Structural Validation of Hanger Brackets in Exhaust Systems: Correlation Between Virtual Simulation and Experimental Testing and Its Optimization
Politecnico di Torino
Automotive Engineering
Corso di Laurea in
Ingegneria dell’Autoveicolo
Tesi di Laurea Magistrale
Structural Validation of Hanger Brackets
in Exhaust Systems: Correlation Between
Virtual Simulation and Experimental
Testing and Its Optimization
Relatore: Prof. Andrea Tonoli
Tutor: Ing. Marco Nardi Candidato: Alex Giovinazzo
Aprile 2019
ii
To my parents.
Abstract
Since the last decades, the engineering design activity has shifted from manual
drawings and dimensioning calculations to their computer-aided versions.
Nowadays, in the industrial field, any manufactured product, as well as its
characteristics and the operational processes necessary to build it, is designed
and simulated in advance exploiting the computational capabilities of computers.
By virtue of this technological improvement, design modifications are
applied easily and their effects are checked instantaneously, allowing a reduction
of the product development time. Once the iterative adaptation process
has finished, the project is validated.
Although virtual analysis results, manufactured goods have to be tested in
a physical manner to confirm that the final objects comply with the imposed
requirements. Here, a second validation arises.
As a matter of fact, the two validation methods differ because of the impossibility
of replicating identically the physical test in a virtual environment.
To overcome this obstacle, simplifying assumptions are considered, but this
unavoidably creates differences.
The aim of this Thesis project is to analyze the two structural validation
methods (experimental and virtual) to understand the dissimilarities and the
effects that they exert on the correlation and to propose new validation procedures
that provide more correlated results between the two methodologies.
The present work is the summary of six months of internship within the
Exhaust Systems R&D Testing department at Magneti Marelli S.p.A., an italian
industry with worldwide diffusion devoted to the production of automotive
components. The focuses of the investigation are the structural validation
methods of hanger brackets in exhaust systems.
After the introduction of the state-of-the-art methods adopted by the Company
for the fatigue life validation in exhaust hanger brackets, a complete case
study analysis provides the evidence of the inconsistencies related to the procedures.
Different alternatives to the usual methods are proposed: evaluation of
load levels on each bracket equivalent to the experimental driving test, different
computational validation method based on structural vibrational analysis and
identification of an average cumulative load curve, reveal to reduce the gap
between the methodologies. Eventually, some guidelines for the verification
and application of the innovative validation dispositions are proposed.
Contents
1 Introduction 1
1.1 The Exhaust System: an overview . . . . . . . . . . . . . . . . 1
1.2 Purpose of the work . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Design and Validation Methods . . . . . . . . . . . . . . . . . . 6
1.4 List of the exhaust systems analysed . . . . . . . . . . . . . . . 7
1.4.1 Model 356 . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.2 Model 520 without muffler . . . . . . . . . . . . . . . . . 8
1.4.3 Model 520 with rear muffler . . . . . . . . . . . . . . . . 8
1.4.4 Model 952 . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Virtual validation 10
2.1 Model preparation and Mesh . . . . . . . . . . . . . . . . . . . 11
2.2 Damage evaluation: Road Load Simulation . . . . . . . . . . . 15
3 Experimental validation 19
3.1 Fatigue test and W¨ohler’s curve computation . . . . . . . . . . 20
3.2 Data acquisition on the Proving Ground . . . . . . . . . . . . . 22
3.2.1 Test exhaust line preparation . . . . . . . . . . . . . . . 23
3.3 Data analysis and comparison with W¨ohler’s curve . . . . . . . 27
3.3.1 Strain gauges calibration . . . . . . . . . . . . . . . . . . 27
3.3.2 Damage evaluation and Validation criterion . . . . . . . 30
4 Equivalent load 32
4.1 Differences between the methods . . . . . . . . . . . . . . . . . 32
4.1.1 Correlation proposals . . . . . . . . . . . . . . . . . . . . 33
4.2 Equivalent load . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4 Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5 Results comparison . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.5.1 Virtual calibration . . . . . . . . . . . . . . . . . . . . . 37
4.5.2 Computation of the brackets loads . . . . . . . . . . . . 40
4.6 Comment and critical issues . . . . . . . . . . . . . . . . . . . . 40
iv
CONTENTS v
5 Vibrational analysis 44
5.1 Initial observations . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.1 Calibration at the Road Simulation Bench . . . . . . . . 48
5.2.2 Virtual Vibrational analysis . . . . . . . . . . . . . . . . 51
5.3 Results comparison . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.1 Simulation of road acceleration spectra . . . . . . . . . . 53
5.3.2 Modal deformation . . . . . . . . . . . . . . . . . . . . . 55
5.4 Comments and observations . . . . . . . . . . . . . . . . . . . . 63
6 Global cumulative curve 65
6.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7 Conclusion 68
A Strain calibration factors 69
B Road Simulation Bench description 71
Bibliography 73
List of Figures
1.1 Exhaust line subdivision into Hot-End and Cold-End . . . . . . 3
1.2 Monolith flow distribution . . . . . . . . . . . . . . . . . . . . . 3
1.3 Exhaust muffler components nomenclature . . . . . . . . . . . . 5
1.4 Exhaust line under-body constraints . . . . . . . . . . . . . . . 6
1.5 Steps in the validation process . . . . . . . . . . . . . . . . . . . 7
1.6 Layout of the 356 line . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Layout of the 520 line without muffler . . . . . . . . . . . . . . 8
1.8 Layout of the 520 line with muffler . . . . . . . . . . . . . . . . 8
1.9 Layout of the 952 line . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Bracket and weld bead mesh . . . . . . . . . . . . . . . . . . . . 12
2.2 Mesh of a junction between two surfaces . . . . . . . . . . . . . 12
2.3 CBUSH and Rigids employment in FE analysis . . . . . . . . . 13
2.4 Converters substrates internal structure . . . . . . . . . . . . . 14
2.5 Haigh diagram working point identification . . . . . . . . . . . 15
2.6 Graphical representation of Safety Factor . . . . . . . . . . . . 16
2.7 Haigh diagram of base and welded material and temperature effect 17
2.8 Stress and Safety Factor maps . . . . . . . . . . . . . . . . . . . 18
3.1 Sinusoidal symmetric load . . . . . . . . . . . . . . . . . . . . . 21
3.2 Hydraulic jack . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 W¨ohler’s curve from fatigue test . . . . . . . . . . . . . . . . . . 22
3.4 Gas deviation upstream Cold-End . . . . . . . . . . . . . . . . 23
3.5 Gas deviation downstream SCRUF . . . . . . . . . . . . . . . . 24
3.6 Scheme of a strain gauge . . . . . . . . . . . . . . . . . . . . . . 24
3.7 Strain gauges positioning . . . . . . . . . . . . . . . . . . . . . 25
3.8 Strain gauges electrical connection . . . . . . . . . . . . . . . . 26
3.9 Strain gages calibration bench . . . . . . . . . . . . . . . . . . . 28
3.10 Calibration strain time history . . . . . . . . . . . . . . . . . . 28
3.11 Load-Strain calibration characteristic . . . . . . . . . . . . . . . 29
3.12 Strain-to-Load time history conversion . . . . . . . . . . . . . . 29
3.13 Graphical representation of Miner’s equation components . . . 30
vi
LIST OF FIGURES vii
4.1 Different strain (or load) cycles . . . . . . . . . . . . . . . . . . 34
4.2 Equivalent load graphical representation . . . . . . . . . . . . . 36
4.3 Virtual calibration constraints . . . . . . . . . . . . . . . . . . . 37
4.4 Stress experimental calibration . . . . . . . . . . . . . . . . . . 38
4.5 Correspondence of stress measurement points . . . . . . . . . . 39
4.6 Scheme of bracket load computation from stress map . . . . . . 40
4.7 Equivalent loads-to-Mass ratios . . . . . . . . . . . . . . . . . . 43
5.1 Under-body and brackets accelerometers . . . . . . . . . . . . . 45
5.2 Road acceleration spectra (FFT) . . . . . . . . . . . . . . . . . 47
5.3 Road Simulation Bench . . . . . . . . . . . . . . . . . . . . . . 48
5.4 RSB reproduced counter-bracket . . . . . . . . . . . . . . . . . 49
5.5 Exhaust line mounted on RSB . . . . . . . . . . . . . . . . . . . 50
5.6 Rubber isolators dynamic stiffness . . . . . . . . . . . . . . . . 51
5.7 Rubber isolators damping coefficient variation . . . . . . . . . . 52
5.8 FEM accelerations application points . . . . . . . . . . . . . . . 53
5.9 Comparison between experimental outcomes and numerical vibrational
analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.10 RSB acceleration spectra (FFT) . . . . . . . . . . . . . . . . . . 56
5.11 Composition of a colour map . . . . . . . . . . . . . . . . . . . 57
5.12 Proving Ground surface . . . . . . . . . . . . . . . . . . . . . . 57
5.13 356 - Colour maps of tailpipe bracket acceleration and deformation 58
5.14 356 - Modal shape at 18.5 Hz . . . . . . . . . . . . . . . . . . . 59
5.15 356 - Colour maps of penultimate bracket acceleration and deformation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.16 356 - Modal shape at 13.1 Hz . . . . . . . . . . . . . . . . . . . 60
5.17 520- Colour maps of penultimate bracket acceleration and deformation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.18 520 - Modal shape at 10.1 Hz . . . . . . . . . . . . . . . . . . . 61
5.19 263 - Colour maps of tailpipe bracket acceleration and deformation 62
5.20 263 - Modal shape at 22.8 Hz . . . . . . . . . . . . . . . . . . . 62
6.1 Superposition of normalized cumulative curves . . . . . . . . . . 66
6.2 Global normalized cumulative curve . . . . . . . . . . . . . . . 67
B.1 Road Simulation Bench . . . . . . . . . . . . . . . . . . . . . . 72
List of Tables
4.1 Differences between validating methods . . . . . . . . . . . . . . 33
4.2 Example of table for the computation of Equivalent loads . . . 36
4.3 Comparison between experimental and virtual stress calibration 39
4.4 Comparison between Equivalent an 4g-caused brackets loads . . 40
5.1 Acceleration spectra matrix for each pavement . . . . . . . . . . 46
5.2 Comparison between isolators and brackets maximum forces . . 55
5.3 Comparison of experimental and vibrational simulation outcomes 63
A.1 520 - Strain calibration coefficients . . . . . . . . . . . . . . . . 69
A.2 356 - Strain calibration coefficients . . . . . . . . . . . . . . . . 70
viii
List of Acronyms
CAD Computer Aided Design
CAE Computer Aided Engineering
CE Cold-End
HE Hot-End
ECU Engine Control Unit
DV Design Validation
PV Product Validation
FE Finite Element
FEA Finite Element Analysis
RLDA Road Load Data Acquisition
SF Safety Factor
DAQ Data Acquisition system
MIL Malfunction Indication Lamp
SCR Selective Catalytic Reduction
DPF Diesel Particulate Filter
EMI Electro-Magnetic Interferences
RSB Road Simulation Bench
FFT Fast Fourier Transform
ix
List of Symbols
f Frequency [Hz]
g Gravity acceleration [9.81m/s2]
A,B W¨ohler’s curve parameters
R Electric resistance [⌦]
ΔR Electric resistance variation
" Material strain
Ks Strain gauge resistance factor
l Generic length
Δl Length variation
μstrain Practical measurement unit of the mechanical strain [μm/m]
Fi Generic force/load
di Damage contribution of the load level Fi
ni Number of counted occurrences of the load Fi
Ni Number of repetitions of load Fi that leads to component failure
D Damage according to Miner’s rule
Feq Equivalent load
neq Equivalent number of cycles
Neq Number of repetitions of load Feq at failure
E 1 ÷ 4 Indication of the polar location around a bracket
σ Statistical standard deviation
x
Chapter 1
Introduction
1.1 The Exhaust System: an overview
In the past, the exhaust system of a vehicle was merely considered as the set
of elements aimed at collecting burnt gases from the engine outlet ports and
dispersing them towards the environment, in a way that minimized the interaction
with the occupants. Indeed, the exhaust pipes of passenger cars end
typically behind the vehicle, in a position close to the ground, whilst in some
industrial vehicles vertical ducts discharge combustion gases above the vehicle
roof, to avoid gas recirculation in the cabin even in case of stationary operations
(e.g. earth moving machines). This is fundamental because combustion
products contain toxic substances, like carbon monoxide (CO), benzene or nitrogen
oxides (NOx), which are harmful for human beings and may lead to a
loss of consciousness if inhaled in high concentration.
In the last decades, this mere transportation purpose has been flanked by
several further roles, some of which gained a preponderant place over the others.
In particular, the new implemented functions are, following a hierarchical
order:
• abatement of the pollutants deriving from the non-ideal combustion processes
that occur in the engine, through chemical catalysis of the exhaust
gas stream;
• tailpipe noise, principally deriving from combustion events, and shell
noise reduction, in order to achieve type-approval acoustic limitations
and to improve internal comfort;
• minimization of the resistance the exhaust gas has to face in crossing the
pipes, mainly caused by internal elements (catalytic converters, filters
and traps, muffler diaphragms, flow interaction, etc.) to avoid an engine
throttling effect and a reduction of its volumetric efficiency;
1
CHAPTER 1. INTRODUCTION 2
• thermal insulation between hot parts, in particular manifolds and catalytic
converters, and nearby components, employing heat shields;
• vibration insulation between the suspended line and the chassis, made
through rubber isolators, to enhance riding comfort;
• aesthetic appearance, provided by chromed stainless steel tailpipe terminations;
• in particular applications, like sport cars, the exhaust system is shaped
in order to convert the combustion noise into a specific "sound", which
imparts the vehicle a distinctive personality, still respecting noise limitations
imposed by the legislation.
Since many of these characteristics are fundamental for correct vehicle operation,
as well as for its commercialization, it is of paramount importance
to preserve all them during the entire vehicle life span. This is a challenging
goal because, although the high level requirements imposed by the customer
(namely the car maker), the price of the entire system must be kept as low as
possible. Albeit this marketing rule applies to any type of product and goods,
in the specific case of the exhaust system it is particularly important because,
in the final customer’s mind (typically the driver/owner), the exhaust does not
carry any added value to the vehicle, thus he is not willing to spend further
money for special components, even if they are guaranteed to withstand highly
severe conditions.
Furthermore, the working environment of the system is adverse: water, deicing
salt, stones, etc. are elements that impact unavoidably with the exhaust
line during normal vehicle operations. For this reason, the definition of the
system must be carried with the objectives in mind. The design is even more
complicated by the narrow space available in the under-body: suspension assembly,
shafts and axles, fuel/urea tanks and rear bumper are all elements that
reside close to the exhaust, but that must not interfere with it. That is the
reason of the complex shapes given to the piping: they must fit the available
space, not protruding in the internal compartment volume.
In view of the very different objectives that an exhaust system has to accomplish
and of the different boundary conditions to which the line is subjected,
it is usual to subdivide it into two sections (Figure 1.1):
• Hot-End (HE);
• Cold-End (CE).
The former, as the name suggests, is the first tract of the line, from the
engine outlet ports, up to the flexible joint. The elements belonging to this
subgroup have to cope with hot and aggressive gas either for its collection from
CHAPTER 1. INTRODUCTION 3
Figure 1.1: Exhaust line subdivision into Hot-End and Cold-End and
related components belonging to each subgroup
the engine (exhaust manifold and piping) and for the promotion of chemical
reactions (catalytic converters and filters). Because of the extreme temperature
involved, which can reach almost 1 000◦C in high performance sport cars, and of
the high vibration levels transmitted by the engine head, Hot-End components
must be designed to withstand infinite thermo-mechanical fatigue in a corrosive
environment. Moreover, exhaust manifolds are designed to avoid cross-flow
among the ducts, whilst conical tracts of converters housings are shaped in a
way that distributes evenly the gas over the inlet surface of the monolith, to
maximize the conversion efficiency: accurate fluid-dynamic analyses reveal to
be fundamental for these components.
Figure 1.2: Example of flow distribution analysis on a converter monolith
CHAPTER 1. INTRODUCTION 4
To sum up, since this subset integrates, further to the piping, some chemical
structures and electronic devices, able to cope with the engine control unit
(ECU) to apply the best injection strategies, its design is mainly related to
engine requirements, hence it is very often carried along with the car maker or
in a joint-venture with the engine manufacturer.
The Cold-End subgroup, by convention, starts downstream the flexible
decoupler and includes all the components up to the tailpipe. The main constituents
of this sub-assembly are the mufflers, the pipes, the hanger brackets
and the elastic isolators with which the line is anchored to the vehicle
under-body. Although the gas may reach the environment with a temperature
significantly higher than the atmospheric one, in the order of 90 ÷ 100◦C at
maximum, the designation of cold indicates that the thermal effects on the
components are negligible with respect to mechanical stresses. As a matter of
fact, every analysis and experimental test made on these elements is carried at
room temperature, with paltry effects on the results.
The Cold-End design is principally depending on vehicle strategy. As explained,
the main drivers of the project, especially for conventional cars, are
internal comfort and available space present in the under-body, always considering
cost minimization. This leads to the reduction of components redundancy,
like silencers, by properly shaping few key elements. On premium cars,
the Cold-End is also responsible of imparting a distinctive "personality" to
the vehicle. Chromed tailpipe terminations and a deep exhaust sound provide
good appearance and pleasant feeling to the driver, of course at an higher
production cost.
1.2 Purpose of the work
The following dissertation collects and synthesizes the results and the experiences
of a six-months internship in the R&D Testing Department of the
Exhaust Systems division of Magneti Marelli S.p.A. in Venaria Reale, Turin
(Italy). The Company has numerous plants diffused all over the world which
design and produce several automotive spare parts and components, among
which also exhaust systems.
The proposed Thesis is focused on the analysis optimization of some components
belonging to the Cold-End segment of the exhaust system. Particular
attention has been dedicated to structural validation of hanger brackets. The
outcomes of this activity could be adapted to other elements of the line, for
instance welded junctions between pipes and muffler end caps, for which similar
validation procedures are employed.
CHAPTER 1. INTRODUCTION 5
Figure 1.3: Nomenclature of exhaust muffler components
More in depth, the cardinal objective of the investigation is to identify an
innovative virtual validation method featuring a better correlation with the
experimental test. In fact, at the present time, fatigue life accreditation on
these components is based on best practices, explained in Chapters 2 and 3,
established by the Company in accordance with the customers. Although these
standards revealed to be satisfactory in guaranteeing components resistance all
along vehicle service life, the research has been carried to reduce the discrepancies
that exist between virtual and experimental methods, in such a way that
both lead to comparable results.
All the analyses and conclusions proposed are the outcomes of physical
tests that the author had the opportunity to set up and perform on the exhaust
lines of some models and the elaboration of data gathered by him and by the
Company on previous projects. Several approaches, explained in the details
in Chapter 4.1.1, have been undertaken and their results have been examined
to identify the best fitting technique. Further to this, the same analyses have
been conduced on exhaust systems of various cars and the results have been
compared among each other with the intention of discovering some relations
with a global validity and not merely tailored on a specific case study.
Eventually, further to the interim conclusion reached at the end of the
traineeship period, an insight into possible open points worthy to be developed
will be proposed.
CHAPTER 1. INTRODUCTION 6
1.3 Design and Validation Methods
The responsibility of an exhaust systems’ manufacturer is to design and produce
exhaust lines that achieve the requirements imposed by the customer,
typically a car maker. Usually, the project starts with the recognition of topological
boundary conditions of the vehicle under-body, namely the available
space, the location of the mounts, the presence of components sensible to the
temperature and so forth, which are depicted in Figure 1.4.
Figure 1.4: Scheme of the main constraints on the design of the exhaust
line in a vehicle under-body
Subsequent to the geometrical definition, the exhaust line properties and
behaviours have to be verified and the model characteristics modulated with
the aim of respecting the requisites stipulated in the contract with the customer.
In a first phase, the verification is carried out in a virtual manner,
employing CAD/CAE methods. Thereafter, the first prototypes are built and
the design adequacy is assessed by means of physical tests, the results of which
will determine if the project has to be revised.
Finally, once the design has been thoroughly validated, the mass production
can start. However, the release of this acknowledgement does not imply
that the produced elements will be immune from errors: some components, extracted
randomly from the line, are subjected to a further set of tests, similar to
the validating ones, whose purpose is to certify that the production processes
are suitable to manufacture components that fulfil the requirements agreed. In
Figure 1.5 the principal steps of the validating processes are illustrated.
As it can be easily inferred, the former step is called Virtual validation,
whilst the latter two fall under the name of Experimental validation of the
Design (DV) and of the final Product (PV). In the following Chapters, both
methods will be described in their details, dedicating a particular attention to
the application of them for hanger brackets fatigue life validation.
CHAPTER 1. INTRODUCTION 7
Figure 1.5: Summary of the characteristics inspected during the validation
processes, arranged in a chronological order. On the left of the
Figure there are the design inputs/boundary conditions
1.4 List of the exhaust systems analysed
In this Section, the layouts of the principal exhaust lines analysed are listed as
reference for the results proposed. For all the models, the experimental investigation
has been supported by, and the results compared to, computational
simulations.
For all the vehicles, only the project number is reported, neglecting the
commercial name.
1.4.1 Model 356
The exhaust system shown in Figure 1.6 has been thoroughly scrutinized by
the author, as fundamental case-study. From the application of strain gauges
and under-vehicle accelerometers, the line has been tested on the prescribed
Proving Grounds, to be finally analysed at the Road Simulation Bench.
Figure 1.6: Layout of the line belonging to the model 356
Data concerning the subsequent models, on the contrary, were already available
in the Company. They have been elaborated and analysed to be compared
with the results of the case-study. Nevertheless, for calibration purposes, some
CHAPTER 1. INTRODUCTION 8
extra strain gauges (principally rosettes) have been applied also to some of
these systems.
1.4.2 Model 520 without muffler
For the line presented in Figure 1.7, both brackets strains and counter-brackets
accelerations have been acquired to try to discover a relation among them.
Figure 1.7: Layout of the line belonging to one model 520
1.4.3 Model 520 with rear muffler
This layout, reported in Figure 1.8, has been mainly employed for calibration
purposes and for understanding the relation between equivalent loads at the
brackets and line mass distribution.
Figure 1.8: Layout of the line belonging to another model 520, endowed
with the rear muffler
CHAPTER 1. INTRODUCTION 9
1.4.4 Model 952
Data related to the exhaust line of Figure 1.9, similarly to the previous case,
have been analysed in terms of equivalent loads, in relation to the different
layouts.
Figure 1.9: Layout of the line belonging to the model 952
Lastly, for the evaluation of a global cumulative proposed in Chapter 6,
data of 156 brackets of different models and layouts, collected by the Team
during its testing activities, have been inferred in a statistical perspective.
Still, none of them has been scrutinized with unconventional methods other
than the agreed validating procedure.
Chapter 2
Virtual validation
Once the topological design of the exhaust line has been completed by the
drawing team, a set of virtual analyses is run on it, as evidenced in Figure 1.5.
The aim of such an examination is to ascertain, before the production, that the
components will respect the targets imposed by the customer, thus avoiding
wasting time and money in manufacturing not compliant parts. The characteristics
of the exhaust systems that are checked are, among all:
• Fluid-dynamic behaviour, mainly of the Hot-End group, but also of the
whole assembly, to evaluate the back-pressure that the gases would face
while crossing the exhaust;
• Acoustic response of the line, to understand if the adoption of mufflers
is mandatory, and eventually to determine their dimensions;
• Catalyst surface exploitation (see Figure 1.2) and conversion efficiency
determination to establish the required monolith’s precious metal loading
to achieve the emissions target;
• Mode Shapes of the line, through a modal analysis at room temperature,
to evidence the natural deformations of the system;
• Natural Frequencies of the exhaust system, second outcome of the modal
analysis. For the Hot-End, the eigenfrequencies must lay above the excitation
spectrum produced by the engine, while for the Cold-End, the
customer requirements focus usually on hanger brackets’ natural frequencies
rather than on the whole line;
• Rubber Isolators Reliability, to ensure that the static loads on the elastic
elements due to gravity are below the acceptable thresholds;
• Cold-End Containment, to verify that the application of 1 g vertical (Z)
and lateral (Y ) static accelerations does not lead to interferences with
chassis components and rear bumper;
10
CHAPTER 2. VIRTUAL VALIDATION 11
• Thermal Stresses, through a thermal analysis, especially for the Hot-
End, to ensure that stresses due to thermal elongation do not overcome
material limits;
• Fatigue behaviour, both for the Hot-End, which has to sustain infinite
fatigue life, and for the Cold-End. The latter is inspected through a
damage evaluation or Road Load Simulation, either for the single brackets
and for the whole sub-assembly, to evaluate the damage level of the
components when subjected to established loads.
Going deeper in the details of the last point, which is the core of this
Thesis work, fatigue verification, at this stage, is made comparing local stresses
on the exhaust line generated by the application of a predefined load, to the
fatigue limit of the material, obtained from the corresponding Haigh diagram.
From the ratio of these values, a Safety Factor (SF) for each node of the
Finite Element (FE) model is obtained. In the following Sections, a better
explanation of these processes will be proposed.
2.1 Model preparation and Mesh
For running the computational simulation, it is necessary to assign material
properties to the various components, starting from the input geometry, designed
by the drawing team, and to mesh the parts. Then, according to the type
of analysis to be carried, proper boundary conditions (namely constraints) and
external inputs (normally forces, displacements, accelerations, temperatures,
etc.) are applied to the model.
At this point, the solver is launched and the results of the computation are
visualized in the post-processing phase.
Conventionally, the Finite Element Analysis (FEA) applied to exhaust systems’
Cold-Ends employs four types of elements:
• 3D Hexa elements, featuring a parallelepiped shape, for hanger brackets.
Since first order elements are used, meaning that local stress and strain
have a constant value within the element, to describe the internal stress
distribution (butterfly diagram) of the structure it is necessary to map
the thickness of these features with two rows of hexa elements, as shown
in Figure 2.1;
• 3D Penta elements, prisms with triangular base, for most of the weld
beads. This strategy is both used for the junctions between two solid
bodies and between a solid and a surface;
CHAPTER 2. VIRTUAL VALIDATION 12
Figure 2.1: Enlargement of the welded connection between bracket and
pipe. It is clearly visible the two-layer mapping of the former and the
triangular base of green Penta elements used to model the weld bead
• 2D Shell elements for pipes, muffler housings, end-caps, internal baffles,
etc., subdivided in their turn into Tria (triangles) and Quad (quadrilaterals).
In this case, the material thickness is assigned symmetrically with
respect to the base surface of the drawing. Furthermore, these elements
are employed to model the junction between two surfaces, as represented
in Figure 2.2: in this case, the weld bead is simulated connecting the
nodes of the two shells by means of a set of rigids and covering the gap
with an additional oblique surface (a shell) that represents the actual
surface of the bead.
Figure 2.2: Highlight of the modelling of welded junction between two
surfaces. The green sticks, labelled "RBE2", are the rigids, while the
purple inclined surface represents the weld bead.
CHAPTER 2. VIRTUAL VALIDATION 13
• CBUSH elements for flexible decoupler and rubber isolators. This element,
featuring the same behaviour of a spring, concentrates its stiffness
property, with its relative value depending on the direction, between
its extremities. These nodes are connected to the adjacent components
(pipes in case of flexible decoupler, brackets and counter-brackets for rubber
isolators) through rigids, in such a way that their relative displacement
is transferred identically to the extremities of the aforementioned
elastic element.
• Rigids elements, as announced before, used to simulate infinitely stiff
connection between two mesh nodes.
Figure 2.3: Detail of the application of Rigids and CBUSH elements.
The flexible decoupler is visible in Figure (a), while a rubber isolators
and the connection between counter-bracket and chassis in Figure (b).
The CBUSH resides at the intersection of the convergent rigids lines
For the purpose of the structural analysis, any kind of catalytic monolith
or filter present in the line accounts exclusively as an additional mass, thus
it is unnecessary to model its complex internal structure. Furthermore, since
the monolith’s material is normally ceramic-based1, not suited to withstand
external loads, its actual presence does not improve the structural properties of
the line. In accordance with this principle, whenever the Cold-End incorporates
a catalyst or a filter, its modelling is made employing a non-structural2 shell
with negligible thickness, to which the whole monolith mass is assigned.
1For particular applications, mainly for closed-coupled pre-converters or for motorbikes,
the substrate can be made by a metallic foil shaped in a sinusoidal manner, as depicted in
Figure 2.4.
2In FEA, non-structural property indicates the inability of the element to sustain mechanical
stresses.
CHAPTER 2. VIRTUAL VALIDATION 14
Figure 2.4: Internal structure on converters substrates: the thin ceramic
walls or metallic foil are not suitable to withstand mechanical
stresses
Even if this last sentence might appear inconsistent with the description
developed in Section 1.1, it could happen that some Cold-Ends, as it occurred
in two of the models analysed, are equipped with converters. Historically, it
has been evidenced that this fact occurs immediately after the introduction of
a new technology of emission reduction. The first three-way catalytic converters
were located in an underfloor position. As the time passed, the catalyst
approached the engine outlet ports, up to reaching the so-called close-coupled
position, to better exploit the thermal energy of the burnt gas and reduce its
light-off period.
This two-step introduction process is the natural consequence of two concomitant
factors:
• the necessity of endowing the new produced cars with the incoming technology,
to comply with new regulation standards, thus to be allowed to
sell the vehicle;
• the impossibility of a sudden modification of the design and production
of highly complex components, like the Hot-Ends, which would require
a whole re-arrangement of engine bay space.
At present, a similar process is occurring with the Diesel Selective Catalytic
Reduction strategy introduction: fitting the SCR directly in the engine
compartment, or close to already present elements, like the DPF, is not
straightforward. The SCR of models already in production is placed in the
under-body, thus it is unavoidably integrated in the Cold-End subgroup. In
Section 3.2.1, the countermeasures required to address this problem during
experimental tests on the Cold-End will be illustrated.
Further to the definition of the material properties, the FEA requires also
an identification of the boundary conditions. At this stage of the analysis,
CHAPTER 2. VIRTUAL VALIDATION 15
they principally correspond to the physical constraints to which the counterbrackets
are anchored: since no chassis is modelled, it is sufficient to block all
the degrees of freedom of the nodes at the interface with the under-body to
obtain reliable results.
2.2 Damage evaluation: Road Load Simulation
As mentioned at the beginning of this Chapter, computational fatigue damage
estimation in exhaust hanger brackets is achieved comparing local stresses to
the relative material fatigue limits, obtained from the Haigh diagram.
To identify the coordinates of the working point for each node in such a
plot, it is necessary to discern the overall mechanical stress level into its two
components:
• Mean stress (σm), caused by the presence of a static load;
• Alternating stress (σa), consequence of the application of a dynamic load;
as depicted in Figure 2.5.
Figure 2.5: The coordinates of the working point in the Haigh diagram
are the static and alternating components of the applied load
For the validation of hanger brackets, the common practice lead, on one
hand, to select as static load the gravitational acceleration, thus the weight of
the line. On the other hand, for what concerns the alternating stress value, it
has been selected de facto the one produced by the static application of an
analogous acceleration, but with a magnitude of 4 g, i.e. four times the static
load. This state-of-the-art approximation had to be applied because the simulation
of a real load time history, applying as inputs the data gathered during
CHAPTER 2. VIRTUAL VALIDATION 16
the Road Load Data Acquisition (RLDA) on the Proving Ground, is extremely
time-consuming and could not be afforded. Indeed, it is worth to remark that,
although 4 g represents an average fictitious alternating excitation, its value,
repeated for 500 000 cycles, tends to generate a condition more onerous with
regard to the physical driving test, hence this process, being extremely conservative,
lead to the production of highly reliable components.
Subsequently, a Safety Factor is assigned to each node of the meshed structure.
Its value is computed, according to Equation 2.1, as the ratio between
the material fatigue limit and the actual stress of the element.
SF =
σlim
σwp
(2.1)
This procedure can be outlined in geometrical terms looking at the Haigh
diagram of Figure 2.6. Once the local working point coordinates (namely mean
and alternating components) have been located, the corresponding stress level
is represented by the segment joining that point to the origin. In a similar
manner, the fatigue limit corresponds to the extension of said line until the
intersection with Haigh curve.
Figure 2.6: The Safety Factor is defined as the ratio between the limit
stress (orange segment length) and the local stress (green segment length)
As one can immediately deduce, all the area underneath the Haigh curve
represents a zone for which the Safety Factor is larger than unity, whilst, above
the curve, the local stress exceeds its limit (SF < 1). Whether an operation
point falls in proximity of the limit curve, still remaining below it, the Safety
Factor approaches unity and an alert should be declared: the component is in
a borderline condition.
CHAPTER 2. VIRTUAL VALIDATION 17
The Haigh diagram to which the stresses are compared is evaluated at
500 000 cycles, in accordance with customer requests. For the nodes embedded
in a weld bead and in the heat affected zone adjacent to it, the values of
the Haigh diagram are halved. Even this hypothesis derives from the common
practice, therefore its validity should be verified through fatigue tests on specimens.
Nonetheless, the adoption of this guideline allowed to produce compliant
parts.
When dealing with fatigue, it is also important to consider the working
temperature of the material in order to select the proper diagram: higher temperatures
reduce the material resistance, as evidenced in Figure 2.7.
Figure 2.7: Comparison between the Haigh diagram of a base metal
and its corresponding welded area at different temperatures (Tb > Ta) in
linear plot
The outcomes of the simulation are the stress levels in each node of the
mesh. Using a post-processor, such as PATRAN, it is possible to visualize the
stresses in a Map form, meaning with a chromatic scale on the virtual model
itself, as reported in Figure 2.8 condition (a). Despite this is a conventional
output of the analysis, it is not immediate to check whether the stress exceeds
or not the Haigh limit, especially if the model includes welded elements. To
overcome this issue, the Company has developed an internal software for the
virtual damage evaluation, which is aimed at producing a Safety Factor Map,
like the one reported in Figure 2.8 condition (b). The programme automatically
selects the correct Haigh diagram to gauge the local stress level: node by node,
it calculates the Safety Factor, applying Equation 2.1, and it assigns its value
to the element. Using again a post-processing software, it is possible to re-build
the physical model, upon which the Safety Factor Map is shown.
CHAPTER 2. VIRTUAL VALIDATION 18
Figure 2.8: Stress map (a) and corresponding Safety Factor map (b)
of an exhaust hanger bracket, obtained comparing the stresses of the first
map with the corresponding Haigh diagram
Courtesy of this adjustment, it is straightforward to identify the most fragile
point of the structure. In fact, there is no guarantee that the most stressed
point is also the weakest: since the heat affected zones of a weld bead have
a lower resistance, a lower stress on them might push the material closer to
the limit than a higher stress on the base material. If any zone would result
out of target, namely if its Safety Factor is lower than one (SF < 1), proper
corrective actions, in terms of material or design modifications, can be adopted
and their effectiveness assessed repeating the analysis; alternatively, the line is
declared valid.
Chapter 3
Experimental validation
The Experimental validation consists of a set of physical tests performed on
existing specimens, carried both in the testing facilities and on some specific
Proving Grounds, indicated by the customer. The investigation is aimed at
assessing if the requirements stated in Section 1.1 are achieved by the real
produced components, and eventually at alerting the design department of the
mismatch, possibly before mass production starts up.
The principal examinations carried by the testing department are:
• Material, Weight, Leakage and Dimensional checks. The first three are
carried mainly on the components, while the last inspection is also aimed
at verifying that the critical clearances among under-body components
and exhaust line are respected when this last is fitted underneath the
vehicle;
• Flow distribution, on a fluid-dynamic bench endowed with Pitot tubes,
to ascertain the prediction made during the Virtual simulation about
the homogeneous diffusion of burnt gas over converters surface (see Figure
1.2);
• Back-pressure measurement to assess the throttling effect caused by the
real exhaust system;
• Thermal shock and Hot Vibration tests, especially for the Hot-Ends, to
guarantee infinite thermal fatigue life of these components;
• Shell and Tailpipe noise level evaluation, before and after ageing, to
certify the actual produced noise and its durability over time;
• Time to dry, typically for Cold-End members, to avoid water stagnation
and potential corrosion of them;
19
CHAPTER 3. EXPERIMENTAL VALIDATION 20
• Physical modal analysis on the Hot-Ends, on hanger brackets, on body
counter-brackets and on heat shields, to identify their real modal displacement
and to ensure that the first eigenfrequencies lay out of their
relative excitation range;
• Mechanical fatigue of hanger and body brackets and of welded junctions
between pipes and mufflers, employing the methodologies described in
the following paragraphs, to validate their structural resistance when
subjected to determined loads and road profiles.
For what concerns the last point mentioned, the predominant requisite of
hanger brackets and welded joints is their endurance over the entire vehicle
service life: mechanical fatigue is thus the focus of the investigations made on
these components. The assessment procedure is based on three pillars:
1. Fatigue test and W¨ohler’s curve computation;
2. Data acquisition on the Proving Ground;
3. Data analysis and comparison with W¨ohler’s curve.
3.1 Fatigue test and W¨ohler’s curve computation
The purpose of this preliminary phase is to determine the mechanical fatigue
strength of exhaust hanger brackets and to obtain the component’s experimental
W¨ohler fatigue curve, to which the results of the following steps will be
referred. This assay is entirely carried out in the testing facilities, on devoted
benches.
To determine the fatigue behaviour of the components, fatigue tests are
performed on 10 to 15 physical specimens. The unit under investigation is anchored
to the bench, using suitable constraints, in the same position of the one
assumed under the vehicle. Then, a symmetrical sinusoidal load, characterized
by determined amplitude F and frequency f as illustrated in Figure 3.1, is
applied.
Conventionally, the load is applied by hydraulic jacks along the most critical
direction highlighted during the RLDA (Road Load Data Acquisition) or,
in absence of such an information, according to previous knowledge and experience
it has been evidenced that vertical (Z) direction is the most severe.
Occasionally, if the customer declares it explicitly, other orientations may be
adopted.
Different loads are applied to each specimen to thoroughly explore the
W¨ohler’s plot. If data of RLDA are available, the level of the first load is the
maximum measured during the driving test on the specific component. On
CHAPTER 3. EXPERIMENTAL VALIDATION 21
Figure 3.1: Sinusoidal symmetric load applied during the fatigue characterization
the contrary, if the aforementioned data have not been gathered yet, its value
is tuned on trials made on two exploration samples, also considering prior
experience on comparable parts.
The test is carried under load control: the force entity is monitored by a
load cell placed between the hydraulic jack extremity and the test item, as
displayed in Figure 3.2: a feedback control exploits this signal to adapt the
push-rod stroke in order to maintain the force within the 5% of the value set
by the operator (peak/valley compensation control).
Figure 3.2: Hydraulic jack employed for fatigue characterization: the
black element at the rod tip is the load transducer
Once every parameter has been specified, the test is launched. The rod,
pulsating at a frequency within 5 ÷ 20 Hz, stresses alternatively the bracket
engendering a purely fatigue damage. The system increments the value stored
in a counter whenever a cycle has been completed.
CHAPTER 3. EXPERIMENTAL VALIDATION 22
Since the applied load is kept constant by the controller during each repetition,
an increase in stroke of the hydraulic jack suggests that the sample is
weakening. As the rod displacement exceeds 150% of the initial one, devoted
alerts are triggered and the test is concluded. A visual inspection, even with
penetrating liquids if required, is mandatory to ascertain that the part presents
effectively a crack. In such circumstances, the number of cumulated load cycles
is recorded, along with the value of the load applied, otherwise, if no fracture
occurred, the sample is considered broken at 2 million cycles.
The obtained experimental values are plotted on a bi-logarithmic diagram,
whose abscissa axis indicates the number of cycles whilst the ordinary axis
reports the load applied, and, after their interpolation, the W¨ohler’s curve of
the particular feature is obtained. The regression line that describes the component’s
fatigue behaviour is linear in the logarithmic plot and is represented
by the Equation 3.1.
log10(N) = A + B · log10(S) (3.1)
Figure 3.3: Example of a W¨ohler’s curve of an exhaust bracket obtained
interpolating the results of the fatigue test on a physical component
It would be also possible to obtain plots containing probability curves,
which have been computed according to the ASTM E739-10 international
norm, to obtain a curve more significant for the entire production.
3.2 Data acquisition on the Proving Ground
The purpose of this activity is to acquire data relative to the dynamic loads to
which the exhaust line is subjected during standardized operating conditions,
to be compared with the previously defined W¨ohler’s fatigue curves. To attain
this objective, the vehicle involved in the investigation is equipped with a
CHAPTER 3. EXPERIMENTAL VALIDATION 23
dedicated exhaust system, upon which some sensors have been installed, and
it is driven on specific a Proving Ground, established in accordance with the
customer. During this phase, a Data Acquisition system (DAQ) samples and
records data. An individual acquisition batch is dedicated to each specific
track: the segmentation of the whole test time history, further to shortening
the trial run, allows to understand which is the most severe pavement/condition
and to obtain the overall cumulative by multiplying the contribution of each
track by its relative weighting factor: further details of these procedures are
presented in the next Sections.
3.2.1 Test exhaust line preparation
Gas Deviation As mentioned in Section 1.1, the Cold-End of an exhaust
system has to bear principally mechanical loads, because the thermal effect has
a negligible impact. In order to evaluate exclusively mechanical solicitations
on the line, it is necessary to bypass the hot exhaust gases immediately downstream
the close-coupled catalytic converter(s), possibly before the beginning
of the Cold-End. This countermeasure is implemented by drilling a hole of
suitable diameter in the external surface of the pipe and plugging the duct
by welding the removed part immediately upstream the orifice, as shown in
Figure 3.4.
Figure 3.4: Gas deviation immediately downstream the flexible decoupler,
at the beginning of the Cold-End
In the event that an under-body after-treatment element is integrated in
the Cold-End, for the reasons mentioned in Section 2.1, a bypass would impair
the operation of the sensors, thus of the entire vehicle, since the ECU (Engine
Control Unit) would detect a malfunctioning, lighting on the dashboard a
CHAPTER 3. EXPERIMENTAL VALIDATION 24
proper indicator (MIL) or even limiting the engine power (typical countermeasure
triggered in case of urea shortage in vehicles endowed with SCR). In this
case, as it occurred with one of the models analysed and shown in Figure 3.5,
the deviation must be practised downstream the last sensor.
Figure 3.5: Whenever the Cold-End comprises after-treatment devices,
the gas deviation must «<aqqqqbe drilled downstream all the related sensors,
not to impair vehicle functioning
A secondary advantage provided by the bypass of hot gas is that it enables
the application of low-temperature strain gauges, which are easier to be applied
and have a lower cost with respect to their hot counterpart.
Strain gauges theory The aim of the experimental verification is to acquire
the loads acting on hanger brackets and welded joints during the driving
test in the same points and directions of the fatigue characterization. These
loads are retrieved indirectly from strain measurements on the aforementioned
components obtained applying uni-axial, low-temperature strain gauges with
a grid length of 2mm on the specimens, as shown in Figure 3.6.
Figure 3.6: Scheme of an uni-axial strain gauge
The working principle of these transducers is based on the variation of electrical
resistance of materials when subjected to tensile or compressive forces,
according to Equation 3.2:
ΔR
R
= Ks · " (3.2)
CHAPTER 3. EXPERIMENTAL VALIDATION 25
where R is the gauge nominal resistance at rest, ΔR is the variation of it, Ks
is a gauge factor expressing the sensitivity of the transducer, while " is the
mechanical strain, defined in Equation 3.3, is the relative length variation.
" =
Δl
l
(3.3)
Being the resistance change very modest, a Wheatstone bridge configuration
is employed to magnify the variation and to convert it into a voltage change.
This routine is normally actuated within the acquisition device, selecting the
desired connection type, but it can also be done externally by the operator, as
described in the next Paragraph.
Strain gauges positioning Low-temperature strain gauges are applied on
metallic specimens using a cyano-acrilate based glue. The transducer is maintained
pressed in its position by an adhesive tape until the glue gets dry. At
this point, the gauge is able to track the strain of the substrate material.
Conventionally, four gauges are installed along the circumference of the
elements, at 90 deg among each other, as depicted in Figure 3.7, to acquire
loads along Z and Y (or X) directions. The sensing grid is normal to the
action line of the load, whilst it is parallel to the direction of elongation of the
hanger.
Figure 3.7: Naming convention and relative position of strain gauges
on hanger brackets or welded junctions
The strain gauges can be used individually, in a quarter-bridge configuration
(Figure 3.8 condition (a)), or connecting two opposite sensing elements
(e.g. E1 with E3 and E2 with E4) in a half-bridge topology (same Figure
condition (b)).
CHAPTER 3. EXPERIMENTAL VALIDATION 26
Figure 3.8: Quarter bridge (a) and Half bridge (b) connection layouts
The redundancy provided by the number of sensing elements employed is
not mandatory and can be neglected in presence of external constraints, like
the lack of available space, but it revealed to be convenient in that:
• the former topology grants the acquisition some data even if one of the
two opposite channels is impaired or totally lost (perhaps after mounting
operation beneath the vehicle or if the gauge detaches from the base
material);
• the same connection offers the possibility of comparing opposite channels
readings to check the correctness of acquired data during the postprocessing
analysis operation (they should be opposite in phase in case
of bending load applied to the feature);
• the latter strategy’s benefit is the automatic correction of offsets and
global trends, since only deformations with opposite values are read and
amplified: two strains congruent in amplitude and direction discarded by
the electric behaviour of the circuit itself.
For some peculiar application or analysis, also other sensors like thermocouples
or rosettes (three uni-axial strain gages forming an angle of 45 deg among
them) might be employed: the former are used to sense material temperature,
while the latter measure local mechanical stress.
Driving test The vehicle is finally driven on some specific Proving Grounds,
according to a procedure established by the customer, in the so-called RLDA
test. The tracks are paved with calibrated surfaces aimed at reproducing the
vast majority of possible conditions that the exhaust line would encounter
during its operating life. Data concerning the brackets strains and stresses
(only if rosettes are employed) are recorded per each track, using a specific
acquisition instrumentation and a PC. One run over each track is enough to
capture the relevant data; a second passage is performed some anomalies are
revealed by the operator.
CHAPTER 3. EXPERIMENTAL VALIDATION 27
Data from each sensor is sampled at a rate which allows to capture the
deformation time histories with a satisfactory resolution.
3.3 Data analysis and comparison withW¨ohler’s curve
After the physical trial, the acquired strain time histories are corrected and
analysed. The main corrections are aimed at the removal of false peaks in
the readings, sometimes due to EMI (electro-magnetic interferences) and very
likely present at the beginning and at the end of the data recording, at reducing
the effect of offset with respect to zero and drift, often due to thermal
elongation of hot components, especially if the gas deviation occurs after some
gauged element.
At the end of this refining process, the time histories of every single pavement
are juxtaposed consecutively, applying a proper multiplication factor to
each of them, to obtain a global overall time history. This last would equal, in
terms of damage, the repetition of the driving test over each pavement for the
aforesaid multiplication coefficient: the advantage of such a procedure is evident.
The necessity of the data correction, mentioned at the beginning of this
Section, becomes now apparent: if a time history features few very high peaks
caused for instance by an interference, the multiplication tout court of its data
can lead to a misleading overestimation of the damage, perhaps impairing the
validation result.
3.3.1 Strain gauges calibration
The instrumented exhaust line is dismounted again from the vehicle and the
strain gauges are calibrated in the laboratory, in order to find the relationship
between the load applied on the bracket (or junction) in the same position
and direction of the fatigue test and the corresponding deformation, measured
in μ strain.
1 μ strain =
1 μm
m
= 10−6 [−] (3.4)
As done during the fatigue characterization, the exhaust line is oriented and
positioned in the same way as underneath the vehicle and rigidly constrained
to a fixed reference. Subsequently, some calibrated weights, of one or five kilograms
each, depending on the element to be gauged, are applied progressively,
using a support, in the same points in which loads are detected during the
driving test (Figure 3.9). Both vertical and transversal directions are analysed
if strain gages are applied as depicted in Figure 3.7.
CHAPTER 3. EXPERIMENTAL VALIDATION 28
Figure 3.9: Central pipe hanger calibration: the line is constrained to
the reference block and gauged weights are applied progressively on the
support. In the same time, the hanger strain is recorded by the acquisition
instrument
Concomitantly, the corresponding strains are recorded, both during the
loading and the unloading of the weights, as illustrated in Figure 3.10. Again,
this duplication permits a double check between the readings.
Figure 3.10: Strain time history during the calibration: the symmetry
between the loading and unloading phases indicates the correctness of the
readings
CHAPTER 3. EXPERIMENTAL VALIDATION 29
From the obtained values of deformation, it is possible to extract the calibration
coefficients of each feature (hanger bracket or junction) in the direction
sensed by the strain gauges, as explained above. In the following, an example
is proposed:
Point 1 (Z direction)
Load [daN] Strain [μ strain]
0 0
1 7
2 14
3 21.5
Figure 3.11: Load-Strain characteristic of an exhaust hanger bracket
under calibration
The slope of the regression line obtained interpolating the experimental
points corresponds to the calibration coefficient, which represents the deformation
law of the element with respect to the load applied in a specific direction.
For the previous example, the coefficient is:
Load
Deformation = 0.142
daN
μ strain
Exploiting the calibration parameters of each bracket and each direction,
it is possible to convert the strain time histories gathered from the driving test
into load time histories acting in the same direction of the fatigue test (Figure
3.12).
Figure 3.12: The strain time history of each element (first plot) can be
converted into a load time history (last plot) by multiplying each value
by the relative calibration coefficient
CHAPTER 3. EXPERIMENTAL VALIDATION 30
3.3.2 Damage evaluation and Validation criterion
The cumulative load count, which is the element to be compared with the
W¨ohler’s curve is obtained applying the Rainflow, sometimes named Waterfall,
counting method to the load time history of each pavement. This procedure
synthesises in a table and in a graphical manner the number of occurrences of
a certain load on every bracket or junction during the RLDA test.
Eventually, the cumulative loads of every single pavement are superimposed,
applying to each of them a proper multiplication factor, to obtain a
global overall cumulative. This last would equal, in terms of damage, the
repetition of the driving test over each pavement for the aforementioned coefficients:
the advantage of the computational a procedure is evident. As said, the
plot of the global cumulative, namely the Rainflow diagram, can be directly
compared to the W¨ohler’s diagram, as shown in Figure 3.13.
Figure 3.13: Chart of both W¨ohler and cumulative curves of a component.
In black are evidenced the characteristics necessary for Miner’s
damage evaluation
As a first approximation, to check whether the component can withstand
the target life, it is necessary that the cumulative curve lays completely below
the W¨ohler’s one. Nevertheless, a more robust result is provided by the
computation of the cumulated Damage with Miner’s rule. According to Miner,
each cyclic load causes a damage proportional to its level and to the number of
repetitions, provided that the stress exceeds the endurance limit, below which
fatigue life is not affected, which is accumulated in the part itself, reducing its
residual life.
The damage contribution is evaluated for each load level according to Formula
3.5, starting from the load time history (or cumulative) and W¨ohler’s
CHAPTER 3. EXPERIMENTAL VALIDATION 31
curve of the component.
di(Fi) =
ni
Ni
(3.5)
A comparison with Figure 3.13 clarifies the meaning of the terms appearing in
the Equation 3.5: the damage contribution di caused by the load Fi corresponds
to the ratio between the actual number ni of occurrences of that force and
the maximum number of repetitions Ni of the same load that would lead the
component to fatigue failure. The sum of all these ratios provides the Damage
caused by the specific cumulative, as highlighted in Formula 3.6.
D =
Xitot
i=1
ni
Ni
=
Xitot
i=1
di (3.6)
The component undergoes fatigue failure once the accumulated damage reaches
the value of 1.
The necessity of the data correction, mentioned in Section 3.3, becomes now
apparent: if a time history features few very high peaks caused for instance
by an electro-magnetic interference, the multiplication tout court of its data
can lead to a misleading overestimation of the damage, perhaps impairing the
validation result.
Validation condition At the end of this procedure, the component is deemed
validated by the Testing department whenever the Experimental Safety Factor,
computed on the basis of strain gauges acquisitions and defined as the inverse
of the damage, exceeds the value of 1.2.
SFexperim =
1
D ≥ 1.2 (3.7)
Chapter 4
Equivalent load
4.1 Differences between the methods
The previous Chapters already highlighted the discrepancies that exist between
the two validation methods ordinarily employed.
First of all, the two procedures start from different inputs: while experimental
tests are carried with a real vehicle on different Proving Grounds, thus
the solicitations on the exhaust system that result are thoroughly dynamic,
virtual validation applies only static loads, even to represent a dynamic condition
(remember the assumption made in Section 2.2 selecting as alternating
stress σa the upshot of the application of a static load).
With this simplification, the effect of time-evolving accelerations cannot be
appraised.
Moreover, the outcomes of the analyses are not directly related each other.
From the physical data acquisition, the cumulative load (in kg) acting on each
bracket and the relative damage are obtained using W¨ohler’s curve of the
component and Miner’s rule. On the other hand, the natural result of the
computer simulation is a Stress map (whose values are in MPa), at the utmost
converted into a Safety Factor map, with values referred to 500 000 cycles,
using the Haigh diagram of the material.
Section 3.3.2 points up a further dissonance that exists between the procedures:
the results are referred to different fatigue curves and technically they
cannot be compared as such. While the experimental analysis identifies the
proper W¨ohler’s curve for each component, measured in [kg/cycles], through
the fatigue bench characterization, the virtual simulation relies on Haigh diagrams
of the material, expressed in [MPa/cycles]. The latter differs from the
former in that it neglects the effect of the actual geometry.
In Table 4.1 the analysed differences existing between virtual and experimental
validation methods are summarized.
32
CHAPTER 4. EQUIVALENT LOAD 33
Virtual Experimental
Input 1 g + 4g Proving Ground
Static Dynamic
Output Stress map [MPa] Brackets cumulative load [kg]
Safety Factor map Damage (with Miner)
Fatigue Haigh diagram of Component’s test material and weld beads W¨ohler’s curve
Table 4.1: Summary of the differences between the validating methods
4.1.1 Correlation proposals
To overcome the limitations highlighted in the previous Section, multiple alternatives
have been discussed to determine their appropriateness. In the following
will be explained some solutions that have been proposed and attempted
in order to reduce such discrepancies.
4.2 Equivalent load
The first correlation technique is an heuristic procedure that attempts to abate
the differences, in terms of fatigue reference curves, that exist between Virtual
and Experimental validation methods, as highlighted in the last row of Table
4.1. Considering that the Haigh diagram, to whom mechanical stresses are
compared for the computation of the Computed Safety Factor, is evaluated
at 500 000 cycles, this methodology strives to identify a static load which, applied
500 000 times, is equivalent, in terms of damage, to the cumulative load
deriving from the Proving Ground experimental test.
Eventually, the new results are compared to the conventional 4g procedure
with the expectation of finding a clear and repeatable relation between the
outcomes, ideally a corrective coefficient, to obtain more correlated results.
The details of the methodology, along with the required data and the outcomes
of the comparison will be described in the following.
4.2.1 Objective
The basic purpose of the equivalent load computation is to reduce the whole
load time history (thus the load cumulative), deriving from RLDA data acquisition,
to a single force level which produces the same damage of the driving
test if applied for a specified number of repetitions. Therefore, an equivalent
force will be defined for each single component of the exhaust line for which
deformation data andW¨ohler’s curve have been acquired. In the present study,
only exhaust hanger brackets have been analysed.
More in depth, the objective is to verify whether the application of these
loads on their relative brackets produces stresses comparable to the tradiCHAPTER
4. EQUIVALENT LOAD 34
tional 4g validating test and eventually, whether a clear trend could be found,
to assess the relation existing between them.
4.3 Input data
For each element analysed, being it a hanger bracket or a welded junction, the
data required as input for the evaluation of equivalent loads are:
• W¨ohler’s curve (Equation 3.1), in particular its coefficients A and B,
obtained from the experimental characterization at the hydraulic jacks
(Section 3.1);
• Cumulative of loads, namely a table containing number of occurrences
ni of a determined load Fi, recorded during the RLDA acquisition.
The cumulative is obtained applying the Rainflow counting method to the
complete time history of the driving test. A dedicated software scans the
acquisitions and extracts the number of cycles corresponding to a certain load
(or strain, since they are proportional) range. In practice, when a cycle is
identified, the related entry of the Rainflow matrix is incremented: in this
way, each element of the matrix expresses the number of cycles, evidenced in
the time history, corresponding to each range. The two cycles represented in
Figure 4.1, equal in amplitude and differing only for the extreme values of the
range, would be accounted for in different entries of the matrix.
Figure 4.1: Two strain (or load) cycles with the same range but different
extrema would be registered in different strain (or load) batches
In the peculiar case of the driving test, since the exhaust line oscillates
about its rest position and the boundary conditions to which it is subjected
are unchanged at the end of the test with respect to the initial ones, there is
no specific reason to have cycles with a non-zero mean value. Pursuant to this
consideration, for the evaluation of the equivalent load, only the amplitude
ranges are considered. Although this simplification would underestimate the
fatigue damage, because the effect of mean stress is not taken into account, the
CHAPTER 4. EQUIVALENT LOAD 35
error introduced is not impacting for the purpose of the analysis, being minimal
the unbalance with respect to the origin. By virtue of this consideration, in
this study, the two cycles of Figure 4.1 would be considered equivalent in terms
of fatigue damage.
4.4 Computation
The calculation of the Equivalent load commences with the estimation of the
damage generated by the repetition (ni times) of each load Fi exploiting again
Miner’s rule (as explained in Section 3.3.2). Then, summing all the individual
contributions, the overall damage on the component, relative to the load time
history is obtained:
D =
Xitot
i=1
di =
Xitot
i=1
ni
Ni
. (3.6)
Reached this point, the objective is to identify the unique load level Feq
that, replicated for an arbitrarily number neq of times, engenders on the structure
the same overall damage of the original time history. According to Miner,
this coincides to state that the ratio between the equivalent number of cycles
neq and its relative fatigue limit Neq must equal the aforementioned damage.
Translated in formulas, this statement becomes (Equation 4.1):
D =
Xitot
i=1
ni
Ni
=
neq
Neq
. (4.1)
Inverting Equation 4.1, one gets the unknown Neq (Equation 4.2):
Neq =
neq
D
. (4.2)
Substituting this last value in the W¨ohler’s equation (Equation 3.1), and inverting
the formula, the desired equivalent force Feq is obtained.
log10(Feq) =
log10(Neq) − A
B
(4.3)
The procedures described in this paragraph are synthesized and expressed
in a graphical manner in Figure 4.2.
It is worth to remark that the value neq of cycles is a parameter which, by
its nature, can be imposed in accordance with the objectives to be pursued:
in the presented analysis, the value of neq = 500 000 cycles has been selected
to match with material characterization (Haigh diagram) employed for the
evaluation of the virtual Safety Factor.
CHAPTER 4. EQUIVALENT LOAD 36
" [μ strain] Fi [daN] ni [cycles] Ni [cycles] di [–]
151 8.02 54 95 136.3 0.0117
133 7.05 249 181 520.5 0.0061
129 6.89 614 203 904.8 0.0030
114 6.07 1725 381 225 .2 0.0045
...
...
...
...
...
52 2.76 17 984 19 912 580.9 0.009
44 2.35 27 836 44 109 501.4 0.0006
38 2.03 39 479 92 645 023.2 0.0004
...
...
...
...
...
Table 4.2: Table for the computation of Equivalent loads: Fi is obtained
multiplying half strain range by the calibration coefficient daN
μstrain .
Ni and di have been computed using W¨ohler’s (3.1) and Miner’s (3.6)
Equations respectively
Figure 4.2: Graphical representation of the evaluation of the equivalent
load: the ordinate of the intersection between the W¨ohler’s curve and the
vertical line passing from Neq corresponds to the equivalent load
4.5 Results comparison
There exist two possible alternatives to assess the differences between the results
of the two methods (4g and equivalent loads):
1. Load comparison: compare the equivalent load acting on the bracket
to the force which, applied in the central point of the bracket, generates
the same stress of the 4g static acceleration. In order to deduce such
a force, it is mandatory to retrieve the relation between the simulated
stress produced and the force applied virtually on the bracket, which will
be called virtual calibration and explained in its details in Section 4.5.1;
2. Stress comparison run a second virtual simulation, having as inputs
the equivalent loads on each bracket, and check the stresses in homologous
nodes on the structure.
CHAPTER 4. EQUIVALENT LOAD 37
Although both strategies have been experimented, the results will be proposed
according to the former methodology, while the latter will cover an
ancillary function and will be quoted for completeness.
As mentioned, to collate the two methods it is necessary to identify some
common parameters: in this case-study, bracket loads will be selected as objects
of the comparison. The virtual validation analysis provides a stress map,
consequence of the application of 4g gravity acceleration. It is possible to translate
the stress level obtained into the load applied at the bracket involving a
numerical calibration coefficient: this factor expresses the relation between
force applied in the centre of the bracket and stress of a node, in the same
manner in which the stiffness of a spring relates its deformation to the force
applied at its extremities. Obviously, while in the spring case the axial deformation
is a global property, unambiguously determined, for what concerns
stress calibration factor it is necessary to estimate in both conditions the stress
in the same node, since the relation is tailored on it.
4.5.1 Virtual calibration
The virtual calibration is aimed at obtaining a relation between the load applied
on the bracket and the resultant stress generated on the bracket. This
factor can be easily evaluated by making the ratio between the stress level in
a specific node and the load applied on the single bracket.
Calibration Factor =
Stress
Applied load
(4.4)
Each bracket is isolated from the others by constraining all the circumferential
nodes of the pipe upstream and downstream the feature, as highlighted
with green rectangles green in Figure 4.3, and a predefined load is applied in
Figure 4.3: Virtual calibration load and constraint conditions: green
rectangles indicate the location of the 6-DOFs constraints, while a predefined
load is applied on the centre of the bracket straight portion
CHAPTER 4. EQUIVALENT LOAD 38
the centre of the bracket, along the negative vertical direction. From the stress
map obtained, a node will be selected and exploited for the computation of
the calibration coefficient.
Owing to the analogy between static simulation and experimental test, in
terms of calibrations, it is possible to assess the differences existing between
the methods, given the same boundary conditions, thus to indirectly estimate
the error band that affects the results. During the investigation, both virtual
and experimental calibrations have been acquired and compared each other.
In the same way, in the testing facility, the brackets are characterized experimentally
applying similar constraints and forces, as demonstrated in Figure
4.4. The redundancy of fixtures has been adopted to clone the boundary
Figure 4.4: Experimental calibration for the stress coefficient. In the
specific case, the constraint conditions of the virtual case have been reproduced
to assess also the quality of the simulation
conditions of the virtual test: reducing such differences, it is possible to assess
the correlation between the two experiments.
For the purpose of obtaining a better comparison, further to uni-axial strain
gauges placed in the positions indicated in Figure 3.7, brackets have been be
equipped with Rosettes: these are particular deformation transducers, composed
of three superposed uni-axial strain gauges inclined among each other,
which allow to measure the mechanical stress.
To assess the distance between the two methods, it is fundamental to compare
the outcomes of the virtual calibration in homologous points: the reading
CHAPTER 4. EQUIVALENT LOAD 39
of the mesh node corresponding to the point of application of the rosette must
be selected as shown in Figure 4.5. Said difference has been evaluated according
to the convention expressed in Equation 4.5:
Δ% =
Experimental – Virtual
Virtual
(4.5)
Figure 4.5: To reduce the inaccuracy, it is fundamental that the stress
obtained with the two calibrations has been measured in the same point
Despite the efforts in the identification of the exact gauged point counterpart,
and also because of the approximations in the stress values, the introduction
of errors is unavoidable and, for this reason, must be taken into
account.
All in all, looking at the results proposed in Table 4.3 and considering
the limitations of the investigation, it can be stated that the correlation between
virtual simulation and experimental test results, in static conditions, is
satisfactory.
520 - No muffler
Stress/Load
[MPa/daN]
Exper. Virt. Δ%
PT A 5.40 5.45 -0.9 %
PT B 4.53 4.79 -5.5 %
PT C 4.44 4.21 5.5 %
PT D 4.12 3.29 11.6 %
(a)
356
Stress/Load
[MPa/daN]
Exper. Virt. Δ%
PT A 5.38 5.80 -7.2 %
PT B 5.51 4.37 26.2 %
PT C 5.54 6.13 -9.7 %
PT D 7.85 7.14 9.9 %
(b)
Table 4.3: Comparison between stress calibration coefficients in homologous
points: the modest difference (Δ%) is principally attributable to
the error in the individuation of exactly corresponding nodes
CHAPTER 4. EQUIVALENT LOAD 40
For completeness, in Appendix A also the strain calibration coefficients of
the same models are reported.
4.5.2 Computation of the brackets loads
Once the calibration factors are available, one can obtain the load acting on
the bracket multiplying it by the stress in the same node employed for the
calibration: a schematic of this procedure has been composed in Figure 4.6.
All these passages have been repeated for several models: some results are
proposed in the Tables 4.4.
Figure 4.6: Scheme of the procedure followed to compute brackets loads
starting from the stress map of the feature and the calibration factor
520 - No muffler
Brackets Load [daN]
Equiv. 4g Δ%
PT A 7.3 10.5 -30 %
PT B 10.8 13.6 -21 %
PT C 8.0 6.7 20 %
PT D 6.7 8.4 -20 %
(a)
356
Brackets Load [daN]
Equiv. 4g Δ%
PT A 5.54 5.45 1.5 %
PT B 4.94 8.96 -45 %
PT C 3.26 3.96 -18 %
PT D 2.98 4.87 -39 %
(b)
Table 4.4: Comparison between Equivalent loads (experimental) and
brackets forces corresponding to 4g procedure (virtual results). The absence
of a clear trend between the results highlights the inadequacy of the
method
4.6 Comment and critical issues
Undefined trend Despite the expectations, the Equivalent load method
revealed unsuitable for reducing the gap between the validation methods. In
fact, albeit minor differences between the calibration coefficients have been
CHAPTER 4. EQUIVALENT LOAD 41
detected, principally ascribable to a lack of precision of the method proposed
in Section 4.5.1, the non-existence of an univocal trend between the results
of equivalent loads and customary 4g validation, in terms of bracket forces,
indicates the absence of correlation between the methods. Therefore, in these
circumstances, the innovative procedure cannot be adopted as approval method
in place of the conventional practice, since in general the equivalent loads reveal
to be more severe than 4g ones.
Influence of the layout A supplemental finding, discovered along the analysis
of the equivalent loads of different exhaust systems, evidences the strict
dependence of these forces on the line layout.
The scrutiny was aimed at unveiling a possible relation between the mass
of the line and its related equivalent forces. In practical way, the ratio between
the sum of equivalent loads, expressed in kg, and the corresponding Cold-End
mass has been computed for lines featuring different number of brackets and
including disparate elements placed in various positions. Some meaningful
examples are shown in Figure 4.7.
Equiv. Load
[kg]
PT 1 5.65
PT 2 5.04
PT 3 3.90
PT 4 3.33
PT 5 3.03
Tot. 20.95
Line Mass
[kg]
Front 2.76
Cent. 5.94
Rear 2.02
Tot. 10.72
Equiv.
Mass
Tot. 1.955
(a)
CHAPTER 4. EQUIVALENT LOAD 42
Equiv. Load
[kg]
PT 1 4.83
PT 2 10.03
PT 5 5.98
PT 6 7.00
Tot. 27.84
Line Mass
[kg]
Front 3.17
Cent. 4.46
Rear 3.11
Tot. 10.74
Equiv.
Mass
Tot. 2.590
(b)
Equiv. Load
[kg]
PT 1 2.75
PT 2 14.27
PT 4 15.24
PT 5 13.10
Tot. 45.36
Line Mass
[kg]
Front 3.00
Cent. 1.44
Rear 8.50
Tot. 12.94
Equiv.
Mass
Tot. 3.505
(c)
CHAPTER 4. EQUIVALENT LOAD 43
Equiv. Load
[kg]
PT 1 6.74
PT 2 12.37
PT 3 16.29
PT 6 12.28
Tot. 47.68
Line Mass
[kg]
Front 3.40
Rear 8.16
Tot. 11.56
Equiv.
Mass
Tot. 4.127
(d)
Figure 4.7: Ratios between the sum of the brackets equivalent loads,
expressed in kilograms, and the Cold-End mass for models featuring different
layouts
As one can immediately infer from the tables of the previous Figure, the
presence of mufflers, especially if mounted at the end of the line, acting as
a suspended mass, magnifies the damage on the related brackets, thus their
corresponding equivalent load. As a result, it has been evidenced that it is not
straightforward to deduce the equivalent forces merely from topological and
physical characteristics of the line, reaffirming the importance of the RLDA.
Moreover, the lack of correlation among the results presented suggests that
the incongruity between the methods shall reside in their inputs. The investigation
presented in the next Chapter will be centred on this aspect.
Chapter 5
Vibrational analysis
The results shown in the previous Chapter (Table 4.4) evidence the lack of
correlation in the comparison of a static simulation with a dynamic test: from
this fact originates the impossibility of reducing the driving test to a single
equivalent force.
A further strategy attempted to link up the two methods consists in a
frequency analysis of the exhaust system, both in a virtual environment and
on physical components. This approach addresses the discrepancies existing
in the types of input of the validating methods, which have been stated in the
first row of Table 4.1.
5.1 Initial observations
It has been evidenced that the 4g static simulation generates forces on the
brackets in relation to the centre of gravity and to the mass distribution of
the exhaust line. If brackets reaction forces had distributed in the same manner
also during the driving test, a relation between the outcomes of the two
procedures would have existed. Nevertheless, the examination made on several
exhaust lines, in terms of ratios between sum of equivalent forces and
total mass of the Cold-End, exhibits a substantial variability of this parameter
with the line layout. As a consequence, it has been hypothesised that the line
mounted under the vehicle deforms in a different manner, presumably according
to its modal shapes. The resulting force distribution would be function of
the relative displacement between exhaust hanger bracket and body counterbracket
caused by the natural oscillation of the line, more than by its weight
repartition. Obviously this consideration applies when the line is subjected to
dynamic input conditions, as it occurs during the test on the Proving Ground.
Objective The purpose of the vibrational investigation is double. The former
is to analyse experimental data, namely strains on the brackets and, when
44
CHAPTER 5. VIBRATIONAL ANALYSIS 45
acquired, accelerations, to understand whether the deformations of the line
suspended under the vehicle correspond to its modal shapes.
The latter, nonetheless central purpose of the vibrational analysis is to
identify some characteristic inputs for the virtual simulation, in terms of an
acceleration spectra with respect to the frequency and amplitudes of them,
ideally identical for all the vehicles, which could represent of all the different
pavements encountered during the driving test and, therefore which could flank
the conventional validation procedure. In this manner, the Safety Factors
obtained from the virtual computation are supposed to be more correlated
with those extracted from the driving test.
5.2 Procedure
The analysis commences from the experimental acquisition of the input accelerations
that excite the brackets during the driving test. To accomplish
this goal, the vehicle under investigation is equipped with some mono-axial
accelerometers, placed in correspondence of the counter-brackets roots. Moreover,
other accelerometers of the tri-axial type can be attached to some hanger
brackets to better track the behaviour of the exhaust line during the trial.
These configurations are shown in Figure 5.1.
Figure 5.1: Mono-axial (a) and tri-axial (b) accelerometers applied
respectively at the counter-bracket root and at the bracket tip
These transducers, similarly to what occurs with strain gauges, are connected
to an acquisition device which records the time history of the accelerations
detected at their application point at a very high rate. Also in this case,
an exact replica of the acceleration profile in a virtual simulation would require
an unacceptable time, thus it is not practised. To provide a more serviceable
CHAPTER 5. VIBRATIONAL ANALYSIS 46
input, after an observation of the gathered data to clean them from misrepresentations,
acceleration time histories of each track are stitched together to
form an unique sequence, considering that a change in the order of the single
samples should not affect the final result. Then, data are filtered in the
frequency range which causes the highest oscillations and damage (typically
from 5 to 30 Hz) and transposed into the frequency domain exploiting the Fast
Fourier Transform (FFT). Accelerations related to frequencies close to zero are
discarded because they are principally caused by a variation in ground slope,
thus insignificant for damage evaluation, or by software issues when applying
the domain transformation. This countermeasure is also taken in case the
acquisition is provided as input to the Road Simulation Bench, explained in
Section 5.2.1 and Appendix B: to simulate such low-frequencies accelerations,
the bench would need to extend its actuators beyond their maximum stroke,
hence impairing the effectiveness of the test.
For every pavement, the peak acceleration at each frequency is recorded
employing the peak-hold method. These data are then put in matrix form, an
extract of which is reported in Table 5.1, having as coordinates the tracks and
the analysed frequencies.
Freq. Accelerations for each type of pavement [m/s2]
[Hz] Track 1 Track 2 Track 3 Track 4 · · · Max.
10 1.42 0.91 3.11 1.63 · · · 3.11
11 2.10 1.04 2.19 1.78 · · · 2.19
12 6.14 1.23 3.11 2.80 · · · 6.14
13 6.79 1.82 4.07 3.73 · · · 6.79
14 5.12 2.06 3.70 3.10 · · · 5.12
15 4.42 1.88 3.28 4.17 · · · 4.42
...
...
...
...
...
. . . ...
50 0.54 0.16 0.10 0.51 · · · 1.09
Table 5.1: Extract of the acceleration spectra matrix for each pavement:
the overall maximum value of each row, highlighted in red, is tracked to
identify the acceleration envelop
The overall maxima (last column of the matrix) of each frequency batch
are then extracted and provided as input for the virtual simulation: their
graphical representation is reported in Figure 5.2 for the same models analysed
in Section 4.5.1.
From Figure 5.2 (b), comparing the acceleration spectra of the brackets
with respect to their relative counter-brackets, one can infer that not all the
brackets acceleration peaks are caused by a corresponding maximum of the
input, as it occurs around the frequency of 18.5 Hz. This fact already suggests
that the line under the vehicle does not merely replicate the displacements of
the body, but probably deforms in accordance with its modal shapes. The analCHAPTER
5. VIBRATIONAL ANALYSIS 47
ysis in this perspective has been carried after the RSB and virtual vibrational
simulations and will be proposed in Section 5.3.2.
(a)
(b)
Figure 5.2: Acceleration spectra relative to two models analysed. Figure
(b) contains also the accelerations of the first and last exhaust brackets.
To understand the Input/Output relation, their values should be compared
to counter-brackets (Scocca) A and D respectively
CHAPTER 5. VIBRATIONAL ANALYSIS 48
5.2.1 Calibration at the Road Simulation Bench
Before going in depth with the examination of the road profile, whose excitation
spectrum is wide and complicated by the non-null phase between accelerations
on different brackets, a preliminary trial has been run to understand how the
exhaust system moves under the vehicle, to assess, also for this type of analysis,
the gap that exists between virtual simulation and experimental test. For
this purpose, it would be necessary to apply a simpler input to the physical
exhaust line, namely an oscillation characterized by constant amplitude and
frequency, easily reproducible at the computer for the comparison of the results.
Since the application of time-invariant inputs is not immediate with the line
mounted under the vehicle, the investigation has been carried exploiting the
Road Simulation Bench (RSB), available in the Department (Figure 5.3).
Figure 5.3: Road Simulation Bench room: the yellow arms are connected
to hydraulic actuators reproducing vehicle body accelerations,
while the three interlinked jacks, placed on the right of the picture below
the gas burner simulate the vibrational behaviour of the engine
This facility allowed to apply as inputs pure tone sinusoidal displacements
or sweeps in frequency at fixed amplitude, in phase among each other, to the
counter-brackets of an instrumented exhaust line to compare the outcomes
of a physical specimen to those of a virtual analysis. Deeper notions about
the purpose and the details of the Road Simulation Bench are reported in
Appendix B.
Bench set up To run the acquisition activity, which has been carried for
one of the models previously analysed, the line is fixed to the hydraulic jacks
of the bench, which reproduce vehicle counter-brackets, in the same manner
CHAPTER 5. VIBRATIONAL ANALYSIS 49
and using the same elastic isolators prescribed for the normal operation under
the car. To set up the test properly, each hydraulic actuator must be disposed
close to the exhaust system, placed initially on the ground, in correspondence
of the brackets avoiding any possible interference between the specimen and
the actuator arms that could arise during operation. Then, the reproduced
counter-brackets are fastened to the tips of the actuator arms, as highlighted
in Figure 5.4. That location corresponds also to the zone in which mono-axial
accelerometers, required by the bench as feedback signal, are attached.
Figure 5.4: The same disposition and shape of vehicle counter-brackets
is cloned for the bench simulation. These features are rigidly connected
to actuator arm tips through bolts
Once completed this operation, the oil pump is switched on, at reduced
power, to provide enough pressure to maintain the actuators in their neutral
working position, namely at mid span of the overall displacement. At this
point, with the half-raised actuators, it is possible to start suspending the line
with the proper isolators. This carefulness is taken to have a homogeneous reference
relative to which the line is disposed and to avoid differences in height,
caused by residual pressures in the cylinder, at rest that would introduce undesired
distortions during system operation.
Once the line is suspended, it is important to verify that its position corresponds
to the designed one, that isolators are not twisted nor stretched in an
unnatural manner and that the vertical movement of the hydraulic jacks does
not produce displacements of the line others than vertical. The comparisons
between the actual mounting conditions and the designed ones are depicted
in Figure 5.5. Only after these checks have been terminated, it is possible to
definitively fix the actuator bases to the ground seismic mass.
CHAPTER 5. VIBRATIONAL ANALYSIS 50
(a)
(b)
Figure 5.5: Rear (a) and global (b) view of the exhaust line mounted
on the bench and comparison with its design condition
Test After the connection of the acquisition devices for strains and accelerations,
the test can be launched. This kind of trial performed at the RSB
is largely simpler than the reproduction of a durability test explained in Appendix
B and does not require any calibration of the bench itself.
For each actuator the displacement law is defined by the following parameters:
• type of signal, such as sinusoidal wave, triangular wave, ect.;
• amplitude, namely maximum displacement from the rest condition of the
actuator;
• frequency of the signal;
• phase angle with respect to any other actuator;
CHAPTER 5. VIBRATIONAL ANALYSIS 51
• time duration of the trial.
In the presented case, the most significant tests have been carried choosing
as inputs a constant-frequency, fixed-amplitude sinusoidal displacement of
each actuator with null phase among each other and some frequency sweeps,
from 0 to 50 Hz, always with the actuators in phase, keeping constant the
amplitude: this last case generates on the counter-brackets an acceleration
increasing with a quadratic law.
Before launching the test, a synchronization signal is fed simultaneously
to both acquisition devices to allow, during data post-processing operations,
a correct superposition of causes (accelerations of the counter-brackets) and
effects (brackets strains), helpful to understand any possible relation among
them.
The outcomes of this trial will be compared with those coming from the
virtual simulation of the exhaust line to which similar inputs are applied.
5.2.2 Virtual Vibrational analysis
The computational vibrational simulation exploits the same configurations already
settled for the static 4g simulation. Despite this, since the test presents
different boundary conditions and desired outputs, some adaptations must be
applied.
The first operation to be carried is to modify the stiffness of rubber isolators
and of the flexible decoupler. While this characteristic is a constant
value in static conditions, when the elastic element is subjected to dynamic
deformations, its response varies as function of the excitation frequency. In
Figure 5.6 this characteristic is shown for two generic rubber isolators.
Figure 5.6: Variation of the dynamic stiffness of two rubber isolators
as function of the frequency
CHAPTER 5. VIBRATIONAL ANALYSIS 52
For very low excitation frequencies it is not possible to deduce the stiffness
from the previous chart: for this reason, the static stiffness value has been
assumed for a frequency f = 0 Hz. The other missing data are obtained by
interpolation.
A similar behaviour can be recognised for the damping coefficient of elastic
elements (Figure 5.7).
Figure 5.7: Variation of the damping coefficient of two rubber isolators
as function of the frequency
These properties are attributed to the elastic CBUSH elements using the
PBUSH card. It is necessary to specify there the pointer to a table containing
the dynamic characteristics of the related element: thanks to this expedient,
the software automatically selects the proper stiffness and damping depending
on the instantaneous frequency that solicits the element.
In a similar manner, also material hysteresis has to be taken into consideration:
this is done applying a 2% damping factor to all metallic elements over the
whole frequency range.
Afterwards, it is necessary to declare the Dynamic Loads, defining DLOAD
properties. Similarly to what occurred for the stiffness, each load too is defined
in a table, expressing its variation law in the frequency domain. For the
purpose of the present investigation, these tables contain the counter-brackets
acceleration spectra measured during the driving test (reported graphically in
Figure 5.2) and during the RSB trial. In contrast to the static analysis, in
which the whole structure was subjected to a distributed load, these dynamic
actions must be applied in correspondence of the counter-brackets constraints
only, as represented in Figure 5.8: to achieve this, the DLOAD container must
include the identification numbers of the application nodes and the direction
along which the load must be applied.
Eventually, before launching the simulation, it is customary to define speCHAPTER
5. VIBRATIONAL ANALYSIS 53
cific sets of node IDs for which the output is required: this strategy permits
to shorten the computational time, which, with these expedients, is approximately
15 minutes.
Figure 5.8: Application points of the input accelerations for numerical
vibrational analysis
5.3 Results comparison
5.3.1 Simulation of road acceleration spectra
The first trials were aimed at simulating the effect of the counter-brackets
accelerations spectra measured on the Proving Grounds (Figure 5.2). The
outputs of the numerical analysis selected for comparison with the experimental
test are the spectra of the reactions at the isolator elements. These forces
are presumed to equal brackets loads, calculated according to the experimental
procedure, (strain value times the calibration coefficient) for given testing
conditions. Going deeper in the details, since the input of the simulation is
constituted by the peaks accelerations encountered during the road test, it is
straightforward to imagine that the maximum bracket force is caused by the
maximum acceleration. In particular, the global maximum of each bracket is
supposed to correspond to the highest load registered in the Rainflow diagram.
As a matter of fact, this consideration did not prove to be valid generally,
since the correlation has been found only for few brackets. Figure 5.9 and
Table 5.2 show the absence of correlation between the outcomes of the two
methods. The discrepancies can be ascribed to the simplifications introduced
in the model and to the loss of information, in particular of the relative phase
among the counter-brackets accelerations, which occurs when transposing data
from the time domain to that of the frequency.
CHAPTER 5. VIBRATIONAL ANALYSIS 54
(a)
(b)
(c)
CHAPTER 5. VIBRATIONAL ANALYSIS 55
(d)
Figure 5.9: Graphical comparison between brackets (experimental) and
CBUSH isolators (virtual) maximum forces obtained applying as input
of the simulation the road acceleration spectra. Notice: the portion of
the spectrum at very low frequencies has to be neglected
Freq. Numerical Proving Ground Δ%
[Hz] CBUSH [N] Max [N] [–]
(a) PT 1 13 116 91.8 -20.8%
(b) PT 2 13 196 197.6 1%
(c) PT 5 13 208 132 -36.5%
(d) PT 6 13 48 159.1 231%
Table 5.2: Comparison between isolators CBUSH (virtual) and brackets
(experimental) maximum forces: the inputs for the simulation are the
acceleration spectra obtained from the driving test
5.3.2 Modal deformation
RSB test Comparing the inputs, reported in Figure 5.2 (a), with the outputs
of the numerical analysis of Figure 5.9, it can be evidenced that the line
deformations concentrate around the excitation frequency of 13 Hz, while the
local acceleration peak around 18 Hz is filtered out.
An analogous behaviour has been observed on another line (the one of
the 356) which has been mounted on the Road Simulation Bench: in spite of
an excitation over the whole frequency range from 0 to 50 Hz, the brackets
response, in terms of accelerations, condensate around few frequencies. This
Input/Output relation is illustrated in Figure 5.10.
The quadratically increasing trend of the counter-brackets accelerations is
caused by a linear growth of the frequency at a fixed amplitude of the displacement.
The descending part, on the other hand, is attributable to the
impossibility of the system of satisfying both requests of frequency and amplitude:
the control strategy prioritizes the tracking of the former, releasing the
constraint of the latter.
CHAPTER 5. VIBRATIONAL ANALYSIS 56
Figure 5.10: Acceleration spectra of the model tested at the RSB.
The inputs (Scocca) are the accelerations imposed by hydraulic actuators,
while dash-dotted line tracks the accelerations at the tips of brackets
1 and 5
Looking at the modal analysis outcomes, these frequencies reveal to coincide
with resonances of the whole Cold-End. From this intuition, the idea
of analysing the road acquisitions in terms of modal deformations has been
advanced.
RLDA time-frequency analysis In this perspective, several strains and
accelerations acquisitions of the driving tests have been examined in the frequency
and time domain contemporary by realizing some colour maps. These
graphs collect in an unique chart several acceleration or strain spectra calculated
at each time interval, as illustrated in Figure 5.11.
The colour maps are obtained shortening the time period between two
FFTs computation, to have smoother transitions, and expressing the vertical
(amplitude) development with a chromatic scale.
The advantage brought by such a representation is the possibility to analyse
the frequency spectrum in time to understand the input/output behaviour
of the exhaust line. In particular, the availability of colour maps representing
counter-brackets accelerations and brackets strains allows to identify resonances,
which are supposed to occur whether the line response concentrates
around particular frequencies, even if the input has marginal amplitude related
to said frequency. Among all the proving grounds, the diagrams proposed and
analysed in the following are referred to the most severe ones.
The first batch of colour maps is related to a track paved with cobblestones.
The initial 200m, featuring a totally random surface profile, are covered at
a speed within 25 to 30 km/h, which is reduced to 20 to 25 km/h for the
CHAPTER 5. VIBRATIONAL ANALYSIS 57
Figure 5.11: Scheme of the data contained in a colour map
subsequent 200m. In this last portion, the cobbles are disposed to produce an
oblique undulation with respect to the lane axis, as reported in Figure 5.12.
Figure 5.12: Surface profile of one of the most severe Proving Grounds.
Colour maps are referred to acquisition on this track
Despite the last regularity highlighted in the pavement, this track is known
to produce a random excitation on the exhaust line over the whole frequency
spectrum from 0 to 30 Hz.
The three plots reported in Figure 5.13, referred to the tailpipe hanger
bracket, represent the spectra over the time of the counter-bracket acceleration
(a), the input, those of the bracket acceleration (b) and of the bracket
strain (c), the outputs. The randomness of the road profile is evidenced by
the absence of strong peaks of counter-brackets acceleration within the freCHAPTER
5. VIBRATIONAL ANALYSIS 58
(a)
(b)
(c)
Figure 5.13: Colour maps of tailpipe counter-bracket (a) and bracket
(b) accelerations and corresponding bracket strain (c) of 356 model exhaust
to highlight the Input/Output relation. The line resonance is evidenced
in purple
CHAPTER 5. VIBRATIONAL ANALYSIS 59
quency range (at least, up to 30 Hz). The line resonance can be perceived
looking across the three plots at fixed frequencies. Focusing on the frequency
of 18.25 Hz, it is noticeable that non-negligible or even the maximum bracket
strains (c) and accelerations (b) concentrate around this frequency, although
the corresponding input acceleration (a) is moderate, as highlighted in the
Figure. The hypothesis of line resonance is confirmed by the modal shape
assumed at 18.5 Hz, shown in Figure 5.14.
Figure 5.14: Modal shape of the 356 model line at 18.5 Hz: the highest
deflection is localized at the tailpipe
A comparable behaviour, caused by the resonance around 13 Hz, occurs for
the fourth bracket of the same line. Similarly to the previous one, Figure 5.15
contains counter-bracket acceleration (a) and the related bracket strain (b). It
can be observed that a relevant deformation is present against a lack in the
input, in the neighbourhood of 14.2 Hz. Also in this case, the conjecture of the
resonance is in accordance with the natural deformation at 13.1 Hz reported
in Figure 5.16.
Figure 5.17, representing the same data referred to the penultimate bracket
the 520 exhaust system, reinforces what has been supposed in the previous
paragraphs. 10 Hz is in fact the natural frequency of this line, causing the
deformation reported in Figure 5.18.
The amplification of a weak input is flanked also by the attenuation of
intense accelerations. Figure 5.19, showing again the same data, points out that
the strong accelerations measured at low frequencies are completely filtered out
and do not cause bracket deformation.
CHAPTER 5. VIBRATIONAL ANALYSIS 60
(a)
(b)
Figure 5.15: Colour maps of the fourth counter-bracket acceleration
(a) and bracket strain (b) of the 356 line
Figure 5.16: Modal shape of the 356 line at 13.1 Hz
CHAPTER 5. VIBRATIONAL ANALYSIS 61
(a)
(b)
Figure 5.17: Colour maps of fourth counter-bracket acceleration (a)
and corresponding bracket strain (b) of 520 model exhaust line
Figure 5.18: Modal shape of the 520 line at 10.1 Hz
CHAPTER 5. VIBRATIONAL ANALYSIS 62
(a)
(b)
Figure 5.19: Colour maps of tailpipe counter-bracket acceleration (a)
and corresponding bracket strain (b) of 263 model exhaust line. The
input attenuation at low frequencies is evidenced in yellow
Figure 5.20: Modal shape of the 263 line at 22.8 Hz
CHAPTER 5. VIBRATIONAL ANALYSIS 63
5.4 Comments and observations
The results shown confirm the hypothesis according to which the exhaust line
assumes its modal characteristic shapes when subjected to oscillating inputs.
Nevertheless,a certain difference between resonance frequencies obtained from
numerical modal analysis and those revealed by the colour maps can be noticed.
This discrepancy can be mainly attributed to the constraints, absent in the
virtual analysis, to the assumptions made for the isolators characteristics and
to the damping coefficient of 2% assigned to the material for the calculation.
As explained this a de facto value selected for vibrational analyses: correlation
tests should be carried to assess a more appropriate damping coefficient.
The subsequent step would be the application of such an analysis for the
validation. To achieve this, in the first instance, it is necessary to determine the
acceleration amplitudes and the frequency range, namely the spectrum, to be
applied as input of the numerical analysis to reproduce the experimental road
test in a virtual environment. From the colour maps reported in this Chapter
and from the charts of Figure 5.2, the frequency range of 0 ÷ 30 Hz appears
to be suitable for the purpose. For what concerns the acceleration amplitude,
things are slightly more complex. The experimental input depends on the specific
vehicle characteristics (mass, suspension behaviour, wheelbase,etc.) and,
thus it is unlikely to identify a general input applicable to all the cars. For
this reason, the first trials have been performed with the most simple solution,
generally valid, such as a fixed amplitude. Then, the outputs of the calculation
have been compared to the measured values: the simulated maxima have been
multiplied by tailored coefficients to minimize the difference with respect to
the highest load of the cumulative, making the results comparable. Owing to
the fact that an increase in the input amplitude would cause a proportional
growth of the corresponding output, multiplying the initial input by the aforementioned
coefficient one is supposed to obtain the desired amplitude. The
outcomes of the process just described are collected in Table 5.3, in which Δ%
has been obtained with the previously mentioned Equation 4.5.
Max Exp. Max Vibr. Freq. Max Exp. Max Vibr. Max
Stress Stress Vibr. Force Force Loads
[MPa] [MPa] [Hz] [daN] [daN] Δ%
PT A 39.6 36.3 15 7.94 6.96 14%
PT B 50 41.4 15 9.06 9.48 -4%
PT C 50 66.6 15 9.03 10.86 -17%
PT D 89.7 82.8 26 11.43 11.64 -2%
Table 5.3: Comparison of the outcomes of experimental road test and
vibrational simulation. The reduction of the absolute value of the percent
difference between the methods highlights a better correlation
CHAPTER 5. VIBRATIONAL ANALYSIS 64
As it is immediate to infer from the last column that the distance among
the outcomes of the two analysis methods has decreased in absolute value with
respect to the results proposed in Table 4.4. This fact indicates that the
After an iteration of this process for several vehicles and exhaust lines, it
should be possible to extract the values for the validation through statistical
computations.
Last but not least, an element that needs a dedicated tuning is the Safety
Factor. Since the examination conditions are different from the static ones, it
is necessary to verify whether the Haigh diagram is still a satisfactory basis
for comparison or to identify the parameters to be checked with their corresponding
thresholds. Another alternative could be to extract a damage level
corresponding to the vibrational analysis, to be related to the experimental
one. Eventually, to better correlate the virtual evaluation with the testing
procedure, load cumulative curves could be generated starting from the peaks
stresses highlighted by the numerical analysis, always retrieving the corresponding
forces through the calibration coefficients. Actually this procedure
would require a general shape of the cumulative, which would be rescaled according
to the highest load. An initial approach to this problem is proposed
in the next Chapter.
Chapter 6
Global cumulative curve
Along the evaluation of the hanger brackets damage, it has been evidenced
that the cumulative load curves feature always a recurring shape, although
the values of the forces and number of cycles may vary in relation to the
element analysed. As mentioned at the end of the last Chapter, to evaluate
the numerical damage on exhaust brackets starting from the load that causes
the maximum stress during the vibrational analysis, it would be necessary to
know the shape of the Rainflow curve. In the following, an attempt to obtain
a global curve is proposed.
6.1 Procedure
In order to obtain a result valid, in principle, for all conventional1 brackets,
the computation has been made on a statistical basis: data of several vehicles
and exhaust layouts, gathered by the Company during its testing activities,
have been collected and elaborated. In particular, for the computation of the
average normalized curve presented in this Thesis, 156 cumulative curves of
the same number of exhaust hanger brackets have been employed.
To disregard the differences in terms of maximum loads, the curves have
been normalized by dividing each ordinate value by the maximum force measured
on the corresponding bracket. In this manner, the ensuing plots, sharing
the same ordinate axis, can be superimposed, as shown in Figure 6.1, to assess
the effective shape correspondence.
Despite the high variation perceived at the right tail of the plot, mainly
concerned with infinite fatigue life, the initial expectations are satisfactorily
met, since the lines superposition in the left and central zone of the chart
is unobjectionable. These are the areas primarily involved in the damage
estimation, thus a lower spread of the data would allow to deduce results with
a wider applicability basin.
1It can happen that particular shapes or specific customer requests do not allow the
straightforward application of such a result.
65
CHAPTER 6. GLOBAL CUMULATIVE CURVE 66
Figure 6.1: Superposition of several cumulative curves normalized with
respect to their maximum loads
Afterwards, the trend line has been obtained by making the average of all
the curves. To avoid an excessive data fitting in the tail zone, which would impair
the effectiveness of the global cumulative, the computation of the average
curve has been truncated to 107 cycles.
6.2 Result
To better visualize the dispersion of data, the standard deviation has been
computed and the curves at ±2σ plotted. The final result is reported in
Figure 6.2.
The plausible applications of such a result are, as mentioned, the procurement
of a cumulative curve from a numerical simulation, rather than from a
driving test, to extract the damage and the safety factor of brackets.
Another elements for which a statistical analysis could be profitable are
W¨ohler’s curves: by averaging the results obtained during the fatigue characterization
of numerous brackets, it would be possible to derive an average
fatigue curve, along with its probabilistic bands, to be employed for all the
brackets.
If the dispersion of such curves would be excessive, it could be interesting
to investigate whether a relation between hanger characteristics and the
corresponding fatigue curve could be found. In this way, the fatigue test on
specimens at the bench could be avoided, since the proper limit curve should
CHAPTER 6. GLOBAL CUMULATIVE CURVE 67
Figure 6.2: Global normalized cumulative curve with the dispersion
band of ±2σ
be retrieved from the model built.
Chapter 7
Conclusion
Although not all the analyses that have been performed and proposed in this
Thesis brought to the result expected at the beginning, each of them has
provided its little contribution to achieve a more significant result. Many times
the best intuitions come out when the austerity of the traditional methods and
convictions falls.
The correlation analysis discussed in this work allowed to demonstrate how
the exhaust line deforms under the vehicle during its operation. This finding
triggers the possibility of applying a virtual simulation that better reflects the
real working conditions of the exhaust line, especially for what concerns the
loads distribution.
The value of the investigation is confirmed by the reduction of the distance
between experimental and numerical validating procedures obtained with the
innovative solutions proposed. Last column of Tables 4.4 and 5.3 evidence
how the vibrational analysis approaches the experimental results with respect
to the conventional application of the 4g static acceleration.
As a matter of facts, the traditional CAE validation method will not be
substituted until the proper inputs for the vibrational simulation are found
and the process would demonstrate reliable. This is the field in which future
developments are supposed to be focused. Whether the continuation of the investigation
would allow to attain satisfactory results, the innovative procedure
can be phased-in for a future application.
In this preliminary phase, the studies followed a reverse path, starting
from the results to obtain the inputs: this regression process is the typical
strategy applied to extract a model from a batch of available outcomes and
the corresponding sources. Nevertheless, the global objective is to identify
a proactive validation method, which would produce the require results in a
shorter time, perhaps avoiding some (or any) physical test.
68
Appendix A
Strain calibration factors
In this Appendix, some of the strain calibration factors, in particular those
related to the same models analysed in Section 4.5.1, are reported. Similarly to
what has been evidenced for the stress coefficients in Table 4.3, also in this case
the differences between the two validating methods are contained. It is worth
to remind that the most impacting source of error is the imprecision in the
application point of the load during the calibration and in the selection of nodes
homologous to the strain-gauged ones. Nevertheless, in similar conditions, the
results of both studies are correlated.
520 - No muffler
Deformation/Load
[μ strain/daN]
Experim. Virtual Δ%
PT1 E1 11.2 10.5 6 %
PT1 E3 -11.2 -10 12 %
PT2 E1 11.6 10.9 6 %
PT2 E3 -13.0 -11.3 15 %
PT3 E1 13.0 11.7 11 %
PT3 E3 -11.8 -9.6 23 %
PT4 E1 8.6 7.4 17 %
PT4 E3 -8.0 -7.8 3%
Table A.1: Experimental and numerical strain calibration coefficients
for the model 520 without rear muffler
69
APPENDIX A. STRAIN CALIBRATION FACTORS 70
356
Deformation/Load
[μ strain/daN]
Experim. Virtual Δ%
PT1 E1 10.1 6.5 56%
PT1 E3 11.2 8.31 35 %
PT2 E1 9.5 8.3 15 %
PT2 E3 10.4 10.5 -1 %
PT3 E1 11.4 13.9 -18 %
PT3 E3 14.6 13 12 %
PT4 E1 15.8 15.7 1 %
PT4 E3 13.6 14.4 -5 %
PT5 E1 14.9 14.8 0 %
PT5 E3 12.9 13.2 -2 %
(b)
Table A.2: Experimental and numerical strain calibration coefficients
for the model 356
Appendix B
Road Simulation Bench
description
The Road Simulation Bench was built as a solution to simulate the thermostructural
durability test of the complete exhaust system, following the car
makers designated Proving Ground, with the aim at defining the reliability level
of the components on the field. Conventionally, the car makers perform onvehicle
tests on specific tracks to assess both vehicle and components reliability.
The advantages of the RSB are:
• the complete automation of the test, which requires neither the constant
presence of an operator nor the availability of the vehicle for the whole
trial, but exclusively for the data acquisition;
• the shortening of the time required to run the analysis, from three months
of driving tests to three weeks of simulation;
• the increased repeatability of the conditions over time (influence of the
driver and driving conditions);
• the possibility of testing several lines of the same vehicle model, since
their input are in principle the same;
• etc.
The bench is constituted by seven hydraulically powered actuators, similar
to hydraulic jacks, mounted in a vertical direction. Three of them are aimed
a reproducing the engine oscillations, thus can reach 300 Hz and a maximum
force of 16 kN, while the latter four, featuring a maximum frequency and force
of 10 kN and 50 Hz respectively, with a peak-to-peak displacement amplitude
of 150mm, are designed to replicate under-floor accelerations. Eventually, a
methane burner can provide, on request, a 600 kg/h hot air mass-flow at a
maximum temperature of 1 000 ◦C.
71
APPENDIX B. ROAD SIMULATION BENCH DESCRIPTION 72
Figure B.1: Road Simulation Bench room: the yellow arms are connected
to hydraulic actuators reproducing vehicle body accelerations,
while the three interlinked jacks, placed on the right of the picture below
the gas burner simulate the vibrational behaviour of the engine
For a conventional durability test, after the collection of data on the Proving
Ground and the filtering of them, to remove non significant parts and shortening
the test time, an instrumented exhaust line is mounted on the bench, in
the same manner as under the vehicle: hydraulic actuators can be displaced
to reproduce the position of the under-body counter-brackets.
Once the set-up is complete, the bench starts a self-calibration: while moving
one actuator at a time, it measures the intensities of the consequent accelerations
and records them in an array of transfer functions (the coordinates of this
matrix indicate the actuator moved and the accelerometer read). This process
is repeated to minimize the error between the accelerations measured and the
target the machine was supposed to measure. At the end of the calibration,
the bench is aware of the type of displacement it has to provide in order to
reproduce the same accelerations evidenced during the driving test, thus to
replicate the durability test conditions, even on a new line of the same type
not endowed with instruments.
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Acknowledgements
Before concluding this Thesis, I would like to thank all the people that sustained
me not only for the realization of this project, but also during my whole
Academic career.
First of all, I would like to thank Prof. Andrea Tonoli for having accepted
to follow me in this project.
In the same manner, I want to thank Eng. Marco Nardi, who gave me the
opportunity to undertake this path in Magneti Marelli, by integrating me in
his Team, providing all the required tools: in absence of his commitment this
project could not have been realized.
A special recognition goes to Doct. Federico Ogliaro, my tutor ad honorem,
for his collaboration: since the first moment, he supervised my activity every
single day with patience, illustrating me all the methods and procedures of his
professional expertise with great competence.
In this perspective, I would also like to thank all the members of the Testing
Department Team for their contributions both for the realization of this Thesis
and for having increased my knowledge, illustrating me their working activities.
My particular gratitude goes to my Parents, who provided me an inestimable
moral support and always supported my decisions, permitting the
accomplishment of this career. Without your confidence, I would never have
reached such an achievement.
Last but not least, my heartfelt thanks go to Joëlle, always by my side,
who encouraged me with endless love and who trusts me more than I do. Your
support has been fundamental, not only for the realization of this Thesis.
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