components along these edges.
In a second configuration, the rigid body elements connecting the headliner to the structure
are removed and the headliner is held in place by the boundary conditions along the front and
rear edges of the headliner.
In the third configuration, the rigid body elements are present and the boundary conditions
along the front and rear edges are removed.
2.3.5. Headliner Damping Properties
Ordinarily, damping within fluid-structure analysis in Nastran is obtained by using global
structural and fluid damping factors paramG and P aramGF L respectively [16, 17]. In this
model, the damping was achieved in a different method. Data from other laboratory measurements together with the models described in [5] were used to calculate numerical values for the
frequency dependant surface impedance of the headliner.
In order to test the sensitivity of the model to the surface impedance of the headliner, calculations were performed with three different values. Values of 0.5, 1.0, and 2.0 times the nominal
estimated surface impedance were used. Additionally, the surface impedance was removed completely to see its effect.
2.3.6. Effect of a Finite Cavity
During measurements, the interior side of the roof structure faced the anechoic room at
MWL. This chamber represents an infinite cavity with zero reflection of sound waves at the
walls. Within the numerical model, a finite cavity was used for the passenger compartment. It
was desired to study the effects of this cavity on the vibrational vibrational response of the structure. Two variations on the nominal stiffness configuration were calculated. In one variant, a
surface impedance was applied to all external surfaces of the passenger compartment acoustic
cavity to simulate an infinite cavity. In the second variant, the passenger compartment acoustic
11
cavity was removed entirely. It was thought that external impedance configuration should reduce
the impact of acoustic resonance modes within the cavity. In the second configuration, removing
the cavity would completely eliminate any effects caused by acoustic modes of the passenger
cavity, however the lack of coupling between the roof cavity and the passenger cavity may effect
the resonant behavior of the roof cavity, and thus the structures vibrational response.
Direct frequency response analysis was carried out using NXNastran. A load of 50.0 N
was applied at the mid point of the drivers side A-pillar. Frequency intervals of 5.0 Hz were
used within the frequency range 100-500Hz. Fluid-structure coupling was performed using the
advanced search method (AS) in NXNastran 6.0 and specifying restricting structural coupling
to only the exterior roof panel and the interior lining. Structural response of the roof panel and
the headliner was taken from the nodal values of velocity from nodes located as close to the
measured points as possible.
3. Results
3.1. Sound Transmission Loss
Figure 9 shows the SRI calculated from laboratory measurements in 1/3 octave bands. All
9 measurement sections are included as well as the mean values for sections 1–7 and 8–9. It
should be noted that while values of SRI for each subsection are included in figure 9, due to the
relatively small area and short measuring time, these individual values should only be considered
for reference purposes.
Figure 9: SRI values in 1/3 octave bands for roof subsections - Full vehicle with headliner
12
Figure 10 shows the directly measured SRI for the roof as tested in MWL in addition to the
results from full vehicle testing at SAAB with and without the headliner.
Figure 10: SRI in 1/3 octave bands - Full vehicle with and without headliner and component with headliner
Figure 11 shows the numerical values of STL as calculated with the hierarchical code together
with the measured values.
3.2. Mechanical Vibration
Figures 12 through 21 show results for measured and numerical vibro-mechanical response
of the inner headliner and outer roof as tested and in the configurations described in section 2.3.3
through section 2.3.6. All results are plotted using a dB scale on the vertical axis with 10 dB
between the tick marks. A detailed explanation of these figures is left to section 4.2.
13
Figure 11: Measured and Numerical Sound Transmission Loss in 1/3 octave bands
4. Discussion
4.1. Sound Transmission Loss Measurement
In general, in figure 9, the trends for the individual sections agree with each other with the
exception of a few measuring points. The largest deviation from the mean values occurs for
subsection 8 in the region of 630 Hz, and subsection 7 from 1250 Hz and upwards. Lowered
absorption for subsection 7 is most likely due to a combination of geometry and material configurations in the region. As subsection 7 lies along the front header beam, the double wall effect
present in the rest of the roof is less dominant. This is also an area where a significant amount of
interior details (lamps etc) are attached to the headliner. Section 7 is also adjacent to the windshield, which is less efficient at preventing sound transmission. A peak in absorption for sections
1, 2, and 3 at the 800 Hz measurement point can also be seen. This is most likely due to the
geometry of the vehicle in that region. A transverse beam with attachment points for the rear
tailgate takes up a significant amount of space in this region.
In figure 10 it can be seen that up to 1600 Hz, there is very good agreement between the
full vehicle testing performed at SAAB and the laboratory testing performed at MWL. Above
1600 Hz there is significant deviation between the laboratory measurements and the mean value
calculated from the full vehicle testing. While this may partially be caused by leakage through
door seals etc, it is believed that the glass in the windshield and side windows may be a larger
contributor. Glass has a reduced sound reduction index compared to the full roof structure in the
frequency range in question. An indicator that sound leakage takes place can be seen in curve
for subsection 8 in figure 9. Section 8 is measured further away from the glass surfaces, and any
14
Figure 12: Measured Velocity Response of Headliner
Figure 13: Numerical Velocity Response of Headliner with Nominal Stiffness Properties
15
Figure 14: Measured & Numerical Velocity Response of Headliner including variations in Headliner Stiffness
Figure 15: Headliner response with Impedance on exterior surfaces and passenger cavity removed
16
Figure 16: Headliner response with boundary conditions and rigid element coupling removed compared with nominal
response and measure response
Figure 17: Measured Velocity Response of Outer Roof
17
Figure 18: Numerical Velocity Response of Outer Roof
Figure 19: Measured & Numerical Velocity Response of Outer roof for variations in Headliner Stiffness
18
Velocity
Figure 20: Outer roof response with Impedance on exterior surfaces and passenger cavity removed
Measured Mean
Nominal Stiffness
No BC at Edges
No RBE Coupling
100
150
200
250
300
350
400
450
500
Frequency
Figure 21: Outer roof vibrational response with variation of Headliner BC’s
19
potential leakage sources, and shows a higher sound reduction index through the frequency range
in question. For the laboratory case where the glass was removed and replaced with MDF and
insulation, the curve does not deviate as in full vehicle testing. For reference purposes, the curve
for sound reduction index without the inner roof panel as obtained at SAAB is also included.
It is immediately obvious that the headliner construction contributes considerably to the sound
transmission loss properties of the roof construction.
Figure 11 shows rather good agreement between the sound transmission loss calculated and
the measured values up to about 500 Hz. Above this frequency the oblique incidence waves in
the measured transmission loss become dominant. Since these are not present in the simplified
model, the conclusion is that the simplified model provides sufficiently accurate sound transmission loss prediction for the full vehicle in the mid-frequency range.
4.2. Vibro-Acoustic Analysis
Figure 12 shows the measured frequency response functions of all 21 points measured on
the inner roof together with the mean level of vibration across the frequency range of 100-500
Hz. Dashed lines show the measured values for individual points, and the solid line shows the
average value. It can be seen that envelope in the measurements is more narrow for the lower
frequency measurements and widens slightly in the higher frequencies. Maximum response in
general stays within approximately 10 dB of the mean value. In the discussion of the sensitivity
analysis below, the mean value of the vibration level will be used.
Figure 13 shows the numerical results for the inner roof for 21 points located at approximately
the same location as in measurements. Direct frequency response was performed in 5.0 Hz steps
between 100 and 500Hz.
Figure 14 shows the comparison of the measured mean vibration level and the numerical values for the nominal, high and low stiffness configurations as computed with Nastran. In general,
rather good agreement can be seen through the majority of the frequency spectrum studied for all
three stiffness configurations. Each stiffness configuration follows approximately the same trend
with some slight variation. The results show that a reduction in stiffness leads to an increased
vibrational velocity level and vice-versa. This behavior may be attributed to the coupling to the
acoustic cavities. The stiffer the headliner, the less the impact of the acoustic pressure on the
level of vibration. Below 250 Hz, the low stiffness configuration shows slightly better agreement to the measured results, however above 250Hz, the nominal configuration appears to better
follow the measured curve.
Figure 15 shows the effects of the finite cavity and impedance on the results. Measured results and the nominal stiffness case are plotted for reference. In general, it can be seen that both
removing the passenger cavity and applying an external impedance reduce the peek response of
the headliner at localised maxima. This effect is most prevalent at the four nominal stiffness response peaks in the region from 250-300 Hz. Removal of the surface impedance at the headliner
produces an increased level of vibration across the spectrum, exceeding measured levels for a
large portion of the spectrum. Altering of the magnitude of impedance from 0.5 to 2.0 times
the nominal value had almost no effect on the response compared to the nominal case and these
results are therefore omitted.
Figure 16 shows the effect of boundary conditions and structural coupling on the headliner.
In the case where the front and rear end boundary conditions have been removed, it can be seen
that the curve follows quite well the case of nominal stiffness. Around 150 Hz, the case of
removed boundary conditions shows better agreement with the measured values. Arguably, the
20
same is true above 400 Hz. For the case in which the RBE coupling has been removed, there is
a very clear reduction in vibration levels, and a much poorer agreement between the calculations
and measurement.
Figure 17 shows the measurement data for the outer roof of the structure. In total, 180 points
were measured. Again, as for the case of the headliner, it can be seen that the envelope in the
measurements is limited to approximately 10 dB around the mean.
Figure 18 shows the numerical simulation data for the outer roof panel wherein nominal
headliner properties were used in the model.
Figure 19 shows a comparison of the measured mean vibration level and the numerical mean
vibration level for the model using high, nominal, and low stiffness. For all three cases of stiffness, the general trend is quite similar and it is not obvious which, if any, has a larger effect on
vibration level. Measured data and numerical data show very good agreement, with the exception
of the region below 150 Hz. This maximum deviation is approximately 10 dB.
Figure 20 shows the effect of the passenger cavity and impedance variations on the outer
roof’s vibration level. There is a general good agreement between measurements and numerical
results. While a small amount of variation does exist between the four numerical cases, the
variation is relatively small. This would seem to indicate that for the external structure, the
acoustic effects of the passenger cavity have little effect.
Figure 21 shows the effect of the headliner boundary conditions and attachment on the vibration level of the outer roof. While all three numerical solutions follow quite closely the same
general trend, it is obvious that the rigid coupling between the headliner and the structure deviates
the most from the measured data.
In the majority of the above mentioned figures, a rather good agreement between measurement data and numerical data has been found. Sources found in the literature [18, 19, 20] show
that the difference between the numerical results and the measured data can lie well within the
statistical spread for structural borne noise within larger populations of production vehicles. As
only one vehicle was measured, this hypothesis cannot be tested.
An interesting trend can be noted by observing that both the numerical results for the headliner and outer roof exhibit a somewhat better agreement with the measured data at higher frequencies. An obvious explanation for this result is of course the difference in boundary conditions between tests and simulation.
Within the model, it has been assumed that all intersections between the pillars and the steel
plates are welded completely. This is most likely not the case in the actual structure. Additionally, in the model it has been assumed that all edges of the steel plates are fixed. In the actual
structure, the continuity of the welds may be questionable. Any discrepancy between the boundary conditions of the model compared to the laboratory will of course affect the agreement of
results. This is emphasised for low frequencies.
Another large difference between the model and the measured structure is the acoustic environment. In MWL, the outer sheet metal was in contact with the air in the reverberation room,
while the headliner was in contact with the fluid in the anechoic room. While some attempts to
emulate the anechoic room were made, the effects of the reverberant room were not included.
Results have been presented for calculations using a wide range of properties for the inner
headliner. As may be expected, the variations of stiffness, boundary conditions , and damping
have a larger impact on the behavior of the headliner than on the outer roof. However, interestingly, a tenfold change in the stiffness of the headliner has marginal effect on its vibrational
behavior. Reducing the effect of the passenger cavity also has little effect on the headliner’s
vibrational level.
21
One change that is significant is the removal of the rigid element coupling between the headliner and the steel structure. For both the case of the headliner vibration levels and the outer roof
vibration levels, removal of the physical coupling between the two showed the most pronounced
effect indicating a primarily structure borne transmission being dominant. It is perhaps not surprising that the removal of a coupling between two structures immersed in a fluid will have a
significant effect in the systems vibrational behavior; however that this effect would be the most
important effect regarding the properties of the headliner is significant.
Calculations with variations in impedance as described in section 2.3.5 showed almost no
difference, varying only in the fifth or sixth decimal point and are therefore not included. This
is in itself a quite interesting result, as it would indicate that the damping properties of the headliner do not have a significant effect on the mechanical response of the structure, so long as the
damping is of an approximate magnitude.
The modelling of the headliner performed in this work was at a quite simplistic level and
oversimplifications were no doubt made. Nevertheless, agreement between measurements and
numerical models are quite good.
5. CONCLUSIONS
Sound transmission loss measurements have been performed on a full vehicle and on the
component level. Very good agreement between results for both cases has been found. In certain
frequency areas, glass windows are the most likely cause of reduced sound reduction capability
for a trimmed body panel. Confirmation has been made of the significant contribution to sound
transmission loss by the headliner in the vehicle. Results show that for trimmed body panels,
in-situ measurement is sufficient for measuring the sound reduction index of the trimmed panel.
Numerical methods have also been used to estimate sound reduction index for trimmed body
panels. These results show that geometrically simple models using hierarchical finite element
code can give very accurate and reliable results for the sound reduction capability of trimmed
body panels in the frequency range up to 500 Hz.
Vibro-mechanical testing of a roof structure has also been performed and the vibrational behavior of a roof headliner and outer roof panel have been measured. A finite element model
was constructed with special consideration given to dividing the air cavity within the passenger
compartment into two separate sections and including the headliner. The headliner was modelled
using 3D elements and given equivalent homogeneous properties based on basic sandwich theory. Fluid damping was accomplished using surface normal impedance calculated based on the
assumed construction of the headliner.
Very good agreement was achieved between the measured vibration levels and their numerical equivalents for both the headliner and outer roof panel.
Large changes in stiffness of the headliner have little effect on its vibrational behavior, as
well as altering the damping properties of the headliner has almost no effect on the vibrational
behavior of the system. Removing the damping completely does however affect the systems
behavior.
Applying a surface impedance to the passenger acoustic cavity or removing it entirely from
the model has a slight impact on the systems behavior, mostly in reducing peak vibrational responses due to the cavity. This would indicate that it is necessary to have the cavity present for
predicting actual acoustic phenomena inside a production vehicle.
22
The coupling between the headliner and the structure was found to be the single most important factor of those studied. The presence or absence of a rigid coupling between the headliner
and the surrounding structure has a significant effect on the system response.
The results also show that the material properties of the headliner are not important. As long
as the headliner provides some sort of fluid damping of an approximate magnitude its specific
construction is not a factor in its acoustic performance. Special attention should however be paid
to the method by which the headliner is attached to its surrounding structure. In this model, rigid
links were used as a simplification, however, based on the results of the simulations performed,
it is likely that the stiffness of actual fasteners will impact on the behavior of the headliner and
the surrounding structure.
Results of this work indicate that the standard practice of ignoring the vibro-mechanical impact of trim components within the vehicle may result in incorrect computational results. Two
models have been developed to calculate the sound transmission loss and vibro-mechanical response of a trimmed body component, both of which show very good agreement with measured
results. The accuracy of the modelling methods combined with the simplicity of their implementation would make them excellent candidates for industrial use, which would allow engineers
to better understand the trim as an engineering component rather than a band-aid solution to a
misunderstood acoustic phenomena within a finished vehicle.
6. ACKNOWLEDGEMENTS
This work was performed within the Centre for ECO 2 Vehicle Design with financial support
from the Swedish Agency for Innovation Systems (VINNOVA), KTH, and Saab Automobile AB.
The assistance of associate professor Leping Feng, KTH MWL, in the measurements performed
is also acknowledged.
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[14] P. Göransson. Tailored acoustic and vibrational damping in porous solids – engineering performance in aerospace
applications. Aerospace Science and Technology, 12:26–41, 2008.
[15] P. Göransson. Acoustic and vibrational damping in porous solids. Phil. Trans. R. Soc. A, 364:89–108, 2005.
[16] UGS Corporation. NX Nastran Quick Reference Guide, 2007.
[17] UGS Corporation. NX Nastran Advanded Dynamic Analysis Users Guide, 2007.
[18] M.S. Kompella and R.J. Bernard. Variation of structural-acoustic characteristics of automotive vehicles. Noise
Control Engineering Journal, 44(2):93–99, 1996.
[19] E.Hills, B.R.Mace, and N.S. Ferguson. Acoustic response variability in automotive vehicles. Journal of Sound and
Vibration, 321:286–304, 2009.
[20] J.-F. Durand, C. Soize, and L. Gagliardini. Structural-acoustic modeling of automotive vehicles in presence
of uncertainties and experimental identification and validation. Journal of the Acoustical Society of America,
124(3):1513–1525, 2008.
24
Introduction
Paper B
71
STRUCTURAL-ACOUSTIC DESIGN OF A MULTI-FUNCTIONAL
SANDWICH PANEL IN AN AUTOMOTIVE CONTEXT
Christopher J. Cameron , Per Wennhage , Peter Göransson , Sven Rahmqvist†
Centre for ECO2 Vehicle Design
KTH Aeronautical and Vehicle Engineering,
Kungliga Tekniska Högskolan (KTH)
SE-100 44 STOCKHOLM, SWEDEN
e-mail: [email protected], web page: http://www.eco2vehicledesign.kth.se
† Technical
Integration Engineer - Body Structure and Closures
Noise & Vibration Center
Saab Automobile AB
A2-1 TRV-05
SE-461 80, TROLLHÄTTAN, SWEDEN
ABSTRACT: This paper deals with the design and weight optimization of a multi-functional
vehicle body panel in an automotive context. An existing vehicle design has provided functional
design requirements regarding static, dynamic, and acoustic behaviour of the components of a
car roof. A novel, multifunctional panel is proposed which integrates the component requirements present in a traditional roof system within a single module. The acoustic properties of two
configurations of the novel panel are examined using numerical methods including advanced
poro-elastic modelling tools compatible with Nastran, and compared with numerical results of
a finite element model of the existing construction.
KEY WORDS: Sandwich Structures, Acoustic Modelling, Design Optimization.
INTRODUCTION
Common to all vehicles which transport either people or goods, is the need for certain functionality, such as protection and comfort, usually provided by a vehicle compartment, with
different requirements depending on the vehicle application. For a passenger carrying vehicle, the compartment in general consists of the following components: body structure, acoustic
treatments, and interior trim. Traditionally, these components have been designed, produced
and assembled separately, each fulfilling different aspects of the protective functions, almost
without exception with considerable weight penalty and often times with poor manufacturing
efficiency and ergonomics during assembly.
To alleviate this, an approach based on simultaneous consideration of several such functions has been investigated. The main objective was to explore the potential benefits that may
1
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
be realized in a multi-functional, integrated multi-layered sandwich design. In this study, the
performance in terms of noise, vibration, and harshness (NVH) characteristics and structural
requirements of a proposed multi-functional component has been examined in an automotive
context.
The vehicle of study in this case was a Saab 9-3 SportCombi. In selecting a panel for the
study several areas of the vehicle were considered. The roof panel was chosen because it was of
relatively simple geometry and relatively platform independent. Other panels such as the hood,
doors and floor panel were considered, but deemed too constrained by regulatory legislation
[1, 2] and too geometrically complex for an initial study. The roof structure is also subject to
legislation however to a lesser extent [3].
In the frequency range below 500Hz, the primary source of interior noise is structure borne
vibration from sources such as the power train or suspension system. Booming noise is the
name given to the acoustic resonances within a vehicle’s passenger cavity, usually under the
frequency of 250 Hz [4]. The air cavity within the passenger compartment of a typical European
station waggon will have a first acoustic mode in the region of 65-75Hz [5]. Even very small
levels of vibration across large panel areas (such as the roof) can cause significant increases in
sound pressure inside a vehicle interior [6] and potentially excite the cavities resonant modes of
acoustic vibration. This is a major cause of discomfort for the passengers and for this reason,
the roof is an acoustically relevant panel for study.
While a certain amount of local damping can be obtained by carefully designing joints within
the structure [7], the traditional method of controlling structural borne vibration is with damping treatments in the form of visco-elastic material layers [8] . These damping treatments vary
in form (free layer, constrained layer, bake-on,etc) and effectiveness, and a great deal of experimentation is usually involved in deciding the location and thickness of the damping layers
[9, 10, 11].
In higher frequency ranges, air borne sound is prevalent, and sound management within the
passenger compartment can be controlled via absorption [12]. This can be accomplished with
absorbent insulation, interior trim components, seats, and floor matting [5]. Within the roof
structure of a conventionally designed vehicle, the headliner and absorbent insulation coupled
with the air gap between the headliner and the outer sheet metal are key components in minimizing unwanted external air borne sound from entering the vehicle.
In the current paper, which is an extension of work originally presented at ICSS-8 [13], a
design concept is discussed wherein the components shown in Figure 1 are replaced with a
multi-layer sandwich construction. By integrating the functionalities of structural components,
acoustic treatments, and trim components into a single module which can offer mass savings,
potential for acoustic improvements, and reduced assembly line time and effort, a novel method
of addressing the requirements of a passenger enclosure were addressed. Two configurations
were developed, one with a perforated inner face sheet and one without, which represented
slightly different methods of dealing with acoustic fluid-structure interaction. Both configu2
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
rations were mass optimized according to current design requirements. Non–linear buckling
analysis was performed to evaluate transverse load capacity. Finally, the NVH characteristics
of the two configurations are evaluated numerically and compared with the conventional construction. Results of the optimization, buckling analysis, and acoustic analysis are given as well
as a discussion of their interpretation.
Outer Sheet Metal Anti-Flutter Adhesive
Anti-Flutter Adhesive
Front Transverse Beam
Headliner
Front Header Beam
Rear Transverse Beam
Rear Header Beam
Acoustic Absorbent
Panel Damping Treatment
Figure 1: A Schematic cross-section of a conventional roof construction. Components in italics are not altered or
replaced in the new concept.
METHOD
Engineering documentation provided by Saab Automobile AB (SAAB) was used together
with static and dynamic finite element analysis of a the existing construction in order to establish
the current state of the art. NXNastran 6.0 was used for static displacement analysis and modal
analysis. Abaqus 6.7EF was used for non–linear buckling analysis.
A novel design was suggested and two configurations of the new panel were weight optimized against a set of static and dynamic constraints.
Non-linear buckling analysis of the optimized panels was performed to asses their in-plane
loading capability in comparison to the existing construction.
NVH analysis was performed using the previously defined structural models and a vehicle
fluid cavity, i.e. the air within the passenger compartment. Frequency response analysis including coupled fluid-structure effects was the method chosen. A model corresponding to the
existing construction including the effects of the headliner trim was used to establish baseline
behaviour. A second model corresponding to the proposed novel sandwich construction with
integrated acoustic trim was created including new capabilities of modelling fluid-structure interactions in low-density poro-elastic foam materials. The acoustic performance of both the
3
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
baseline and concept configurations was assessed by exciting a point within fluid the cavity
with an acoustic load and calculating the average sound pressure in the entire cavity.
BASELINE CONFIGURATION
Structural Modelling
A full vehicle model of the welded steel body and framework,often referred to as body in
white (BIW), was provided by SAAB. As part of a testing program, SAAB also provided a
complete roof assembly which had been removed from a production vehicle. The full vehicle
FE model was reduced to match the provided roof structure as closely as possible . Figure 2
shows a the roof as removed from the vehicle and the FE model geometry. Note that in Figure
2 glass windows from the production vehicle have been replaced by medium density fibreboard
(MDF) panels for acoustic testing purposes.
Figure 2: Roof structure removed from car and FE model.
The baseline configuration consists of short sections of the A, B, C, and D pillars, as well
as longitudinal and lateral roof beams. The model used a combination of shell, solid, and rigid
elements to represent various components such as sheet metal, adhesives, and spot welds.
Structural Target Setting
Static and dynamic stiffness requirements for body panels and the complete body in white
were defined in the provided engineering documentation. Two requirements most relevant for
the roof panel dictated static deflection under a prescribed load and minimum frequency for the
first eigenmode of the panel.
Structural elements of the roof structure were not defined on an individual basis but assessed
globally in the complete body in white. Further examination of the structural components in the
roof assembly, in this case the lateral roof beams, was deemed necessary to further develop the
4
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
structural requirements for the new design.
Buckling analysis was considered a suitable method to evaluate the response of the roof
beams located approximately between the B and C pillars in lateral loading. The front beam
consists of a single pressed sheet metal component spot welded at each end to the longitudinal
rails. A connection to the roof sheet metal is achieved using an elastic adhesive. The rear beam
consists of two stamped steel components spot welded together forming a closed profile. Again,
spot welds connect the beam to the longitudinal rails and a connection to the outer sheet metal
is achieved by elastic adhesive. Both beams were analyzed using the modified Riks method in
Abaqus.
The modified Riks method implemented in Abaqus standard is an incremental method of
solving non-linear static problems such as buckling with snap through behaviour [14, 15]. By
using a load proportionality factor and simultaneously varying the load and displacement, and
calculating an equilibrium solution, the algorithm is capable of following the unstable collapse
of a structure based on the assumptions that the response is smooth and no sudden bifurcations
exist [16]. This seemed an appropriate method for the buckling analysis due to the nature of the
problem and the geometry of the beam; slightly curved, thus having an initial instability.
As the rear beam is a closed profile rather than a pressed sheet it withstood a significantly
higher buckling load and was deemed the more appropriate reference component.
Buckling analysis of the rear beam was performed in the following manner. The lower edge
of one end of the beam was constrained in the translational degrees of freedom (DOF) but
allowed to rotate. On the opposing end of the beam, the global x and z translational degrees of
freedom were restricted, and a unit load in the global y direction was applied. For clarification,
see Figure 3.
Nodal Load
x
DOF x, y, z = 0
y
DOF x, z = 0
z
Nodal Load
DOF x, y, z = 0
DOF x, z = 0
y
Figure 3: Rear beam boundary conditions and snap through buckling
To enable the large deformations present in the buckling analysis, plasticity was introduced
into the model. Elastic, perfectly plastic material behaviour was modelled in Abaqus by spec5
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
ifying the yield stress, above which no further accumulation of stress occurs for plastic strains
[16, 17].
A global y displacement of 200 mm for the end of the beam to which the load was applied
was used as a parameter to stop the iterations during the modified Riks analysis. Within this
distance, a maximum value for the load proportionality factor was reached, and snap-through
buckling of the beam achieved (see Figure 3). By multiplying the maximum value of the load
proportionality factor with the applied load for the buckling analysis, a value of the critical
buckling load of the beam was obtained.
Modelling of Headliner Trim
In coupled fluid-structure analysis of the full vehicle, industrial practise is to ignore the
acoustic effects of the inner headliner. The mass contribution of the inner roof trim may possibly be accounted for by adding a distributed non–structural mass to the interior of the roof
sheet metal, or it may be ignored completely. While the headliner does have sound absorption
capabilities due to the integration of open celled foam, at frequencies below several hundred
hertz the thickness of the foam provides little contribution in relation to the other interior trim,
such as the seats or carpet. While some limited work has been done in analyzing the effects of
the roof cavity-headliner interaction [18] its effect is not well understood and seldom modelled
numerically. The majority of information available regarding the acoustic or structural properties of headliners comes from the headliner manufacturers themselves [19, 20]. A method for
numerically analyzing the acoustic properties of the acoustic trim would be an interesting step
towards an independent in-situ design methodology and so was developed as part of the work
in this paper.
The headliner studied was a sandwich construction consisting of two stiff fibre reinforced
membranes separated by a foam core. On the interior side of the sandwich a second layer of
relatively soft open–celled foam and a final layer of perforated fabric were used to provide sound
absorption and an aesthetically appealing surface. Materials such as glass fibre reinforced plastics and polyurethane foam are often used in headliner applications [19, 20]. As uncertainties
in the exact material composition existed, experimental testing was performed to obtain actual
mechanical properties. Figure 4 shows a cross-section of the headliner in question.
A square approximately 35cm by 35cm was removed from the centre section of the headliner
where the thickness was determined to be most uniform. The upper and lower membrane were
peeled from the structural foam core, and the soft inner foam layer was peeled from the inner
membrane. Each layer was trimmed to a square 25cm x25cm. The structural foam, assumed to
be urethane, was weighed and its density calculated assuming a uniform thickness of 6.0 mm.
Tensile testing was performed according to ASTM standards [21]. This test method was
used because the inner and outer membranes were of a glass fibre reinforced construction. Tabs
for clamping were not considered necessary as the aim of the testing was to gain basic stiffness
6
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Figure 4: Cross-section of headliner construction
information not ultimate strength. The same testing method was used for testing the foam
samples. While the choice of this test method for the foam samples was not optimal, it was
deemed accurate enough to gain an estimate of the foams properties.
Ten samples measuring 25mm by 250mm were cut from the outer membrane, urethane foam,
and inner membrane respectively. Samples were placed in pneumatic clamps fitted to an Instron
screw driven Universal Testing Machine. An extensometer and a 30kN load cell were used to
record the load vs displacement behaviour of the samples. The extensometer was attached to
the sample using rubber bands. A picture of the sample in the test rig can be seen in Figure 5.
Displacement control was used to regulate the rate of loading of the specimens.
Stress vs strain plots were obtained by post–processing the test results using Matlab TM .
Within the initial elastic region of the deformation, a first order polynomial curve was fitted
to the data to achieve a value for the Young’s modulus. This was repeated for each of the test
specimens, and average values for each layer were calculated. Tensile Young’s moduli of 9.1
GPa for the outer membrane and 4.8 GPa for the inner membrane were obtained. A tensile
modulus of 8.8 MPa was obtained for the urethane foam.
For a glass fibre reinforced phenolic composite, values of Young’s modulus in the range 4.5
- 7.5 GPa, depending upon whether the fibres are continuous or chopped, can be found within
the literature [22]. This agrees well with test data for the inner and outer membranes, however
it implies that another matrix material or some additional form of reinforcement is likely used
in the outer membrane.
A density of 55.7 kg/m 3 was obtained for the urethane foam. According to [23] the relationship between the polymeric solid and its corresponding open–celled foam can be described as
in Equation (1).
7
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Figure 5: Tensile testing of headliner components
Ef oam
≈
Esolid
ρf oam
ρsolid
2
(1)
Using the relationship in Equation (1) for the density calculated from the sample and using
properties for solid polyurethane found in [23], a Young’s modulus for the foam of 3.45 MPa
was obtained. A compressive modulus of 10 MPa was listed in [22] for a polyurethane foam
of slightly lower density (30kg/m 3). This data would seem to indicate a somewhat exaggerated estimate of the urethane foams properties achieved by tensile testing or perhaps a slightly
different chemical makeup of the structural foam.
In the vehicle, the headliner effectively separates two fluid cavities, the fluid within the passenger compartment and the fluid between the headliner and the outer sheet metal. In order
to achieve the physical distance between the two cavities, and to avoid mesh geometry and
coupling difficulties between the fluid and the headliner, it was necessary to model the headliner using solid elements. In reality, the thickness of the headliner varies somewhat across the
panel, due to the manufacturing process which often involves pressing [19], however a uniform
thickness model was considered sufficient.
Accurate modelling of each individual layer of the headliner as shown in Figure 4 using
only solid elements would be computationally quite expensive due to the small thicknesses and
necessity for a great number of elements. Hybrid solid-shell sandwich configurations were also
problematic due to the restrictions of the fluid-structure coupling capabilities of Nastran.
A modelling approach which could eliminate the requirement for excessive numbers of elements and which was more suitable to an industrial environment was desired. This was achieved
8
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
by modelling the headliner with equivalent homogeneous isotropic properties based on the mechanical properties measured and basic sandwich theory.
The upper three layers within the headliner make up a classical sandwich structure with
dissimilar face sheets. The stiffness contribution of the aesthetic fabric treatment and the soft,
porous acoustic foam to the overall stiffness of the headliner can be ignored.
Flexural rigidity for a unit width sandwich beam of arbitrary cross section with dissimilar
face sheets can be expressed in the following manner [24]:
D=
Ez 2 dz =
E1 t31 E2 t32 Ec t3c
+
+
+ E1 t1 (d − e)2 + E2 t2 e2 + Ec tc
12
12
12
2
tc + t2
−e
(2)
2
Where:
e=
E1 t1 d
E1 t1 + E2 t2
d−e=
d=
E2 t2 d
E1 t1 + E2 t2
t1
t2
+ tc +
2
2
The variable t denotes thickness, and E the Young’s modulus for each respective layer.
Subscripts 1 and 2 denote the upper and lower face sheets. Subscript c denotes the core material.
In this case, the face materials are the two fibre reinforced membranes and the core the urethane
foam layer. Lower case z denotes the vertical coordinate of the sandwich cross-section where
z = 0 is the neutral axis of the sandwich structure.
A number of square samples were cut from the headliner and the thickness for each of the
layers were measured. Thicknesses of the membranes, inner foam layer, and porous fabric layer
were constant. The thickness of the structural foam varied from 1.5 mm to 6.0 mm, however
based on samples taken and an estimate of compressed to non-compressed area, a nominal
thickness of 4.0 mm was used in the FE model. The inner foam/fabric layer was constant at 2.0
mm.
Two layers of hexagonal solid (brick) elements were used to construct the headliner model
following the geometry of the headliner’s inner surface. The total thickness for the entire headliner in the model was 6.0 mm. Holes for attachment of lighting, etc., were ignored.
Using values of flexural rigidity calculated for an estimated core thickness of 4.0 mm and the
measured stiffness for each of the various layers together with the mesh thickness of 6.0 mm,
an equivalent value of Young’s modulus, E equiv , for the solid can be obtained as follows:
9
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Eequiv = D
D
= (6.0)3 = 622.0[MP a]
z 2 dz
(3)
3
Equivalent density was calculated by using the actual mass of the headliner and the volume
of the headliner model according to:
ρequiv =
Mactual
Vmodel
(4)
In the vehicle, the headliner was equipped with wiring and lighting systems. This mass
was accounted for within the equivalent density calculation. The local stiffness effects of these
components were ignored.
The headliner was attached to the structural model with rigid body elements at the actual
attachment points. Nodes along the bottom front and rear edges were locked in translational
degrees of freedom to approximate in vehicle conditions.
Acoustic Cavity Modelling
The internal geometry of the BIW was used to create air cavities for the two different analysis
cases. For the conventional construction, the air cavity of the enclosed passenger compartment
was split into two fluid volumes; fluid within the cab but below the headliner, and fluid between
the headliner and the outer sheet metal of the roof. The two fluid cavities are connected by air
channels within the A, B, C,and D pillars. These channels provide a fluid coupling between
the cavities and the headliner provides a fluid–structure interface. To account for the acoustic
absorption of the headliner, an acoustic impedance was applied to the cavity face in contact
with the interior side of the headliner. Validation of the entire model including the headliner
and split cavity was performed using acoustic and vibro-mechanical testing at the Markus Wallenberg Laboratory for sound and vibration research at KTH. Complete results are not included
here, however the results of testing indicated that the modelling method agreed very well with
experimental results up to 500 Hz [25].
For the case of the sandwich panels, a single cavity was used based on the same external
geometry of the BIW and the underside of the sandwich panel. The same cavity was used for
the evaluation of both sandwich panel configurations.
The cavity for the conventional configuration as well as the sandwich configuration were
essentially identical in outer geometry and total volume. The cavities were mesh incompatible
(i.e. no coincident nodes or elements) with the structural mesh geometry and consisted of
approximately 1.5 million CTETRA elements each. Typical properties for air were used for
describing the fluid cavities. Figure 6 shows a section view of the two models used for acoustic
calculations.
10
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Existing Structure
Roof
Air Cavity
Headliner
Sandwich Panel
Passenger Compartment
Air Cavity
Passenger Compartment
Air Cavity
Figure 6: Partial section view of the two structural–acoustic models
Acoustic Target Setting
Acoustic targets for the new concept were defined using the FE model of the baseline structure.
Purely acoustic loading of the structure was achieved by applying an acoustic pressure to a
single node within the vehicles passenger cavity. The node was located approximately at the
drivers head and excited over the frequency range of 100-500 Hz in 2.5 Hz steps. The average
acoustic pressure within the passenger cavity at each frequency was calculated using 270 nodes
randomly distributed throughout the passenger cavity for the conventional configuration.
While this load cases was rather simplistic, it was deemed suitable for a preliminary NVH
assessment.
MODELLING OF THE NEW PANEL CONCEPT
Both configurations of the proposed concept consisted of four components; external face
sheets of isotropic material, a structural foam layer of typical polymeric sandwich core foam,
and a single layer of lightweight, open–celled acoustic foam (see Figure 7). While structural
polymer foam does offer a certain amount of damping [26], these properties were ignored within
the model, as the damping treatments in the conventional model were also ignored.
In one panel configuration, the interior face sheet was perforated to allow fluid interaction
between the passenger cavity and the acoustic foam, thus providing sound absorption in the
interior of the panel. Geometry of the perforations is shown in Figure 7.
The non-perforated face sheets were modelled using aluminium because it is a lighter alternative to steel and is considered as a suitable material for mass production in the automotive
industry [27]. For the structural optimization, both foam components were modelled as homogeneous elastic solids. Properties of a typical closed cell polymer foam sandwich core material
were used for the structural foam component in the model. The acoustic foam modelled was
11
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Outer Face Sheet
d
Structural Foam
Sy
Acoustic Foam
y
x
Inner Face Sheet
Sx
Figure 7: The four layer sandwich structure and perforation geometry
considerably softer than the other components. Material properties of the various layers as used
in numerical analysis can be seen in Table 1.
Perforations on the interior face sheet are advantageous from an acoustic perspective because a proportion of incident sound waves pass into the structure and are absorbed rather than
reflected. By allowing the air to flow within the open celled acoustic foam, additional structural
and acoustic damping can be obtained. This phenomena is explained in detail in [28, 29]. As
the degree of perforation in the face sheet is increased, so is the level of fluid-structure interaction between the passenger compartment fluid cavity and the absorbent foam (see Figure 8),
however the structural capability of the face sheet is obviously reduced, a compromise which
needs to be monitored closely.
Figure 8: Incident sound wave behaviour for non-perforated and perforated face sheets
For the non-perforated sandwich panel, all four layers were considered isotropic and homogeneous.
For the perforated inner panel, modelling of individual perforations of such small geometry
would create an extremely large number of elements in the model and make later acoustic analysis extremely difficult due to structural–acoustic coupling. Instead, a method of modelling the
inner face sheet using a homogeneous mesh with perforation-equivalent properties was desired.
For a panel perforated with circular holes in a rectangular pattern as in Figure 7, the relative
density ρ∗ , based on the pre-drilled panel volume, can simply be calculated using the materials
bulk density ρ and the hole pattern geometry. This relation is shown in Equation 5:
12
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Outer Face Sheet
Material
E (MPa)
G (MPa)
ρ (kg/m3 )
ν
Structural Foam
Aluminium
70 000
26 000
2710
0.3
Acoustic Foam
Inner Face Sheet
Closed Cell Foam Open Cell Foam
135
0.10
35.0
–
100
30
0.4
0.1
Aluminium
70 000 [46 460]
26000 [–]
2710 [2170]
0.3 [0.27]
Table 1: Material properties in FE model for sandwich panels. In cases where properties differ, perforated values
are shown inside square brackets
π
Sy − d
Sx − d
ρ =ρ 1−
1−
1−
4
Sx
Sy
∗
(5)
For a thin plate ( t d) with holes in a rectangular pattern ( Sx = Sy ) the literature [30, 31]
provides a relationship between the bending stiffness D of a perforated and non–perforated
plate as follows:
D∗
=
D
π
1−
4
2 (2Sx −d)/0.8Sx
Sx − d
1−
Sx
(6)
Where D is simply:
D=
E ∗ t2
12(1 − ν 2 )
(7)
Assuming then that the effect of the change in Poison’s ratio (ν) is negligible, (in addition
to the plate being very thin, according to the literature, for the hole pattern used there is only a
0.1% reduction in Poisson’s ratio [32]) the same relationship can be used to describe the relative
Young’s modulus E ∗ of the perforated plate based on hole geometry as shown in Equation (8) :
∗
E =E
π
1−
4
2 (2Sx −d)/0.8Sx
Sx − d
1−
Sx
(8)
In this study the values d = 2.0 mm and S x = Sy = 4.0 mm were used for the perforated
inner face sheet.
For the analysis performed, the simplifications caused by using equivalent isotropic materials
instead of modelling a perforated plate caused little loss in accuracy in return for exceptional
decreases in modelling complexity and calculation time. It should be noted that effects of
13
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
stress concentrations at the perforations were not accounted for, however the effect of such
concentrations on the analysis performed is expected to be insignificant.
Mesh geometry for the outer sheet metal in the conventional roof was used to construct an
FE model of a sandwich panel. Each panel was modelled using approx. 235000 three dimensional CHEXA [33] elements. Two different sets of boundary conditions were used for the
panel analysis during optimization. For the static displacement analysis, translational degrees
of freedom x, y, z for all nodes along the bottom edge of the panel were constrained. For the
modal analysis, it was necessary to constrain additional nodes along the sides due to the soft
acoustic foam layer. Translational degrees of freedom x, y, z of all nodes along the side edges
and rear edge were constrained in addition to the lower front edge. A comparison of modal
behaviour with the existing structure showed good agreement using these boundary conditions.
See Figure 9 for clarification.
Right Edge
Front Edge
Rear Edge
z
x
y
Left Edge
All Side Nodes
Front Edge
x
Lower Front Edge Nodes
Figure 9: Diagram of complete sandwich panel
STRUCTURAL OPTIMIZATION
Both panel configurations were weight optimized using the method of moving asymptotes[34]
implemented in the optimization software Xopt developed by Alfgam Optimering AB 1 . Geometry manipulation was achieved by the use of a python script to alter the nodal coordinates of
elements.
Design constraints were placed on the static displacement under load as well as the frequency
of the first mode of the panel. Thickness of the internal face sheet, external face sheet, and structural foam layer were chosen as design variables. Changes in thickness were evenly distributed
through each of the element layers in a given material in an effort to maintain an even FE mesh.
The lower limit for each layers thickness was defined so that the aspect ratio of 3D elements
would not exceed 50. At the outset of optimization, this limit was considered sufficiently thin
as to be far below any probable solution.
1
www.alfgam.se
14
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Outer Face Sheet
Min thickness (mm)
Max thickness (mm)
Final thickness (mm)
0.2000
12.0000
0.2000
Structural Foam Acoustic Foam
0.5000
20.0000
4.6004[5.088]
15
15
15
Inner Face Sheet
0.2000
7.0000
0.2000
Table 2: Optimization variables for sandwich panels. In cases where values differ, perforated values are shown
inside square brackets
Perforated Panel
Optimized Mass(% of Conventional)
17.643
Active Constraint
Static displacement
Non-Perforated Panel
18.215
Static displacement
Table 3: Optimization results for perforated and non-perforated panels
Table 2 shows the final thickness of the optimized panel. Inner and outer face sheets for both
panels were reduced to the minimum allowable thickness. Thickness of the structural foam
varied approximately 10% between the perforated and non–perforated panel. Acoustic foam
thickness was held constant at 15 mm.
Table 3 shows further results of the optimization. Final mass of the panels varied by less
than 1% in comparison to the conventional construction. Results show that static displacement
rather than natural frequency was the limiting factor for the optimization of the panels. Convergence to a stable solution was achieved within 10 iterations. Both panels fulfilled displacement
constraints and exceeded frequency constraints by approximately 15%.
PANEL BUCKLING ANALYSIS
After the weight optimization was completed, the panel’s resistance to buckling during inplane loading was examined using the modified Riks method in Abaqus.
Loading and boundary conditions for the panel were as follows.
Nodes along the bottom edge of one side of the panel were clamped by restricting all translational degrees of freedom. Nodes along the bottom edge of the opposite side were restricted
from moving in the x and z directions, as was the case for the beam. A unit nodal load was
applied in the y direction to all nodes which were locked in the x and z directions. As was
the case for the beam buckling analysis, plasticity was also introduced for the materials in the
sandwich panels. Typical yield stress values for aluminium and structural foam were used. No
plasticity was implemented for the acoustic foam as its contribution to stiffness was minimal.
Two stop criteria for the panel buckling analysis were used. The same maximum displacement criterion was applied to the panel as to the beams. Additionally, a maximum load proportionality factor yielding the same maximum buckling load as in the beam analysis was used.
15
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Analysis of both panels resulted in the maximum load proportionality factor being exceeded
before the maximum deformation occurred, i.e. both panels were capable of supporting the
maximum buckling load without snap-through buckling.
ACOUSTIC EVALUATION
Finite element analysis was used to compare the acoustic properties of the two optimized
panels to each other, and to the current state of the art construction. As previously mentioned,
two different models were necessary in order to carry out this analysis; one model for the
current passenger compartment including the headliner and one model for the sandwich panels
with integrated acoustic treatments.
Setup of Analysis
The sandwich panel model consisted of the sandwich panel geometry and the passenger fluid
cavity. For the case of the conventional construction, the partial vehicle model was included in
addition to the roof and passenger fluid cavities. For clarification, refer to Figure 6. Boundary
conditions were placed on the structural components only for acoustic analysis. For the sandwich panels an attempt to emulate in–service conditions was made by restricting all nodes along
both the sides and the rear edge of the panel in x, y, z direction in addition to the nodes along
the front lower edge of the panel. For the conventional construction, the bottom of the pillars
were constrained in x, y, z.
The acoustic volume was coupled to the structure via automated algorithms in Nastran [35].
For a standard fluid–structure coupling, the translational degrees of freedom in a solid element
are linked to the first translational degree of freedom in a fluid element which is interpreted
as pressure [36]. These standard fluid structure couplings were used for the non-perforated
sandwich panel, and the standard construction in analysis.
For the case of the perforated sandwich panel, the software CDH\EXEL by CDH AG2 was
used in combination with NXNastran 6.0. CDH\EXEL is a proprietary software which augments the standard functionality of Nastran in coupled fluid–structure analysis by adding a
fourth degree of freedom to solid elements matrices representing open cell porous materials.
Frequency dependant material properties can be defined in a way not previously possible with
Nastran. The augmented structural elements matrices are used to calculate the effects of fluid
pressure within a porous media. As part of the CDH\EXEL suite, CDH\CONNECT was used
to automatically produce the coupling equations (Multi–Point Constraints(MPC)) between the
fluid cavity and the porous media as well as the porous media to the conventional solid elements.
For a given node in the porous solid, the resulting DOF matrix will appear as in Equation (9)
2
http://www.cdh-ag.com/de/exel.html
16
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
⎡
⎢
⎢
⎣
N astran
Dij (ω)
solid
+Exel
solid Dij (ω)
Exel
coupling D4j (ω)
symm
Exel
f luid D44 (ω)
⎤
⎥
⎥
⎦
(9)
inode
jnode
The acoustic foam and the perforated face sheet in the perforated sandwich panel are modelled using the porous, elastic solid model. Properties such as frequency dependancy and flow
resistivity were taken from laboratory testing performed at KTH.
Results of Acoustic Analysis
Frequency response analysis for the sandwich panel configurations was performed in the
same manor as for the conventional roof. For these calculations, acoustic response within the
cavity was calculated using the sound pressure at approximately 370 randomly situated points
within the cavity. Results for both conventional and sandwich configurations can be seen in
Figure 10.
Conventional Roof
Sound Pressure [dB]
Perforated Panel
Non-Perforated Panel
100
150
200
300
350
250
Frequency [Hz]
400
450
500
Figure 10: Average sound pressure in cavity vs excitation frequency (Y-axis 5 dB steps)
17
Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
Conventional Roof
Sound Pressure [dB]
Perforated Panel
Non-Perforated Panel
100
150
200
250
300
350
Frequency [Hz]
400
450
500
Figure 11: Average sound pressure in cavity vs excitation frequency (Y-axis 5 dB steps)
Looking at the results in Figure 10 it can be seen that the general behaviour of all three
configurations is quite similar. This result is, from an acoustic standpoint, very significant;
despite the fact that mass has been drastically reduced in the system, no noticeable degradation
of the acoustic environment has taken place.
More detailed inspection of Figure 10 reveals that while the step in excitation frequency is
relatively small (2.5 Hz) at certain points, the response levels off somewhat drastically, indicating that some resonance peaks have been slightly missed. While this is arguably a point for
further investigation, it is unlikely that higher frequency resolution would yield a significant
change in the overall response.
Figure 11 shows the same results as obtained in Figure 10, however levels have been averaged over 10 Hz intervals. Here, the differences between the conventional and sandwich
configurations are much clearer. Figure 11 shows without doubt that no degradation of the
acoustic performance has taken place in spite of the significant reduction of mass. It would also
appear, that in the frequency range above 300Hz, the sandwich constructions in fact perform
better overall than the conventional design. Differentiating between the perforated and nonperforated configuration is somewhat more difficult. At some frequencies the perforated panel
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Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
appears to perform better, and at others the non-perforated.
DISCUSSION
From a design perspective, it is interesting to note that during the optimization, the active
constraint was that of static displacement and not dynamic stiffness. It is also interesting to note
that the final thickness of the face sheets is very thin and would likely lead to handling problems
in production. In this case, the thickness of the structural foam was an active variable. Based on
these results, it would be interesting to further investigate the effects of altering the structural
foam or face sheet material properties.
Buckling analysis of the optimized panels shows that despite a non-conventional sandwich
construction, both sandwich panels are capable of supporting an equivalent buckling load compared to that of the transverse beams that the sandwich would be replacing. For this analysis, it
has been assumed that transverse loading would be evenly spread across the entire length of the
sandwich panel. While this may hold true for a number of load cases, it would seem a logical
next step to investigate more localized loading behaviour.
One area of debate is that of the boundary conditions used in analysis of the sandwich panels.
While a great deal of effort has been made in trying to model the two configurations as similar
as possible, it is extremely difficult to apply exactly similar boundary conditions to two fundamentally different constructions. Due to the primitive stage of development of the concept
it could not be included in the framework of the conventional roof and there was little other
choice than to use the boundary conditions described. The effects of variations in the boundary
conditions on the overall output of the work are considered to be minimal.
From an acoustic perspective, the results as presented in Figures 10 and 11, are very promising. A significant reduction in mass of the system has taken place with no degradation of the
acoustic performance. Results would even seem to indicate a slight improvement in performance in certain frequency ranges.
Throughout the optimization the acoustic characteristics of the panel have remained static;
a fixed acoustic foam thickness and fixed perforation pattern have been used. While it is difficult to differentiate the superiority of the perforated or non-perforated sandwich configurations,
what can be said with certainty is that while the non-perforated concept represents a fixed minima in acoustic performance via absorbance, the perforated configuration shows promise in that
it offers room for improvement. Results of the structural optimization indicate that the interior
face sheet can afford a significant reduction in stiffness, and thus a significant increase in the
degree of perforation. This would be advantageous from an acoustic perspective. The significant reduction in mass for the system also allows for a large design space regarding future
optimization of the acoustic functionality while still reducing weight.
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Christopher J. Cameron, Per Wennhage, Peter Göransson and Sven Rahmqvist
CONCLUSIONS
Two different configurations of sandwich panel have been proposed, and weight optimized
against a set of structural requirements obtained from engineering documentation and analysis
of an existing verified FE model. Each panel consists of four layers; two face sheets, one layer
of acoustic foam, and one layer of structural foam. For one of the panels, the inner face sheet
is perforated. The effect of the perforations on the weight optimization has very little effect
on the outcome of the structural optimization, both panels varying only slightly in mass and
thickness. After optimization, the panels were evaluated using non-linear buckling analysis to
asses potential to support transverse loading. Finally, the acoustic properties of the panels are
assessed over a range of frequencies and compared with the current state of the art.
The concept of a multifunctional body panel having structural and acoustic functionality has
been explored, and results show promise. A reduction in mass of more than 80% compared to
the conventional configuration was achieved for both sandwich configurations while still fulfilling static and dynamic stiffness constraints. Both sandwich panels are capable of sustaining
a uniform transverse in–plane load equivalent to the maximum buckling load of the rear transverse beam of the conventional construction. Coupled fluid structure analysis shows that both
sandwich configurations behave similarly to the conventional configuration and despite the vast
reduction in mass, no acoustic degradation occurs and in fact a small improvement may have
been achieved. Results of the optimization yield a broad design space for future structural and
acoustic improvements regarding the materials and configuration of the structural components
and the acoustic treatment.
ACKNOWLEDGEMENTS
This work was performed within the Centre for ECO2 Vehicle Design with financial support
from the Swedish Agency for Innovation Systems (VINNOVA), KTH, and Saab Automobile
AB. The financial support is gratefully acknowledged.
Additionally, the generous provision of the CDH\EXEL software by CDH AG and the assistance of Mr. Mladen Chargin is hereby gratefully acknowledged.
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