acoustic radiation of an automotive component using multi...
TRANSCRIPT
IN DEGREE PROJECT VEHICLE ENGINEERING,SECOND CYCLE, 30 CREDITS
, STOCKHOLM SWEDEN 2020
Acoustic Radiation of an Automotive Component using Multi-Body Dynamics
SHAYAN AGHAEI
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES
ACOUSTIC RADIATION OF AN AUTOMOTIVE
COMPONENT USING MULTI-BODY DYNAMICS
Vehicle Engineering
Master Thesis
Shayan Aghaei
GKN
KTH Royal Institute of Technology
October 2020
1
Acknowledgements
Firstly, I’d like to express my gratitude to Stefano Orzi and Eva Lundberg at GKN for their
guidance and support throughout the duration of this thesis. Secondly, I’d like to thank
Shivanand Ambalavanan, Rafal Czech and Ravi Bandlamudi for their excellent advice and
technical support.
A huge thanks to Ulf Carlsson, my supervisor at KTH, who provided me with excellent insight
and guidance. Also, thank you to Lars Drugge for his advice throughout the project.
Finally, but my no means least, thank you to my friends and family for their unwavering
support.
2
List of Abbreviations
AWD . . . . . . . . . . . . All Wheel Drive
BC . . . . . . . . . . . . . . Boundary Conditions
CAE . . . . . . . . . . . . . Computer Aided Engineering
CMS . . . . . . . . . . . . Component Mode Synthesis
DAE . . . . . . . . . . . . Differential Algebraic Equations
DFT . . . . . . . . . . . . . Discrete Fourier Transfer
DOF . . . . . . . . . . . . Degrees of Freedom
EOL . . . . . . . . . . . . . End-of-Life
FEA . . . . . . . . . . . . . Finite Element Analysis
FSC . . . . . . . . . . . . . Fluid Structure Coupling
FSI . . . . . . . . . . . . . . Fluid Structure Interaction
MBD . . . . . . . . . . . . Multi-body Dynamics
MNF . . . . . . . . . . . . Modal Neutral File
NVH . . . . . . . . . . . . Noise Vibration & Harshness
OSWL . . . . . . . . . . . Overall Sound Power Level
PSD . . . . . . . . . . . . . Power Structural Density
PTU . . . . . . . . . . . . Power Transfer Unit
RDU . . . . . . . . . . . . Rear Differential Unit
SP(L) . . . . . . . . . . . Sound Pressure (Level)
SW(L) . . . . . . . . . . . Sound Power (Level)
TE . . . . . . . . . . . . . . Transmission Error
TRB . . . . . . . . . . . . . Tapered Roller Bearings
3
Abstract
An important facet of creating high-quality vehicles is to create components that are quiet
and smooth under operation. In reality, however, it is challenging to measure the sound that
some automotive components make under load because it requires specialist facilities and
equipment which are expensive to acquire. Furthermore, the motors used in testbeds drown out
the noise emitted from much quieter components, such as a Power Transfer Unit (PTU). This
thesis aims to solve these issues by outlining the steps required to virtually estimate the acoustic
radiation of a PTU using the Transmission Error (TE) as the input excitation via multi-body
dynamics (MBD). MBD is used to estimate the housing vibrations, which can then be coupled
with an acoustic tool to create a radiation analysis. Thus, creating a viable method to measure
the acoustic performance without incurring significant expenses. Furthermore, it enables noise
and vibration analyses to be incorporated more easily into the design stage.
This thesis analysed the sound radiated due to gear whine which arises due to the TE and
occurs at the gear mesh frequency and its multiples. The simulations highlighted that the TE
can be accurately predicted using the methods outlined in this thesis. Similarly, the method
can reliably obtain the vibrations of the housing. The results from this analysis show that at
2000 rpm the PTU was sensitive to vibrations at 500, 1000 and 1500 Hz, the largest amplitude
being at 1000 Hz. Furthermore, the Sound Power Level (SWL) was proportional to the vibration
amplitudes in the system. Analytical calculations were conducted to verify the methods and
showed a strong correlation. However, it was concluded that experiments are required to further
verify the findings in this thesis.
4
Sammanfattning
En viktig aspekt i att skapa fordon av hög kvalitet är att skapa komponenter som är tysta och
smidiga under drift. I verkligheten är det dock svårt att mäta ljudet som vissa fordonskompo-
nenter ger under belastning eftersom det kräver specialanläggningar och utrustning, vilket
är dyrt att skaffa. Dessutom maskerar motorerna som används i testbäddar ut bullret från
mycket tystare komponenter, till exempel en kraftöverföringsenhet (PTU). Detta examensar-
bete syftar till att lösa dessa problem genom att beskriva de steg som krävs för att virtuellt
uppskatta den akustiska strålningen av en PTU med hjälp av transmissionsfelet (TE) som
ingångsexcitation via flerkroppsdynamik (multi-body dynamics, MBD). MBD används för att
uppskatta kåpans vibrationer, som sedan kan kopplas till ett akustiskt verktyg för att skapa en
ljudutstrålningsanalys. Således skapas en genomförbar metod för att mäta den akustiska pre-
standan utan att medföra betydande kostnader. Dessutom möjliggör det att lättare integrera
ljud- och vibrationsanalyser i designfasen.
Detta examensarbete analyserade ljudet som utstrålats på grund av kugghjulsljud, som uppstår
på grund av TE och uppträder vid kuggingreppsfrekvensen och dess multiplar. Simuleringarna
belyste att TE kan förutsägas exakt med de metoder som beskrivs i detta examensarbete. På
samma sätt kan metoden på ett tillförlitligt sätt uppnå kåpans vibrationer. Resultaten från
denna analys visar att vid 2000 rpm var PTU känslig för vibrationer vid 500, 1000 och 1500 Hz,
den största amplituden var vid 1000 Hz. Dessutom var ljudeffektsnivån (SWL) proportionell
mot vibrationsamplituderna i systemet. Analytiska beräkningar genomfördes för att verifiera
metoderna och visade en stark korrelation. Dock drogs slutsatsen att experiment krävs för att
ytterligare verifiera resultaten i detta arbete.
5
Contents
1 Introduction 8
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Purpose and Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Frame of Reference 11
2.1 Machine Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Hypoid Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Hypoid Gear Contact Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 Gear Mesh Stiffness and Gear Mesh Frequency . . . . . . . . . . . . . . . 12
2.1.4 Transmission Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.5 Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Noise, Vibration and Harshness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Vibrations - The Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Acoustics - The Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Airborne and Structure-Borne Noise . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4 Sound Field Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.5 Transfer Path Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.6 Computer Aided Engineering Techniques . . . . . . . . . . . . . . . . . . 20
2.3 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Component Mode Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Modal Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Craig Bampton Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Acoustic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Methodology 26
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2 Generating Flexible Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Multi-body Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 The Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2 Flexible Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Modelling Process in Adams . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.4 Contact Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6
3.3.5 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Acoustic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.1 Acoustic Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.2 Creating the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.3 Analysis Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.4 Far Field Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.5 Environment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.6 Analysis Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.7 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Results and Analysis 45
4.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1 Transmission Error Validation . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.2 Housing Vibration Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Acoustic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.1 Analytical Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5 Conclusions 60
7
1 Introduction
This section gives an insight into the background of this project, the importance of this thesis
and the aims.
1.1 Background
Manufacturers within the automotive sector are confronted with the challenge of creating
intricate designs of vehicles and their components, which is a highly demanding task as
the industry grows to become more competitive. Managing the amount of noise and vibra-
tions that radiate throughout the cabin and to by-standers is an important facet of creating
innovative and supreme vehicles.
As a consequence of this demand for enhanced ride quality, the Noise, Vibration and Harsh-
ness (NVH) behaviour of components must be analysed effectively to identify design areas to
improve. This is a key area of development for component manufacturers in the sector, such
as GKN Automotive, who are eagerly seeking to develop reliable and accurate methods to
predict the NVH characteristics of their parts.
GKN Automotive is one of the world’s largest manufacturer of driveline parts. The plant in
Köping (Sweden) is focused on developing and manufacturing driveline systems, particularly
all-wheel-drive (AWD) components systems. GKN can provide an AWD system with con-
nect/disconnect features for better fuel optimisation. The AWD system consists of a Power
Transfer Unit (PTU) and Rear Drive Unit (RDU). The PTU is connected to the gearbox and
transfers torque rearwards to the coupling. The RDU distributes the torque to the rear wheels.
The layout of this system can be seen in figure 1. The PTU and its subcomponents can be
seen in more depth in figure 2.
8
Figure 1: AWD System
Figure 2: PTU [1]
The PTU consists of a hypoid gear set (crown and pinion), the tubular shaft, tapered roller
bearings (TRBs), the housing, the cover plate and the companion flange (figure 2). It is
widely known that a key contributor to the noise and vibrations in hypoid gears is due to the
Transmission Error (TE). Studies in the automotive sector have evidenced that the TE gives
rise to significant vibrations and is the fundamental cause of gear whine [2]. In extreme cases,
TE can cause vehicles to fail environmental EU regulations on sound pollution and noise
control [3].
The human ear is extremely agitated by gear whine due to its tonality. Therefore, it is vital to
create virtual models which can use the TE as an excitation source for the acoustic radiation.
The virtual model must accurately predict the TE, the noise transfer path and the sound
9
heard by the receiver. In the future, these models can help designers improve aspects of the
gear design to reduce the TE, thus improving the NVH performance.
1.2 Purpose and Aims
Previous studies on both the PTU and RDU conducted at GKN have shown that reliable
virtual models of these components are feasible through various software [4] [5] [1]. These
models have demonstrated that it is possible to simulate the dynamic behaviour of these
components under load effectively, up to 2000 Hz. More extensive research on the PTU has
confirmed that a modal analysis is possible and even the non-linear effects of bearings can
be considered. However, previous studies solely focused on structural/vibrational analysis,
e.g. a modal analysis, or the TE.
This thesis builds on previous research to create a more robust model of the PTU under
dynamic load as well as including the acoustic radiation during operation. The main ob-
jectives of this thesis are to estimate the acoustic performance of the PTU by integrating
different simulation tools and validating the model. It is necessary to simulate the acoustic
radiation virtually because it is difficult to measure the sound in reality due to the motors in
the testbeds drowning out any noise made by the PTU. Furthermore, acoustic testing requires
expensive equipment and facilities. Therefore, a virtual method of predicting the acoustic
radiation would significantly reduce costs and the time to market.
To summarise, the aims of this thesis are:
• Create a Multi-Body Dynamic model of the PTU
• Validate the model by using test data
• Create a model which can predict the acoustic radiation
• Validate the radiation results
• Understand the limitations and possible improvements
10
2 Frame of Reference
This section gives an overview of the knowledge required to understand this thesis.
2.1 Machine Design
2.1.1 Hypoid Gears
The PTU consists of a hypoid gear set, a smaller gear (the pinion) and larger gear (the crown
gear). Hypoid gears are a type of bevel gear which are used extensively in the automotive
sector to transmit power between perpendicular shafts to the rear axle. A key design benefit
of hypoid gears is that the axes are offset. This offset can be either positive or negative, as
shown in figure 3. Thus, enabling the shaft that drives the pinion to be raised or lowered at
the cost of reducing mechanical efficiency.
Figure 3: Offset in Hypoid Gears [6]
2.1.2 Hypoid Gear Contact Ratio
The contact ratio represents the average number of teeth meshing at the same time. The
contact ratio refers to ratio of the length of the arc of contact (blue line figure 4) to the circular
pitch (orange line figure 4). The benefit of having a higher contact ratio is that the load is
11
shared more equally, resulting in less wear. Furthermore, the average stiffness of the gear is
higher. A higher stiffness means better transmission accuracy due to less tooth deflection
resulting in a lower TE. Thus, a higher contact ratio results in less noise since TE is the main
source of gear noise in driveline parts [7] (see sections 2.1.4 and 2.1.3).
Figure 4: Contact Ratio [7]
2.1.3 Gear Mesh Stiffness and Gear Mesh Frequency
Gear mesh stiffness is a material property of the gear which resists deformation. The value is
dependent on the gear material, tooth curvature, tooth loading, contact ratio and angular
position of the gear [1]. Since the gear contact and tooth loading changes with time (due
to tooth bending), the gear mesh stiffness is dynamic rather than a constant value. This
results in a variation of the force acting on the gear teeth, generating a TE and thus causing
vibrations. Gear mesh stiffness can be calculated using equation 1.
Km = F
el −eo(1)
where: Km = Gear mesh stiffness
F = Contact force in the line of action
el = translational loaded TE
eo = translational unloaded TE
The gear mesh frequency is the rate at which gear teeth mate together. It can be calculated
as shown in equation 2. The shaft speed refers to the input shaft when there are multiple
12
gears. The number of teeth refers to the pinion, which in this case is 15. This value is
important because it has been shown that the gear mesh frequency and its harmonics are
the frequencies which contribute heavily to the noise and vibration of gears, particularly
gear whine [3] [8]. Table 1 shows the gear meshing frequencies of the speeds analysed in this
thesis.
Gear Mesh Frequency = Nteeth ∗Rotsha f t (2)
where: Nteeth = Number of teeth
Rotsha f t = Rotation speed of the shaft (rotations/s)
Table 1: Gear Mesh Frequencies Analysed in this Thesis
Gear Mesh Frequency (Hz)
Speed (rpm) Fundamental First Harmonic Second Harmonic
60 15 30 45
2000 500 1000 1500
2.1.4 Transmission Error
TE is the main excitation source of gear noise during vehicle operation, particularly gear
whine [8]. It produces a particularly aggravating noise due to its tonality. TE arises due to gear
teeth imperfections during manufacturing and assembly [9]. The imperfections inhibit the
gear from transmitting the rotational input correctly, causing a variation in the speed ratio.
Consequently, the gear ratio is altered slightly and varies with time. These deviations are the
main cause of oscillating forces on the gear teeth, which result in noise and vibrations. The
oscillations produced as a result of TE can range between a high or low frequency, depending
on the teeth characteristics, such as friction, teeth deflections and geometry.
TE can be defined as ’the difference between the actual position of the output gear and the
position it would occupy if the gear drive were perfectly conjugate’ [10]. This is expressed in
mathematical terms in equation 3 and a graphical representation can be observed in figure
5.
T E =Θg ear −(
Rpi ni on
Rg ear
)Θpi ni on (3)
13
where: Θg ear = Angular position of the gear
Θpi ni on = Angular position of the pinion
Rpi ni on = Pitch circle radius of the pinion
Rg ear = Pitch circle radius of the gear
Figure 5: Transmission Error [5]
2.1.5 Bearings
The PTU contains four TRBs. From figure 8 in section 2.2.5, it is evident that the TRBs must
be modelled with a high level of precision as it is important to capture the bearing forces, for
noise and vibration analyses. TRBs consist of an outer ring, an inner ring, roller and cage.
Figure 6 below shows the individual parts and their arrangement.
Figure 6: TRB Geometry [11]
14
TRBs are advantageous compared to traditional ball bearings because they reduce friction and
in turn, reduce heat generated under operation. The reduced friction and heat dramatically
reduce the wear. Hence, TRBs are widely used in automotive applications. Furthermore, the
taper enables it to transfer loads evenly whilst rolling when compared to other bearings.
Bearings play a crucial role in the NVH behaviour of the PTU as they transmit vibrations
from the hypoid gear to the housing (see section 2.2.5). Also, they generate dynamic forces
and thus sound, due to rolling element contact forces. Previous studies have shown that
properties such as the bearing stiffness, bearing damping and bearing position can affect the
transmission of excitations [12]. However, modelling bearings is challenging as they exhibit
non-linear behaviour which means the stiffness and damping of the bearings change with
load and speed [13]. This can be difficult to model and most software solutions attempt to
linearise these. In most cases, this is a reasonable simplification. However, a non-linearised
solution will yield more accurate results, particularly regarding NVH.
2.2 Noise, Vibration and Harshness
Noise and vibrations are an inevitable by-product of mechanical machines. NVH, in auto-
motive applications, is the study of the sounds and vibrations concerning vehicles and their
components.
2.2.1 Vibrations - The Fundamentals
Vibration is defined as the periodic back-and-forth motion of particles of an elastic body
or an elastic medium. Commonly, this is a result of a physical system being displaced from
its equilibrium condition. All bodies containing mass and elasticity are capable of experi-
encing vibrations [14]. Thus, most machines and structures engineers deal with experience
vibrations to some degree [15].
There are two classes of vibrations:
• Free vibration — A system oscillating due to the forces inherent in a system and no
external forces are present. A system that vibrates freely will vibrate at one or more of
its natural frequencies.
• Forced vibrations — Vibration that is caused by an external force. If the excitation is
oscillatory, the system is forced to vibrate at the excitation frequency.
Key terms in vibrations [15]:
15
• Natural frequency — The frequency at which a system/object oscillates when not
subjected to an external force or damping force. All systems and components have
at least one natural frequency and it is dependent on its mass and stiffness. Note,
sometimes this may be referred to as an eigenfrequency.
• Mode shape — The motion pattern of a system oscillating at a frequency. Commonly
bending, torsion or a mixture of the two.
• Resonance — Dangerously large oscillations that occur when a system is excited by a
frequency close to its natural frequency. Resonance can be the cause of major structural
failure.
• Damping — The energy dissipation due to friction and other resistances. Low damping
has only a minor effect on the natural frequency, which is why natural frequency is
often calculated without damping. However, high damping can significantly reduce
vibration amplitudes.
2.2.2 Acoustics - The Fundamentals
Acoustics is the study of mechanical waves in solids, gases and liquids.
Sound is the oscillation as pressure, stress, particle displacement/velocity is propagated as
an acoustic wave through a transmission medium with internal forces, such as a gas, liquid
or solid.
A wave is a disturbance travelling through a medium from one location to another, transport-
ing energy. Waves can be reflected, superposed, refracted and diffracted at boundaries, as
specified in figure 7.
16
Figure 7: Basics of Sound Waves
The relationship between the speed of sound, frequency and wavelength is given in equation
4. The wave propagation speeds are generally not dependent on the wave characteristics
such as frequency and amplitude. Instead, they are a characteristic of the media in which
they travel as observed in equation 5, e.g. the speed of sound in air at 20◦C is 340 m/s.
c = f λ (4)
where: c = Speed of sound
f = Frequency
λ= Wavelength
c =√
elastic properties
inertial properties=
√β
ρ(5)
where: β= Bulk modulus
ρ = Density
Sound is usually defined in terms of Sound Pressure (SP) measured in Pa (as observed in
figure 7) or in its logarithmic form the Sound Pressure Level (SPL). The SPL is measured in
decibels (dB). This is a logarithmic ratio scale (as highlighted in equation 6) between the
17
measured effective sound pressure (Pr ms) and a reference sound pressure (Pr e f ), usually the
threshold of hearing, i.e. 20x10−5 Pa.
SPL (dB) = 20log10
(Pr ms
Pr e f
)= 20log10 Pr ms −20log10 Pr e f (6)
Measuring sound in terms of SP is advantageous because it can be measured directly using
a microphone and it will be similar to what the human ear will hear when using a special
weighting formula. On the other hand, a drawback of measuring sound in terms of SP is that
it is highly dependent on the surrounding environment. The sound you hear will change
depending on your distance from the source, whether there are walls or floors which will
reflect or absorb the sound. Therefore, it is difficult to draw a direct comparison between two
independent results as they are situationally dependent. Instead, one can quantify sound in
terms of Sound Power (SW) or its logarithmic version the Sound Power Level (SWL).
SW is the rate acoustic energy is emitted by a source. The difference between SP and SW can
be exemplified by considering the difference between the power and temperature produced
by a heater. If you stand close to the heater, the temperature will feel much higher than if you
stand further away from the heater. Thus, it may be said that the temperature that you feel,
similar to the sound pressure you hear, depends on your distance from the heater (or sound
source) and the environment you are in, e.g. whether you are in a small room or large room.
However, the power consumed by the heater will stay the same regardless of the environment.
Power is measured in Watts (W). However, for acoustic purposes, SWL can be measured in dB,
relative to a reference power (Wr e f ) of 10−12 W . Equation 7 shows SWL in terms of dB.
SWL (dB) = 10log10
(W
Wr e f
)(7)
2.2.3 Airborne and Structure-Borne Noise
Acoustic phenomena occur in three different forms, structure-borne noise, airborne noise or
a combination of the two. These relate to the medium (transfer path/mechanisms), through
which they radiate. A comparison between structure-borne noise and airborne noise can be
found in table 2.
18
Table 2: Comparison of Structure-borne and Airborne Noise
Airborne Noise Structure-borne Noise
Transmitted through the air directly to the re-
ceiver in the form of longitudinal waves
Transmitted from the source to the receiver
along structural paths as longitudinal and
transversal waves
Sound waves in the air meet a structure via:
- Openings and sealing
- Cabin walls which vibrate and radiate sound
- Passing the wall or cabin
Caused by:
- Panels/walls vibrating due to vibrations of a
connected structure
- Vibrating panels/walls radiate sound into a
cabin/room etc.
Fluid-Structure Interaction (FSI), sometimes referred to as Fluid-Structure Coupling (FSC), is
the interaction between a structure, e.g. floor, panel or wall and a fluid volume, e.g. room or
cabin.
2.2.4 Sound Field Definitions
Sound fields refer to a region largely based on the distance from the acoustic source. The
definitions of the free, near, far and direct field can be found below [16]:
Free field is defined as a region in space where sound may propagate free from any form of
obstruction.
Near field is the region close to the source of the sound, where the sound pressure and
acoustic particle velocity are not in-phase. The region’s distance from the source is equal to
a wavelength of sound or equal to three times the largest dimension of the sound source,
whichever is largest.
Far field is the region which begins where the near field ends and extends to infinity. Note, in
reality, this transition is very gradual. In this region, the sound pressure will generally decay
at a rate of 6 dB every time the distance from the source is doubled.
Direct field of a sound source is the region where the sound has not been inhibited by any
reflection or obstacles.
19
2.2.5 Transfer Path Analysis
Transfer path analysis is a systematic method to understand the relation between multiple
sources of noise and vibration and their effect on perceived user comfort and health [17]. The
aim is to understand the energy propagation paths between the source and the receiver. The
method can be used to evaluate the importance of the contribution of different excitation
sources. Figure 8 highlights the energy transfer path of the PTU.
Figure 8: Transfer Path
The gear excitation is caused by the TE (see section 2.1.4) which acts on the internal dynamics
of the system resulting in the shaft moving laterally. Consequently, the bearings experience
dynamic forces. These forces transfer from the bearings to the housing causing the housing to
vibrate, which induces noise [18]. From figure 8, it is evident that not every sub-component
of the PTU is required to capture the acoustic behaviour, i.e. the flange. Furthermore, a model
which can accurately capture the gear excitation (TE) and housing vibrations is necessary to
predict the noise radiation.
2.2.6 Computer Aided Engineering Techniques
The task of NVH engineers is to create methods to predict, analyse and reduce the noise and
vibration that radiates. Several techniques can be employed to achieve this. For instance,
analytically, experimentally or through other means. It is imperative that NVH issues are
detected and resolved early in the design phase. Early detection can significantly reduce the
number of design iterations, keeping costs low as NVH problems typically require revised
20
designs. Late detection, e.g. during the prototype phase, can cause significant increases in
the development time and unsatisfactory solutions being implemented [19].
A particularly effective way of predicting and improving the NVH characteristics of compo-
nents is through Computer-Aided Engineering (CAE). CAE is ‘the use of computer software to
simulate the performance of a product to improve the design or facilitate solving engineering
problems’ in various engineering disciplines [20].
Usually CAE consists of the following [20]:
1. Pre-processing — model the geometry and assign physical properties (e.g. by applying
loads and constraints).
2. Solving — model is solved using the appropriate mathematical and physical con-
cepts/formulas.
3. Post-processing – Review of the results and further analysis.
As a result of the improving computational power, NVH engineers now have the means
to utilise both Multi-Body Dynamic (MBD) simulations and Finite Element Analysis (FEA)
techniques in conjunction with acoustic tools. These simulation techniques enable one
to predict the vibrational and acoustic behaviour of parts to a high degree of reliability
if the models can capture the important physics at play. The key benefit of using CAE
techniques for analysis is that no prototypes are needed, cutting vast amounts of time and
costs. Furthermore, problem areas can be detected early in the design phase which, as
previously mentioned, is paramount to rectifying NVH issues. As a result, CAE techniques are
widely used to solve NVH problems.
Despite substantial yearly improvements in computational power, very large models which
contain many elements still require significant resources when solving complex engineering
problems. Simplifications must be made to these models which can reduce computation
time for more information see section 2.3.1 and 2.3.3. Sometimes, the simplifications are
made at the expense of their accuracy. Moreover, no model can fully capture reality meaning
that some effects may be unaccounted for. Consequently, results obtained via CAE should be
validated with experimental tests.
21
2.3 Finite Element Analysis
2.3.1 Component Mode Synthesis
Component Mode Synthesis (CMS) is a modal coupling technique used to describe compo-
nents by their modal displacement, coupled together (synthesis) via their common bound-
aries to perform a dynamic analysis [21]. In other words, components are subdivided into
their substructures and are analysed independently to obtain natural frequencies and mode
shapes. Then, by applying boundary conditions, the modal participation, a measure of how
strongly a given mode contributes to the response of a structure, can be determined [22]. This
technique is advantageous because it significantly reduces the Degrees of Freedom (DOF) of
a system, reducing the computational time.
2.3.2 Modal Superposition
Modal superposition may be applied to both free and forced vibration cases. This method
uses the free vibration mode shapes to uncouple the equations of motions, which become
the modal coordinates. Solutions for the modal coordinates are obtained by solving each
equation of motion separately. Then, a superposition of the modal coordinates gives the
solution of the original equations. Figure 9 displays the method of modal superposition, i.e.
how the left-hand side is created by adding the contributions of these loads.
Figure 9: Modal Superposition
2.3.3 Craig Bampton Analysis
A common CMS technique is the Craig-Bampton method. The Craig-Bampton method allows
users to select a subset of DOF which will not undergo modal superposition [23]. The DOF
are selected at specific nodes where attachments are placed. These nodes become interface
nodes after completion. This enables users to fully capture the effects of attachments on
22
bodies as these are preserved with no loss of resolution regardless of the frequency.
To conduct a Craig-Bampton analysis, the FE model is divided into boundary DOF and
interior DOF and solved for two sets of modes, constraint modes and fixed boundary modes,
where:
• Constraint modes — Modes obtained when each boundary DOF is given a unit displace-
ment whilst simultaneously fixing all other DOF [1][24]. This represents the external
mating features. Constraint modes can be observed in figure 10.
Figure 10: Constraint Modes [1]
• Fixed boundary normal modes — Boundary DOF are fixed and modes are calculated
by deducing the eigen-value solution. These modes represent the internal dynamic
properties of the body [1][24]. Fixed boundary normal modes can be found in figure 11.
Figure 11: Fixed Boundary Modes [1]
2.4 Acoustic Simulations
Generally, it is difficult to conclusively predict the acoustic radiation of moving bodies, such
as transmissions and gearboxes, due to the interaction between subcomponents which
causes vibrations and fluctuations in contact forces. These fluctuations are difficult to
capture accurately, and consequently, the traditional modelling process is extremely time-
consuming.
23
Conventionally, acoustic simulations are conducted in three main steps, as exhibited in figure
12. Firstly, an MBD simulation is created to calculate the loads on the structure. Next, an
FE analysis is conducted to calculate the vibration of the structure from the applied loads.
Finally, the acoustic simulation is solved by using the vibration Boundary Conditions (BC)
obtained through the FE analysis.
Figure 12: Conventional Method To Conducting Acoustic Simulations
The conventional method is robust. However, the compatibility between the different soft-
ware is not always seamless. For example, an MBD simulation is usually conducted in the
time-domain, but this cannot be directly exported to the acoustic tool. Hence, a conversion is
required to convert the structure’s response to the frequency-domain, only then can the acous-
tic software read the surface vibrations. As a result, this method is incredibly time-consuming
and laborious.
Recent advancements in this area has given rise to the capability of directly coupling MBD
software with the acoustic software through the use of a plugin. The main benefits of using
such a plugin is that all processes are automated, meaning that all results are calculated in
the MBD interface. This automation significantly reduces the effort, time and costs required
to get reliable acoustic data which will help NVH engineers shorten the design phase of
products. The newer process can be seen in figure 13.
Figure 13: Simplified Method To Conduct Acoustic Simulations
24
The Adams2Actran plugin can predict the noise radiation by using the vibrations of the
flexible body calculated by Adams. The benefit of the plugin is that it creates the acoustic
meshes automatically without leaving the Adams interface. Instead, Actran runs in the
background. First, the program creates an exterior 2D mesh, generally referred to as the
shrink wrap but may also be called the boundary condition mesh, around the outer face of
the vibrating body. A 3D mesh is created around the shrink wrap, which is called the finite
fluid volume. A non-reflective boundary condition is added to the outer face of the finite fluid
volume to represent the propagation in the air. Actran achieves the non-reflective boundary
conditions by implementing infinite elements on the outer face of the 3D mesh, which also
enables pressure values to be computed outside of the fluid volume.
The velocity field of the radiating structure is computed by Adams and projected onto Actran’s
shrink wrap (BC mesh). This is used as a velocity boundary condition and is propagated by
Actran in the infinite field. The acoustic analysis can be conducted in either the time domain
or frequency domain. In both cases, a direct solver is used.
There are two coupling methods between a vibrating structure and the surrounding air, one-
way coupling and two-way coupling. Two-way coupling is when vibrations induce noise
and noise induces vibration. Conversely, one-way coupling only considers noise induced
by vibrations. Figure 14 illustrates the difference between one-way and two-way coupling.
Two-way coupling is more commonly used in cases where the fluid is water, e.g. submarine
analyses. Generally, one-way coupling is sufficient for the radiation in air and is the coupling
method used in this thesis.
(a) One-way Coupling (b) Two-way Coupling
Figure 14: The Difference Between One-way and Two-way Fluid-Structure Coupling [25]
25
3 Methodology
This section provides information on the methodology used to produce the virtual model of the
PTU and how to conduct the simulations.
3.1 Overview
Initially, a transfer path analysis was conducted to gain an understanding of the physics
involved and how the components interact with each other to produce the noise. Moreover,
the transfer path analysis determined which components were required to be modelled and
which components required more detail. As mentioned in section 2.2.5, the TE excitation
and housing vibrations were identified as critical factors which needed to be modelled
correctly.
Secondly, a methodology was created to determine the steps required to produce a viable
virtual model that can be used by both the acoustic software and the multi-body dynamics
software. The methodology was split into three different stages. The first stage was pre-
processing, where the components were meshed, and the correct file types were obtained.
The second stage was the MBD, where simulations were conducted to capture the correct
housing behaviour and TE. Finally, the acoustic simulations were conducted to determine
the sound power level and acoustic radiation. Figure 15 illustrates the methodology.
Figure 15: Overview of the Methodology
From figure 16 it can be observed that the SimLab software was used to discretise the com-
ponents and add connection points to prepare for an FE analysis. The files were exported
in the BDF format. More information can be found in section 3.2.1. The files were then
imported into MSC Marc, and a reduction in the DOF, via a Craig-Bampton analysis, was
26
conducted to reduce the computational time and retain the behaviour of attachment points.
A job was created to generate the flexible bodies (i.e. MNF files) which contain the modal
information of the components, obtained through an eigenfrequency analysis. Please consult
section 3.2.2 for more information. The MNF files were imported into MSC Adams, and the
boundary conditions were modelled. Different dynamic loads were simulated to capture
the velocity/acceleration/displacement of the parts under load. Further details on the MBD
simulations can be found in section 3.3. Finally, the Adams2Actran plugin was used to predict
the acoustic behaviour of the PTU.
Figure 16: Software Workflow
3.2 Pre-processing
As observed from figures 15 and 16, the pre-processing stage consisted of meshing, creating
connection points and generating flexible bodies which can be read by Adams to capture the
vibrational behaviour. The main aim of the pre-processing stage was to generate the correct
files, which were both detailed enough to capture the desired effects yet not too large as this
would increase the computational time.
3.2.1 Meshing
The first step of creating the model was to obtain the CAD files and remove any unnecessary
parts or features. For instance, the splines on the pinion were not crucial for this analysis
yet added a considerable amount of time to the simulations. Therefore, it was beneficial to
remove these. Secondly, the logo on the housing was removed.
When generating the mesh, it was essential to ensure that the mesh was adequately fine
enough to represent the curvature of the parts. Otherwise, sections which were circular would
appear angular, e.g. a bolt hole would appear hexagonal instead of circular. On the other
27
hand, an unnecessarily fine mesh will add a significant amount of time to the simulations.
Since the TE must be accurately predicted, a finer mesh was used on the pinion and the gear.
A coarser mesh was used on other components to reduce the computational time as these
did not require high precision. The mesh quality was verified using company guidelines.
The meshes are depicted in figure 17 and the mesh settings can be found in the tables 3 and
4.
(a) Gear Mesh (b) Housing and Cover Plate Mesh
(c) Pinion Mesh (d) Shaft Mesh
Figure 17: Illustration of the Meshes & RBEs
Table 3: 2D Mesh Settings
Mesh Size Geometry ApproxmationSurface
Mesh Quality
ComponentElement
Type
Average
Mesh Size (mm)
Minimum
Element Size (mm)
Grade
Factor
Max Angle Per
Element (Degrees)
Curvature minimum
Element size (mm)
Aspect
Ratio
Pinon & Gear Tri 3 1 0.5 1.5 45 2 10
Tub Shaft, Housing & Cvr Plate Tri 3 3 0.5 1.5 45 2 10
28
Table 4: 3D Mesh Settings
Mesh Size Geometry Approxmation Quality
ComponentElement
Type
Average
Mesh Size (mm)
Internal
Grading
Max Angle Per
Element (Degrees)
Curvature minimum
Element size (mm)
Tet Collapse
Min Value
Min Jacobian-
Ratio Value
Pinon & Gear Tet 10 4 0.5 20 2 0.12 0.7
Tub Shaft, Housing & Cvr Plate Tet 10 4 0.5 20 2 0.12 0.7
After creating the mesh, the Rigid Body Element’s (RBE’s) were defined. RBE’s are geo-
metrically rigid links which can be used to transfer load. There are two types of RBE’s,
RBE2 and RBE3. The difference between them is that RBE2 distributes force and moments
equally among all connected nodes. Figure 18a illustrates this using a force of 100 N. On the
other hand, RBE3 distributes the load based on the distance, this can be observed in figure
18b.
RBE’s are used in this thesis for several reasons. As previously mentioned, they can be used
to transfer loads. Secondly, they can be used to represent a bolted connection if it is known
that the bolt will not fail under the applied load. Thirdly, they can be used as connection
points. The RBE’s will be identified as interface nodes in Adams, enabling them to be used as
connection points. These interface nodes became points where the location and direction of
joints, bearings, forces and torques were defined. The mesh for each component, as well as
RBEs, can be seen in figure 17. The final step was to export the files in the BDF format.
(a) RBE2(b) RBE3
Figure 18: The Difference Between RBE2 and RBE3
3.2.2 Generating Flexible Bodies
In this thesis, the program MSC Marc was used to generate the Modal Neutral Files (MNF’s).
MNF’s are a type of file format which contain the data of a flexible body. The files contain
29
information such as the inertia matrix, the mode shapes and their frequencies. These are
obtained through an eigenfrequency analysis. However, a Craig-Bampton modal synthesis
is required because it reduces the DOF, reducing computational time, yet still captures the
elasticity of parts. The MNF’s were created using the following steps:
1. Imported the BDF files created in SimLab
2. Mass properties of each part were specified
3. Geometric properties of the CAD files were inserted (i.e. units)
4. (Glue contact created between the housing and cover plate)
5. The free-set DOF were selected, where RBE’s were defined
6. A Craig-Bampton analysis was created
7. MNF file was chosen as the desired output
An extra step was added when the external housing was considered because the Adams2Actran
plugin only supports the analysis of one MNF. Therefore, a glue contact was generated be-
tween the housing and cover plate using the contact tables feature. When generating the
glue contact, it was ensured that the stress-free initial contact was selected. This method is
viable under the assumption that the mass of the bolts is not significant and the assembly
can be considered as sufficiently clamped. A further benefit is that this closely resembles
the method used to fixate the PTU during testing. This can be seen in figure 19. It can be
observed that the housing side of the PTU is fixated to the test-rig, whereas the cover plate
has been clamped using only the bolts.
30
Figure 19: PTU Mounted in the Test Rig [1]
3.3 Multi-body Dynamics
3.3.1 The Program
In Adams, a body refers to the individual geometry of each subcomponent that make up the
PTU, i.e. pinion, shaft, housing, cover plate, etc. Idealised joints and forces are added to
the bodies which affect how forces are translated throughout the system. Contact instances
are made between areas that are in contact during the simulation to calculate the forces
and motions between them. Finally, motions and external forces are added to the model
to represent the load cases. Multibody dynamic simulations work by solving a system of
Differential-Algebraic Equations (DAE) to calculate the position, acceleration and velocity on
each body [26].
3.3.2 Flexible Bodies
Rigid body dynamics are commonly used when dealing with multi-body systems. However,
introducing flexibility into the system can improve simulations by capturing the system’s
frequencies more accurately, thus producing more reliable results. When considering NVH
behaviours, flexible bodies are required because some elastic deformation must occur for
vibrations to propagate through a system [27]. Consequently, flexible bodies can more
31
accurately predict the inertial properties and compliance. Therefore, all the sub-components
of the PTU were required to be flexible bodies. Adams utilises flexible bodies through MNFs.
The equation of motion for flexible bodies can be calculated from the Lagrange equation
[28] (see equations 8 and 9). Please consult [28] for further details on the mathematics
involved.
d
d t
(∂L
∂ζ
)− ∂L
∂ζ+ ∂E
∂ζ+
(∂Ψ
∂ζ
)T
λ−Q = 0 (8)
Ψ= 0 (9)
where: L = Lagrange item = Kinetic Energy (T) - Potential Energy (V)
ζ = The generalised coordinates
E = The energy dissipation function
Ψ= The constraint equations
λ = Lagrange multipliers for the constrains
Q = Generalised applied forces
3.3.3 Modelling Process in Adams
In short, the following steps were taken to generate the results from the MBD model :
1. Imported the MNFs of the gear, tubular shaft and pinion
2. Added idealised joints
3. Added contacts between the pinion and the gear
4. Applied the motion and resistive torque
5. Added the bearings
6. Added the MNF of the housing and cover plate (one MNF)
7. Added bushings at bolt locations
8. Added markers and desired output calculations (e.g. TE)
9. Simulated the different load cases
32
Firstly, the unit system of Adams was set to match those from the meshing process (mm,
kg, N, Deg, S). The files were individually imported using the create flexible body function.
There were several options for the inertia modelling. Adam’s utilises nine inertia invariants to
calculate the time-varying mass matrix of a flexible body. The invariants are calculated by
analysing each nodes mass, undeformed location and participation in component modes
[29]. The most applicable two were full-coupling and partial-coupling. The difference
between them is that in full-coupling, more invariants are activated, which results in more
precise results. However, this significantly increases computational time for all simulations.
Therefore, after a short study, all components were loaded with the inertia set to partial-
coupling as it provided a good balance between speed and precision.
The boundary conditions were modelled using the joint, joint motions, bushings and torque
functions. First, a fixed joint is used to attach the gear to the shaft. Secondly, a revolute joint
is used to attach the shaft to the ground to enable it to rotate in the direction of the applied
motion from the gearbox. The motion is applied at an interface node on the shaft. Next, the
pinion is attached to the ground using a revolute joint which enables it to turn when it is
excited by the gear. The joining methods can be observed in table 5. A contact was created
between the pinion and the gear. Finally, a resistive torque was placed on the pinion at an
interface node.
It was crucial to define the contact between the gear and the pinion correctly. Therefore, it
was important to conduct a study to calculate the best input parameters which yield reliable
results but are not computationally expensive. This was particularly important when the
bearings were added, as these greatly increased the computational time. The contact settings
can be found in table 6 in section 3.3.4. At this stage, a simple hypoid gear model was created,
as seen in figure 20.
33
Figure 20: Labelled Hypoid Gear Model
Table 5: Joining Methods
Parts Joining Method
Housing - Ground Bushings
Tubular Shaft - Ground Revolute Joints
Ring Gear - Tubular Shaft Fixed Joint
Pinion - Ground Revolute Joint
Pinion - Ring Gear Contact
The bearings were created using the BearingAT module, which required highly detailed
and specific dimensioning. The bearings were attached at the interference nodes (i.e. RBE
locations). The locations of the bearings can be found in figure 21. Bearing B11 and B12 were
located on the pinion, whereas, bearings B22 left and right were located on the tubular shaft.
Note, bearings B22 left and B22 right had the same dimensions.
34
Figure 21: Locations of the Different Bearings
Initially, the housing was imported and fixed joints were used at bolting locations, on the
same side, as shown in figure 19. However, it was later discovered that the fixed joints made
the model unrealistically stiff, resulting in incorrect housing accelerations. The stiffness was
due to the joints being idealised to an infinite stiffness. In reality, joints have more compliance
which is important for a vibration response analysis. Hence, bushings were created at bolting
locations with a very large stiffness of 1E9. This method was beneficial as it enabled some
compliance in the system, thus correlating better with experimental results.
Finally, markers were placed onto the housing, shaft and pinion. These were used to calculate
different quantities using the create function measure utility in Adams. Key quantities that
were measured were the pinion and shaft speed (in rpm) and the angular positions of the
gear and pinion, to calculate the TE as defined by equation 3. A marker was placed on the
housing at the same location as an accelerometer used in testing. The accelerometer and
bushing placements can be observed in figure 22.
35
Figure 22: Accelerometer Placement and Bushing Placement
3.3.4 Contact Mechanics
The contact was created using the IMPACT function in Adams. A simple example of the
IMPACT function can be seen in figure 23. In this example, a ball is falling to the ground.
If the distance between the I and J markers reaches x1, the IMPACT function comes into
effect. However, if the distance between the I and J markers is greater than x1, the force is
zero [30].
The IMPACT function consists of a spring component (k) and a damping component (c).
The stiffness component is proportional to the stiffness coefficient (stiffness per unit length).
Therefore, this changes as the distance between the I and J markers change. The damping
component opposes the direction of motion and reaches the selected maximum value at
the specified penetration depth [30]. The equation defining the IMPACT function can be
observed in equation 10.
36
Figure 23: An Example of the IMPACT Function. A Ball Falling to the Ground [30]
IMPACT =M ax(0,k(x1 − s)2 −ST EP (x, x1 −d ,Cmax , x1,0).x) forx ≤ x1
0 forx ≥ x1
(10)
Initially, the contact between the gear and pinion was modelled using Hertzian contact theory,
similar to other studies in the area [4]. However, as the contact settings had a significant
effect on the results obtained, thorough investigations were conducted to adapt them to
correlate better with real-life test results. An important consideration was the time it took
for simulations to complete, particularly after the addition of the bearings. Therefore, the
settings were fine-tuned to find a balance between speed and accuracy. The settings for the
contact can be found in table 6. It must be noted that some further optimisation may be
required for other tests. In some analyses, the settings were tuned even further to correlate
better with test results.
Table 6: Contact Settings
Setting Value
Stiffness 2E+5
Force Exponent 2
Damping 52
Penetration Depth 0.01
37
3.3.5 Solver
Table 7 shows the solver settings used for all MBD simulations. These settings were selected
as it had the best balance between speed and precision.
Table 7: Solver Settings
Setting Value
Integrator HHT
Formulation I3
Hmax 1E-3
Interpolate Yes
3.4 Acoustic Simulations
3.4.1 Acoustic Pre-Processing
The Adams2Actran plugin can use either the displacement/velocity/acceleration, or the
modes and participation factors of the component as an input to calculate the acoustic
behaviour. This feature is beneficial because the number of calculations required to be
computed in Adams is reduced, which significantly reduces the computational time. A
further benefit is that the results files are smaller, which reduces the latency within the Adams
interface. A shrinkwrap mesh is required to do this in the frequency domain. For radiation
analyses in air, one-way coupling is assumed.
The Adams2Actran plugin can create the acoustic meshes (see section 2.4) automatically for
simple geometries. However, the PTU was too complex, causing the automatic meshing to
fail. Therefore, it was necessary to create the shrinkwrap mesh manually. This was done in
the Actran interface.
The wavelength computation tool within Actran was used to determine the size of the mesh
required. The maximum frequency to be analysed was a key parameter. To simulate up
to 2000 Hz an element size of 28.3 mm was required. An essential requirement for the
shrink wrap is that it cannot enter the original mesh through holes and crevices because the
vibrations will not be captured correctly. Therefore, all holes needed to be filled.
To manually fill the remaining holes, the ’fill holes’ option was utilised in the Actran UI. How-
ever, this did not successfully fill all the gaps in the housing. To manually fill the remaining
38
holes, the surface mesh option was used. After all holes were filled, the exterior shrinkwrap
function was used to generate the shrinkwrap. It was crucial to ensure the shrinkwrap did
not intersect itself and did not enter any holes.
The projection quality of the shrinkwrap was analysed to assess the quality of the shrinkwrap.
A localisation percentage shows the ratio of structure nodes projected. The aim was to get
as close to 100% as possible. The shrink wrap created had a localisation percentage of 92%.
This was achieved using a mesh size of 10 mm as 28.3 mm was not adequately fine enough
to capture the complex geometry of the PTU. The shrinkwrap can be observed in figure
24.
Figure 24: The Shrinkwrap
3.4.2 Creating the Analysis
First, a frequency domain analysis was created as time-domain analyses are more appropriate
for transient cases and will result in large files due to the amount of information which would
be stored. Next, the BDF and MNF files of the housing, the simulation name and time range
to be analysed were specified. Note, the BDF and MNF files must be in the same folder with
the same name. When creating the analysis a field is created asking for the steps to skip.
This steps to skip is dependent on the Nyquist criterion and can be calculated as shown in
equation 11.
39
Steps to Skip =(
tN yqui st
tAd ams
)−1 (11)
where: tN yqui st = 1/(2∗Max frequency to be analysed)
tAd ams = Time step used in Adams
In this thesis, the max frequency that was analysed was 2000 Hz and the time step used in
Adams was 2.5E −4. Therefore, the steps to skip was zero.
3.4.3 Analysis Setup
The analysis setup settings can be observed in table 8. Here, the gap tolerance was specified,
whether an output map should be generated and the memory settings, note -1 means all
available memory. In this analysis, an output map step was not created due to computa-
tional limitations as this requires significant amounts of computational power, memory and
time.
Table 8: Analysis Setup
Setting
Gap Tolerance 0.01 m
Output Map No
Output Map Steps N/A
Memory -1
3.4.4 Far Field Setup
Please consult section 2.2.4 for the definition of far field. The order of infinite elements is used
to compute the SPL outside the finite element area. The infinite elements can be considered
as a polynomial with several interpolation points, equal to the order of infinite elements. A
higher-order will increase the accuracy of the infinite elements and the simulation. However,
this will also significantly increase the computational time. An order of ten was used in this
analysis as this setting produced the best results despite requiring more computational time.
A graphical representation of the infinite elements can be seen in figure 25. The microphones
used for post-processing in terms of SPL can be specified here. As explained in section 2.4, it
is difficult to compare results in terms of SPL directly. Therefore, SWL was used. Microphone
40
Figure 25: Graphical Representation of the Infinite Elements (outside the blue circle) [31]
selection was based on ISO standards for radiation testing. The settings used can be seen in
table 9.
Table 9: Far-Field Setup
Setting
Order of Infinite Elements 10
Microphone Table ISO (default)
Translation of Microphone Centre 0,0,0
Scale Factor for Microphones 1
Microphones for Post-Processing 40
3.4.5 Environment Setup
Table 10 displays the environment settings used in this thesis.
Table 10: Environment Settings
Setting
Acoustic Environment Air at 15 °C
Speed of Sound 340 m/s
Fluid Density 1.22 kg/m3
3.4.6 Analysis Parameters
The Discrete Fourier Transform (DFT) settings dictate the properties of the DFT which
transform the vibrations of the flexible body from the time domain to the frequency domain.
41
The time interval determines the resolution of the analysis. The overlap percentage is required
to obtain better-looking waterfall diagrams. A time interval of 0.1 is recommended for this
analysis. If the time interval is too high, the results do not conform correctly. On the other
hand, if the interval is too low, then any noise will greatly impact the results. Some trial
and error may be required to determine the best parameters to use. The DFT settings can
be found in table 11. The parameter settings used in this study can be found in table 12.
Time windowing defines the form of the window. The Hanning option, which is used in this
analysis, is defined in equation 12.
w(n) = 0.5−0.5cos
(2πn
M −1
)(12)
where: n = Number of sampling points
M = Quantity of same point in the window
w = The window function
The frequency range that was to be analysed was selected. This must conform to the mesh
size of the shrinkwrap and must be cross-referenced with the Nyquist criterion as explained
in section 3.4.2. The radiation frequencies for the green analysis defines the number of
frequencies used for the step in the green analysis (radiation analysis). The higher the
number, the better the accuracy. For this analysis, four radiation frequencies was used.
The number of bands for adaptive volume mesh defines the number of frequency ranges used
for the adaptive mesh. The relative thickness for the perfectly matched layer corresponds
to the number of acoustic wavelengths at the lower limit of each frequency band. The Hexa
mesh option is selected because it creates a better mesh. In the event that the simulation fails
at the meshing stage, this can be turned off. All of the analysis parameters are presented in
table 12.
Table 11: DFT Settings
Setting
Time Windowing Hanning
Time Interval 0.1 s
Overlap of Time Interval 50%
42
Table 12: Analysis Parameters
Setting
Frequency Start 1 Hz
Frequency Step 100 Hz
Frequency End 2000 Hz
Num of Radiation Frequencies for Green Analysis 4
Num of Bands for Adaptive Volume Mesh 6
Relative Thickness for the Perfectly Matched Layer 1
Use Hexa Mesh Yes
3.4.7 Mesh
The final step was to link the manually created shrinkwrap to the analysis, note all files must
be in the same folder. Figure 26 illustrates the ISO configuration of microphones and the
shrinkwrap within the Adams interface. Microphone 40 is highlighted in red.
Figure 26: The Shrinkwrap Within the Adams Interface
(MNF Conversion)
In the event that an MNF version error occurs during Adams2Actran simulations, the Flex
toolkit provided by MSC can be used to covert the MNFs to a readable version by selecting
the settings observed in figure 27. This may occasionally occur due to the software and/or
program version used to generate the MNFs being incompatible with Actran’s drivers.
43
Figure 27: MNF Optimiser Settings (if there is an incompatibility issue)
44
4 Results and Analysis
This section presents the results obtained from the simulations and analyses them. Suggestions
for future work are also presented.
4.1 Model Validation
To validate the model, several simulations were conducted within Adams and these were
compared to test results previously conducted on the PTU in the testbeds. For example, the TE
was tested at different speeds and torques. Furthermore, the housing acceleration response
was measured at specific locations within Adams and compared to test data gathered through
the use of accelerometers.
4.1.1 Transmission Error Validation
There were two different TE tests used to validate the model. The first test was an End-Of-Line
(EOL) test, where a fully assembled unit was taken from the end of the assembly line and
placed into the rig. The test was conducted at a speed of 60 rpm, from table 1 it can be
inferred that the peak amplitude will occur at 15 Hz. The amplitude of the signal at the
first fundamental frequency and first harmonic were measured in µRad . An FFT of the
TE signal was performed within Adams to obtain comparable results. Figure 28 shows the
simulated results obtained from Adams. Table 13 compares the simulated results with the
EOL test.
45
Figure 28: End of Life Simulated Results
Table 13: Comparison of the TE Between the EOL Test and Simulated Results
Frequency (Hz) Simulated Results (uRad) Test Results (uRad)
15 27 28
30 6 5
Further TE tests were compared to the simulated results to ensure that the model was valid
when varying the torque. The tests were conducted at 15 Nm, 100 Nm and -15 Nm. Figures
29, 30 and 31 show the TE signal for the various torques. Table 14 shows a comparison of the
first order TE values calculated from the simulation and the test results.
46
Figure 29: TE at 15 Nm
Figure 30: TE at 100 Nm
47
Figure 31: TE at -15 Nm
Table 14: Comparison of the First Order TE at Different Torques
TE First Order (uRad)
Torque (Nm) Minimum Value (Test) Maximum Value (Test) Simulated Result
15 4.5 20 16.9
100 7.9 15.8 13.5
-15 26 34 26.1
From table 14, it can be observed that the model was able to predict the amplitude of the
TE with an acceptable degree of accuracy as it is similar to the results observed in previous
research [1]. The TE decreases as the torque increases, this occurs due to the overall stiffness
of the model increases as the torque increases, resulting in better gear meshing and thus less
TE fluctuations.
4.1.2 Housing Vibration Validation
To test the vibration of the housing, an accelerometer was placed onto the housing at a
specific location, as specified in figure 32. A speed ramp cycle up to 2000 rpm is run, i.e. the
test starts at 0 rpm and gradually increases to 2000 rpm where it stays constant for some time
48
and returns slowly back to 0 rpm. In Adams, this was achieved by placing a marker at the
same location and creating measures to capture the acceleration at that point.
Figure 32: Accelerometer Location
The vibration was analysed in terms of the Power Spectral Density (PSD). PSD is defined as
the squared value of a signal. It describes the power of a signal or time series distributed over
different frequencies. A PSD is an FFT which converts a time-domain signal to a frequency-
domain signal [32]. The shape of the PSD plot defines the average acceleration of the signal
at any frequency. Figure 33 displays the test results. On the other hand, figures 34 - 37 show
the simulated results obtained in Adams.
49
Figure 33: Housing Accelerations at 2000 rpm from Testing
From the test data (figure 33), the largest peak was observed at 1000 Hz in the Y direction,
and the Y direction remains dominant at 1400 Hz. The largest amplitude at 500 Hz is in the Z
direction and lowest in Y. The amplitude of the accelerations in the Z direction decrease as
frequency increases and becomes very low in comparison to the other directions. There is
only a small peak in all directions at 2000 Hz and this tends towards zero as the frequency
reaches 2500 Hz.
50
Figure 34: Simulated Housing Acceleration in the X Direction at 2000 rpm
Figure 34 displays the simulated results of the housing acceleration in the X-direction. It
can be observed that the simulation correctly predicted the fundamental frequencies which
excited the component, i.e. 500, 1000 and 1500 Hz (as predicted in table 1). However, the
shape of the peaks does not directly match the experimental results. This discrepancy may
be due to the difference in damping between the model and reality or a difference in the
frequency resolution. Investigations should be conducted to decouple the contact parameters
in terms of housing vibrations.
Figure 35 highlights that the simulation can predict the shape of the PSD curves correctly. The
largest peak in all directions occurs at 1000 Hz. However, in the test data, the Y component
retains the largest amplitudes at 1500 Hz. In the simulated data, this is in the X direction
instead.
From figure 36, it can be observed that the simulation correctly predicted that the acceleration
in the Z direction would be relatively low in comparison to the X and Y directions above 500
Hz. The simulation was unable able to predict that the largest amplitude, in the Z direction,
was at 500 Hz. However, the amplitudes do decrease at 1500 Hz. Overall, the simulation was
able to predict what happens to an acceptable degree of accuracy.
51
Figure 35: Simulated Housing Acceleration in the Y Direction at 2000 rpm
Figure 36: Simulated Housing Acceleration in the Z Direction at 2000 rpm
52
Figure 37: Comparison of the Simulated Housing Acceleration in All Directions at 2000 rpm
From figure 37, it can be observed that the simulated system is sensitive to large accelerations
at 500, 1000 and 1500 Hz, whereas the test data shows large displacements at 510, 1028
and 1410 Hz. Overall, the simulation predicted the general shape of the accelerations to an
acceptable level. However, the amplitude of the simulated and test results do not match
exactly. A key contributor to the discrepancy, in addition to those already mentioned, is
that the simulations were conducted during a very short time span due to computational
limitations and time constraints. In contrast, the test data was gathered over approximately
30 seconds, enabling the speed to increase smoothly, steadily and controllably. A smoother
ramp-up would naturally cause lower amplitudes. This is comparable to speeding up from
0-60 mph (0-100 km/h) within two seconds or speeding up within 10 seconds in a passenger
vehicle. The faster the car accelerates, the more the car vibrates and vice-versa.
In the future, extensive research should be conducted to decouple contact parameters and
damping ratios to understand each of their effects on the housing accelerations. Once this has
been validated, and assuming the required computational power is available, a simulation
should be conducted which directly follows the testing protocol, i.e. ramps-up slower and is
simulated for 30 seconds.
To fully visualise the total housing vibrations, the acceleration amplitudes in the X, Y and Z
53
directions, for each frequency, was summed up and plotted in a bar graph. This was achieved
by using the vector sum formula, as presented in equation 13. The results for the experimental
data can be found in figure 38 and the bar graph for the simulated results can be seen in
figure 39.
Vector Sum =√
x2 + y2 + z2 (13)
Figure 38: Vector Sum of the Housing Accelerations from Experimental Data
54
Figure 39: Vector Sum of the Simulated Housing Accelerations
From comparing the vector sum of the experimental and simulated results (figures 38 and 39),
it is evident that the simulation correctly predicted the overall trend of the housing vibrations.
A lower amplitude is observed at 500 Hz. Meanwhile, the highest is at 1000 Hz and 1500 Hz
sits somewhere in-between. It is observed that overall, the simulation was very accurate in
predicting the total vibration. Using this information, it can be inferred that the acoustic
simulations will show the largest excitations at 1000 Hz and the least at 500 Hz.
4.2 Acoustic Simulations
Figure 40 presents the waterfall diagram of the SWL. The system excitations are clearly visible
at 500, 1000 and 1500 Hz. This corroborates with the findings from the experimental data and
simulated data which evidenced large housing vibrations at these frequencies. As predicted
from the vector sum graphs, the most noise occurs at 1000 Hz because this is the frequency
that is most excited at 2000 rpm, the SWL is approximately 50 dB. At 500 Hz, the sound power
is lower, due to less housing vibrations occurring at this frequency. The sound power at 1500
Hz lies between the other two, which is in line with the results from figures 38 and 39.
55
Figure 40: Waterfall Diagram Displaying the Simulated Sound Power Level (SWL) at 2000 rpm
The Overall Sound Power Level (OSWL) value throughout the simulation can be observed in
figure 41. This shows that as the simulation speeds up to 2000 rpm, the OSWL increases and
the curve flattens at approximately 64 dB. The OSWL is calculated in Actran using equation
14. The OSWL is higher than the values shown in the waterfall diagram because it considers
the entire spectrum.
Figure 41: Output Sound Power Level
OSW LdB = 10l og
√∫ fmax
fmi nW 2d f
Wr e f(14)
56
4.2.1 Analytical Validation
To analytically validate the results, the SWL can be estimated using the monopole and
radiation efficiency equation as this will provide an approximate range which the simulation
results should fall either within or close to. The SW can be estimated in watts by using the
monopole model which can be calculated using the surface accelerations, calculated from
markers in Adams and accelerometers in the experimental test, as well as geometrical and
environmental properties. A monopole is an acoustic source that can radiate sound equally
well in all directions. The formula is valid when the air and the system are moving in-phase.
The formula for the monopole model can be found in equation 18. Equations 15, 16 and 17
show the input parameters to calculate the SW in Watts using the monopole model which
was then converted to SWL using equation 7.
k = 2π f
c(15)
v = a
2π f(16)
Qr ms = v ∗ sa = v ∗4πr 2 (17)
Sound Power (Watts) = ρ∗ c
4π∗k2 ∗Qr ms
2 (18)
where: k = Wavelength number (m−1)
f = Frequency (Hz)
c = Speed of sound (m/s)
v = Velocity of the surface (m/s)
a = Surface acceleration (m/s2)
Qr ms = Volumetric flow (m3/s)
sa = Surface area (m2)
ρ = Density of air (kg /m3)
The surface area of the PTU was simplified to a sphere to reduce the complexity of equation
17. The velocity of the surface was obtained using equation 16, which can be used with the
57
acceleration data from both the experimental and simulated results. Thus, providing an
effective way to compare the findings analytically.
Another equation which can be used to calculate the SW in watts is the acoustic radiation
efficiency equation [33]. This equation tends to be more reliable when there are large fre-
quencies. However, it can still be applicable because it is valid if the air is moving in a random
phase with the component, which is possible in this case. The acoustic radiation efficiency is
assumed to be one in this case. However, further studies should be conducted to confirm
whether this is correct and adjust accordingly. Equation 19 displays the formulation used to
obtain the second SW value which was then converted to SWL using equation 7.
Sound Power (Watts) = ρ∗ c ∗ v2 ∗ sa ∗ s (19)
where: ρ = Density of air (kg /m3)
c = Speed of sound (m/s)
v = Average velocity of the surface (m/s)
sa = Surface area (m2)
s = Acoustic radiation efficiency
Table 15: Comparison of the Analytical Calculations with Simulated Data
Analytically Calculated SWL (dB) Simulated SWL (dB)
Frequency (Hz) Using Simulated Accelerations Using Test Data From the Waterfall Diagram
500 39-40 37-38 30
1000 50-55 48-53 50
1500 41-50 42-51 40
From table 15, it can be inferred that the simulations conducted in this thesis show a good
correlation between the simulated results and the analytical calculations, particularly at 1000
and 1500 Hz. Therefore, the results obtained in this thesis have been verified to a certain
degree of reliability. To confirm the reliability of the acoustic simulation, acoustic testing on
the PTU should be conducted and analysed with the results presented in this thesis.
58
4.3 Future Work
Conducting acoustic tests using the same testing procedure is paramount to ensuring the
reliability of the results in this thesis. Other suggested future work includes:
• Conduct MBD using a more advanced gearing module to create the gears, e.g. GearAT.
This enables more detailed contact parameters.
• Conduct an acoustic analysis on individual components, e.g. the pinion, which can be
used in early gear failure detection.
• Conduct experimental tests at different loads and speeds to determine the effectiveness
of the model at varying load cases.
• Study the effects of changing the housing design and material.
59
5 Conclusions
To conclude, the process of creating flexible bodies, required to develop the MBD model,
for each sub-component of the PTU was clearly outlined in this thesis. Idealised joints and
motions were applied to re-create the boundary conditions used in the test rigs. When
attempting to model the bolts, it was found that bushing with a high stiffness provided more
realistic housing vibrations than using fixed joints. A glue contact was used between the
housing and the cover plate.
The MBD model was used to simulate the TE at different torques similar to the real-life tests
conducted. It was shown that the model was able to accurately and reliably predict both the
frequency and amplitudes of the TE. Furthermore, a speed ramp up to 2000 rpm and 100 Nm
of torque was simulated to analyse the housing vibrations of the simulation compared to
tests. From the data, it can be observed that the simulation was able to predict the housing
vibration to an acceptable degree of accuracy and large amplitudes were observed at 500,
1000 and 1500 Hz.
The steps to conduct an acoustic radiation analysis are described in this thesis. The radiation
results showed that 30 dB was observed at 500 Hz, 50 dB at 1000 Hz and 40 dB at 1500 Hz.
The acoustic results corroborated with the housing vibrations measured both within the test
rig and the simulated results. Analytical calculations were used to estimate the SWL to ensure
the validity of the results. In the future, acoustic tests should be conducted to verify that the
simulations are reliable and accurate.
In summary:
• A MBD was created and verified using test data
• A model capable of predicting the acoustic radiation was created
• Analytical calculations were used to verify the validity of the acoustic results
• The next stage is to conduct acoustic tests to verify whether the model is accurate
60
References
[1] Kosaraju N.M, Sellgren U. Dynamic Analysis of an Automotive Power Transfer unit :
Towards prediction of TE and housing vibrations. Machine Design (Div.), Machine
Design (Dept.), School of Industrial Engineering and Management (ITM), KTH; 2019.
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-259683.
[2] Chung C.H.J, Steyer G, Abe T, Clapper M, Shah C. Gear Noise Reduction through
Transmission Error Control and Gear Blank Dynamic Tuning. SAE International; 1999.
Available from: https://doi.org/10.4271/1999-01-1766.
[3] Henriksson M. On noise generation and dynamic transmission error of gears. KTH
(Royal Institute of Technology), PhD Thesis; 2009.
[4] Orzi S. NVH performance prediction in a Rear Drive Unit [Master Thesis]. KTH (Royal
Institute of Technology); 2016.
[5] Lingaiah P. Dynamic behavior characterization of a Power Transfer Unit using Multi
Body Simulation KTH (Royal Institute of Technology), Master Thesis; 2018
[6] Klingelnberg J. Bevel Gear Fundamentals and Applications. 1st ed. Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer Vieweg; 2016.
[7] Baleon S. Why is contact ratio important? adament-precision. 2019;Available from:
https://adamant-precision.ch/blog/importance_of_contact_ratio.
[8] Åkerblom M. Gear Noise and Vibration : A Literature Survey. Machine Design, Super-
seded Departments, KTH; 2001. Available from: http://urn.kb.se/resolve?urn=
urn:nbn:se:kth:diva-9891.
[9] Du Shu. Dynamic modelling and simulation of gear transmission error for gearbox
vibration analysis. University of New South Wales; 1997
[10] Welbourn D.B. Fundamental Knowledge Of Gear Noise: A Survey HS-029 137 (IMechE-
CP-1979-10), "Noise and Vibrations of Engines and Transmissions," Bury St. Edmunds,
1979, pp 9-14.
[11] Koyo J. Tapered Roller Bearing;. Available from: https://www.alibaba.com/
product-detail/Japan-KOYO-Tapered-Roller-Bearing-size_60733999359.
html.
61
[12] Vanhollebeke F, Peeters J, Vandepitte D, Desmet W. Using transfer path analysis to
assess the influence of bearings on structural vibrations of a wind turbine gearbox.
Wind Energy. 2015;18(5):797–810. Available from: https://onlinelibrary.wiley.
com/doi/abs/10.1002/we.1729.
[13] Beloiu D.M. Modeling and Analysis of Powertrain NVH. SAE International; 2012. Avail-
able from: https://doi.org/10.4271/2012-01-0888.
[14] Encyclopaedia of Britannica TE. Vibration. 2016;Available from: https://www.
britannica.com/science/vibration.
[15] Thomson W. Theory Of Vibration With Applications. CrC Press; 2018.
[16] Hansen C.H. Fundamntals of acoustics. American Journal of Physics, Vol. 19, 1951.
[17] Siemens PLM Software. What is transfer path analysis?; 2014. Available from:
https://www.plm.automation.siemens.com/en_us/Images/What_is_transfer_
path_analysis_tcm1023-220904.pdf.
[18] Crocker M.J. Gear Noise And Vibration Identification - The Frequency
Spectrum. John Wiley & Sons; 2007. Available from: https://app.
knovel.com/hotlink/khtml/id:kt007WFMB1/handbook-noise-vibration/
gear-noise-vibration-identification.
[19] Jans J, Wyckaert K, Brughmans M, Kienert M, Van Der Auweraer H, Donders S, et al..
Reducing Body Development Time by Integrating NVH and Durability Analysis from the
Start; 2006. Conference: SAE World Congress & Exhibition
[20] Bahman A.S, Iannuzzo F, Suganuma K. 8 - Computer-aided engineering simulations.
In: Wide Bandgap Power Semiconductor Packaging. Woodhead Publishing; 2018. p.
199–223. Available from: http://www.sciencedirect.com/science/article/pii/
B9780081020944000104.
[21] Wijker J, Springerlink. Mechanical Vibrations in Spacecraft Design. Berlin, Heidelberg
2004.
[22] Welch K. Modal participation factors; 2016. Altair Blog. Available from: https://blog.
altair.com/simsolid-modal-participation-factors/.
62
[23] Mallikarjuna Rao T. Modelling And Simulation Of Research Concept Vehicle Using Mbd-
FEM Approach; 2015. Master Thesis KTH Available from: http://kth.diva-portal.
org/smash/get/diva2:906770/FULLTEXT01.pdf
[24] Sellgren U. Component mode synthesis–a method for efficient dynamic simulation of
complex technical systems. VISP WP5 Document Data, Stockholm. 2003;.
[25] Zhou Z. Actran for Acoustic Radiation Analysis;. FFT. Available from:
https://www.vpe-swiss.ch/fileadmin/user_upload/vpe.hsr.ch/doxs/
Workshops/Akustik_Simulation/MSC_Ze.pdf.
[26] Lindberg D. MSC Adams modelling of mechanical system in A400M Crew Entrance
Door; 2012. Master Thesis Linkoping Institute of Technology, Sweden Available from:
http://liu.diva-portal.org/smash/get/diva2:531245/FULLTEXT01/.
[27] MSC. Generating Flexible Bodies in Adams View Environment;
2018. Available from: https://simulatemore.mscsoftware.com/
generating-flexible-bodies-in-adams-view-environment/.
[28] Zhu C, Liu Y, Cai G, Zhu L. Dynamics Simulation Analysis of Flexible Multibody of
Parallel Robot. Applied Mechanics and Materials. 2007;10-12:647.
[29] MSC Software. Adams Help;.
[30] Šulka P, Sapietova A, Dekys V, Sapieta M. Analysis and synthesis parameters influencing
to the effects of impact. MATEC Web of Conferences. 2018 Jan;157:03018.
[31] FFT & MSc. Adams to Actran Plugin Documentation;.
[32] Elahinia M, Lee E.T, Eun H.C. Structural Damage Detection by Power Spectral Density
Estimation Using Output-Only Measurement. Shock and Vibration. 2016;2016:8761249.
Available from: https://doi.org/10.1155/2016/8761249.
[33] Wallin H.P. Sound and vibration. Stockholm: KTH, Aeronautical and Vehicle Engineering;
2012.
63
TRITA -SCI-GRU 2020:329
www.kth.se