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Measurement and assessment of vibrations induced on a
railway track
João Diogo Castanheira Cortês Damásio Geada
Thesis to obtain the Master of Science Degree in
Mechanical Engineering
Supervisor: Prof. Virgínia Isabel Monteiro Nabais Infante
Examination Committee
Chairperson: Prof. Luis Manuel Varejão de Oliveira Faria
Supervisor: Prof. Virgínia Isabel Monteiro Nabais Infante
Member of the Committee: Prof. António Manuel Relógio Ribeiro
July 2015
Abstract
Increased interest in renewable sources of energy led to the creation of the Helianto project. This project consists
of a modified train carriage capable of operating with photovoltaic energy.
In order to better understand the characteristics and effects of the project, a scaled 1/8 model was built. This way
it was possible to perform, cost-efficiently, a considerable portion of the tests that need to be done to the real
train carriage on several types of railway sections (e.g. curves, straight, breaking, etc.). This work analyses the
railway/bogie interactions, retrieving the maximum amount of coherent experimental results with the aim of
understanding the dynamic behaviour of the scaled model gathering all the necessary conclusions to better
predict the real train’s performance.
From the results achieved using all the data gathered through the model (railway/bogie acceleration and
deformation) it was possible to conclude that the capacitive accelerometers have a measurement error of around
1.5% when comparing them to the piezoelectric ones, for the range of frequencies of 5-200 Hz, that the model
suspension system attenuates around 66% of the vertical accelerations, and that the rolling coefficient stands at
0.0052.
Finally, the comfort and safety requirements of the model were assessed, presenting a track shift force exerted
was of about 59 N, running stability of 31.9N and 0.6 of derailment coefficient, all of which were within the
acceptable boundaries.
Key words:
Helianto project
Experimental results
Railway track
Train
Vibrations
Accelerations
List of programs
Matlab
Excel
Sigview
Resumo
Dado o crescente interesse no que toca a meios renováveis de energia foi criado o projecto Helianto. Este projeto
consiste num comboio modificado capaz de operar com base em energia solar.
Para melhor estudar os efeitos e características do projecto foi-me fornecido um modelo à escala 1/8 para
efectuar de forma económica grande parte dos testes inerentes ao funcionamento do comboio real em diversos
tipos de troço (e.g. curva, recta, travagem, etc.). Com isto em mente, neste trabalho foram então estudadas as
interacções Carril/Bogie de modo a recolher resultados experimentais coerentes e pertinentes para compreender
o comportamento dinâmico do modelo à escala, retirando as elações necessárias para melhor prever o
comportamento do comboio real.
A partir dos resultados obtidos (acelerações e deformações do carril e bogie) foi possível concluir que os
acelerómetros capacitivos apresentam um erro de medição de cerca de 1,5% quando comparados com os
piezoeléctricos, para uma faixa de frequências de 5-200 Hz, que o sistema de modelo de suspensão atenua cerca
de 66% das acelerações verticais, e que o coeficiente de rolamento é de 0,0052.
Finalmente, os requisitos de conforto e segurança do modelo foram avaliados, verificando-se que os valores se
apresentavam dentro dos limites aceitáveis com uma “track shift force” de cerca de 59 N, uma estabilidade de
desempenho de 31,9 N e um coeficiente de descarrilamento de 0,6.
Palavras Chave:
Projecto Helianto
Resultados Experimentais
Carril
Comboio
Vibrações
Acelerações
Table of contents
1. Introduction ......................................................................................................................................... 1
1.1. Motivation .................................................................................................................................... 1
1.2. Objectives ..................................................................................................................................... 5
1.3. Contributions ................................................................................................................................ 6
1.4. Framework of the thesis............................................................................................................... 6
2. Standards and vehicle parameters ...................................................................................................... 7
2.1. Vehicle dynamics parameters ...................................................................................................... 7
2.2. Load conditions ............................................................................................................................ 9
2.3. General principles of railway vehicle testing ............................................................................. 10
2.3.1. Choice of the method to be applied .................................................................................... 11
2.3.2. Helianto case study ............................................................................................................. 11
2.3.3. Helianto standards .............................................................................................................. 12
2.4. Helianto prototype ..................................................................................................................... 16
2.4.1. Prototype variables to assess .............................................................................................. 16
2.5. Measuring devices evaluation .................................................................................................... 18
2.5.1. Assessment of accelerations ............................................................................................... 19
2.5.2. Strain gauge configuration .................................................................................................. 21
2.5.3. Data acquisition systems ..................................................................................................... 23
2.5.4. Other experimental equipment .......................................................................................... 24
2.6. Analyse the capacitive accelerometers ...................................................................................... 26
2.6.1. Objective.............................................................................................................................. 26
2.6.2. Experimental setup and data acquisition for the vibrational test ...................................... 26
2.6.3. Comparison between accelerometer results and ANSYS simulation .................................. 29
2.6.4. Vibration modes .................................................................................................................. 32
2.6.5. Accelerometer results and comparison .............................................................................. 32
2.7. Data acquisition and convertion ................................................................................................ 36
2.7.1. Acquisition scheme ............................................................................................................. 36
2.7.2. Data acquisition software and programming ...................................................................... 37
2.8. Damping assumptions and formulae ......................................................................................... 40
2.8.1. Damping assumptions ......................................................................................................... 40
2.8.2. Damping formulae ............................................................................................................... 40
3. Rail/Bogie instrumentation ............................................................................................................... 42
3.1. Accelerometer positioning ......................................................................................................... 42
3.2. Instrumentation ......................................................................................................................... 43
3.3. Testing order and objective........................................................................................................ 45
3.3.1. List of tests with their explanation: ..................................................................................... 45
Table summing up all the testing .............................................................................................. 45
4. Results, tests and comparisons ......................................................................................................... 47
4.1. Spring-damper effect ................................................................................................................. 47
4.1.1. Damping results ................................................................................................................... 50
4.1.2. Acceleration dumping ......................................................................................................... 52
4.2. Weight differences and their effects .......................................................................................... 53
4.2.1. Accelerometer results ......................................................................................................... 54
4.2.2. Strain gauge results ............................................................................................................. 57
4.3. Velocity results ........................................................................................................................... 61
4.4. Friction Coefficient ..................................................................................................................... 62
4.5. Curve/derailment tests .............................................................................................................. 65
4.6. Curve lateral acceleration .......................................................................................................... 66
4.7. Comfort/safety results ............................................................................................................... 66
4.7.1. Track shift force results ....................................................................................................... 67
4.7.2. Running stability results ...................................................................................................... 68
4.7.3. Risk of derailment results .................................................................................................... 68
4.8. Real vehicle result estimations and model extrapolations ........................................................ 69
4.8.1. Vehicle size relation ............................................................................................................. 69
4.8.2. Track shift force result estimation for the real vehicle ....................................................... 69
4.8.3. Risk of derailment results .................................................................................................... 70
4.8.4. Model extrapolations .......................................................................................................... 71
5. Conclusions ........................................................................................................................................ 73
5.1. Accelerometer results comparison ............................................................................................ 73
5.2. Spring-damper parameters ........................................................................................................ 73
5.3. Accelerometer and strain gauge use for vibration assessment on rails .................................... 73
5.4. Friction coefficient ...................................................................................................................... 74
5.5. Model and real vehicle standards comparisons and extrapolations ......................................... 74
5.6. Review and future work ............................................................................................................. 75
6. References ......................................................................................................................................... 76
7. Appendices ........................................................................................................................................ 79
7.1. Deformation generated by the vibration modes on the railway track part ............................... 79
7.2. Arduino C++ data collecting and storing code ........................................................................... 83
7.3. Matlab data conversion code ................................................................................................... 100
7.4. Railway track part dimensions ................................................................................................. 103
Figure 1.1 - Cost per Watt produced variation since 1985 [1] ................................................................ 1
Figure 1.2 - Solar power global production growth since 2000 [2] ......................................................... 2
Figure 1.3 - Trainspraia passenger mini-train transport. ........................................................................ 3
Figure 1.4 - Railway station equipped with solar panels ......................................................................... 4
Figure 1.5 - Helianto, country version [10]. ............................................................................................ 4
Figure 2.1 - Forces Q and Y directions [12] [13]. ..................................................................................... 7
Figure 2.2 - H forces direction ................................................................................................................. 8
Figure 2.3 - Accelerations felt in vehicle bogie and bottom of body. ..................................................... 9
Figure 2.4 - Method choosing scheme [16]. .......................................................................................... 12
Figure 2.5 - Frequencies to which the human body is most vulnerable. .............................................. 14
Figure 2.6 - Forces applied on the structure of the Bogie [12] [30]. ..................................................... 18
Figure 2.7 - Capacitive accelerometer mounted beneath the rail. ....................................................... 21
Figure 2.8 - Strain gauge rosette ........................................................................................................... 21
Figure 2.9 - Vertical rail rosette reference frames (as seen from the side of the rail). ......................... 22
Figure 2.10 - Horizontal rail rosette reference frames (as seen from the bottom side of the rail). ..... 23
Figure 2.11 - Arduino UNO board. ......................................................................................................... 24
Figure 2.12 - 10A fuse [27]. ................................................................................................................... 25
Figure 2.13 - Fuse suport and electric attachment [28]. ....................................................................... 25
Figure 2.15 - Electric switch [29]. .......................................................................................................... 25
Figure 2.16 - Railway vibration mode test layout. ................................................................................ 27
Figure 2.17 - Vibration modes assesment scheme ............................................................................... 29
Figure 2.20 - Data collecting diagram. ................................................................................................... 36
Figure 2.21 - Convertion program fluxogram. ....................................................................................... 38
Figure 2.22 - Arduino reading program fluxogram. .............................................................................. 39
Figure 3.1 - Overall layout of the carriage. ............................................................................................ 42
Figure 3.2 - Accelerometer positions. ................................................................................................... 42
Figure 3.3 - Accelerometers' positions (top view)................................................................................. 43
Figure 3.4 - Accelerometers' positions (side view). .............................................................................. 43
Figure 3.5 - Arduino board. ................................................................................................................... 44
Figure 4.1 – Sample of the bogie and axle acceleration variation with time during test 1 (filtered) ... 47
Figure 4.2 - Vehicle response to vertical vibrations. ............................................................................. 48
Figure 4.3 - Vehicle suspension. ............................................................................................................ 49
Figure 4.4 - Spring-mass-damper system equivalencies for vehicle suspension. ................................. 49
Figure 4.5 – Process of integration to obtain the velocity and displacement graphs. .......................... 50
Figure 4.6 - Test 1, body floor and axle x-axis acceleration (movement direction) and body floor
vertical axis acceleration (from rail 1 to 2) - filtered. ............................................................................ 54
Figure 4.7 – test 2 x-axis body and axle acceleration (filtered)............................................................. 54
Figure 4.8 - test 3 x-axis body and axle acceleration (filtered). ............................................................ 55
Figure 4.9 - Test 5 x-axis, body amd axle acceleration with extra weight (filtered). ............................ 56
Figure 4.10 - Body vertical acceleration with extra weight (filtered). .................................................. 56
Figure 4.11 - test 6 x-axis acceleration (filtered). .................................................................................. 57
Figure 4.12 - Test 1 vertical strain gauge results (Filtered). .................................................................. 58
Figure 4.13 - Test 1 horizontal strain gauge results (filtered). .............................................................. 58
Figure 4.14 - Test 6 vertical strain gauge results (filtered). ................................................................... 60
Figure 4.15 - Railway track deformation. .............................................................................................. 61
Figure 4.16 - Sample graph of the bogie's accelerometer horizontal velocity variation - test 3. ........ 61
Figure 4.17 - Sample graph of the bogie's accelerometer horizontal velocity variation - test 4. ........ 61
Figure 4.18 - Lateral acceleration variation with time from test in a curve (image filtered at 6Hz low-
pass filter). ............................................................................................................................................. 66
Figure 7.1 - 1st and 2nd rail vibrational modes. .................................................................................... 79
Figure 7.2 - 3rd and 4th rail vibrational modes ..................................................................................... 79
Figure 7.3 - 5th and 6th rail vibrational modes ..................................................................................... 80
Figure 7.4 - 7th and 8th rail vibrational modes ..................................................................................... 80
Figure 7.5 - 9th and 10th rail vibrational modes ................................................................................... 80
Figure 7.6 - 11th and 12th rail vibrational modes ................................................................................. 81
Figure 7.7 - 13th and 14th rail vibrational modes. ................................................................................ 81
Figure 7.8 - 15th and 16th rail vibrational modes. ................................................................................ 81
Figure 7.9 - 17th and 18th rail vibrational modes. ................................................................................ 82
Figure 7.10 - 19th and 20th rail vibrational modes. .............................................................................. 82
Figure 7.11 - 21th and 22th rail vibrational modes. .............................................................................. 82
Figure 7.12 - Railway dimensions and sleeve dimensions. ................................................................. 103
Figure 7.13 - Railway and sleepers dimensions................................................................................... 104
Figure 7.14 - Rail section dimensions. ................................................................................................. 104
List of tables
Table 2.1 - Comfort levels for different values of the frequency-weighted root mean square
acceleration. .......................................................................................................................................... 14
Table 2.2 - Table of comfort with Wz parameter. ................................................................................. 15
Table 2.3 - Qualitative representation of the accelerometer's features [24]. ...................................... 20
Table 2.4 - Material properties of the rails and the sleepers. ............................................................... 28
Table 2.5 - ANSYS Vs experimental vibration modes. ........................................................................... 30
Table 2.6 - Experimental vibration modes measured with capacitive accelerometers Vs piezolelectric
accelerometers. ..................................................................................................................................... 33
Table 2.7 - Railway track part vibration modes. .................................................................................... 35
Table 3.1 - Test summing table. ............................................................................................................ 45
Table 4.1 - Damping ratio and natural frequency. ................................................................................ 52
Table 4.2 - Mean acceleration attenuation. .......................................................................................... 53
Table 4.3 - Railway observed strain with and without extra weight. .................................................... 60
Table 4.4 - Friction force results. ........................................................................................................... 63
Table 4.5 - Test summary table. ............................................................................................................ 65
List of variables
�̈�+– Acceleration felt on the wheelset on the x-axis
�̈�+– Acceleration felt on the wheelset on the y-axis
�̈�+– Acceleration felt on the wheelset on the vertical axis
�̈�∗– Acceleration felt on the body on the x-axis
�̈�∗– Acceleration felt on the body on the y-axis
�̈�+– Acceleration felt on the body on the vertical axis
�̈�𝑚– Average acceleration of the vehicle on the x-axis
�̈�𝑚
– Average acceleration of the vehicle on the y-axis
�̈�𝑚– Average acceleration of the vehicle on the vertical axis
H – Axle forces
Cc – Critical damping coefficient
c – Damping coefficient
𝜉 – Damping ratio
∆𝑥 – Displacement
𝛾𝑥𝑦 – Distortion on the xy plane
𝛾𝑥𝑧 – Distortion on the xz plane
λ – Eigenvalue
𝜔 – Frequency of vibration
T – Frequency period
𝑎𝑤𝑟𝑚𝑠 – Frequency weighted root mean square acceleration
Fa – Friction force
Faw – Friction force with added weight
e – Gauge distance
[K] – Global stiffness matrix
g – Gravitic acceleration
[I] – Identity matrix
Ec – Kinetic energy
Լ (f(t)) – Laplace transfer of a function f
Y – Lateral forces felt by the rail
Y20 Hz,99.85%,lim – Limit lateral force filtered with 20Hz low pass filter with 99.85% of the value
𝑌𝑚𝑎𝑥,𝑙𝑖𝑚 – Limit max later force
𝑌𝑟𝑚𝑠,𝑙𝑖𝑚– Limit root mean square lateral force
∆QH – Load transference
δ – Logarithmic decrement
[M] – Mass matrix
𝜔𝑛 – Natural damped frequency
𝜔𝑑 – Natural frequency
Γtsf – Objective function of track shift force
𝛤𝑟𝑠 – Objective function of running stability
𝛤𝑟𝑑 – Objective function of risk of derailment
η – Overturning criterion
r – Radius of vehicle wheel
R – Reaction force on the rail
𝑎𝑟𝑚𝑠– Root mean square acceleration
k – Spring/stiffness constant
Strain measured on the strain gauge n
Ԑ𝑥 – Strain on the x-axis
Ԑ𝑦 – Strain on the y-axis
Ԑ𝑧 – Strain on the vertical axis
𝑎(𝑡) – Time dependent acceleration
𝑎𝑤(𝑡) – Time dependent frequency weighted acceleration
K1 – Track shift force correction factor
m – Vehicle mass
fa – Vehicle overall friction coefficient
𝑣 – Vehicle velocity
w – Vehicle weight
Wl – Vehicle weight with extra load
Q – Vertical forces felt by the rail
Wz – Wertungszahl criterion
1
1. Introduction
1.1. Motivation
One of the most important challenges that will have to be reached in the decades to come is the energy
sustainability of mankind.
Over the last decade, global energy consumption has undergone some significant changes, one of which was the
significant growth in the use of renewable sources of energy. This gradual technological and mind-set change
enthused the idea of applying some of these new energy sources to the most polluting areas of human activity,
such as transportation.
On the way to attain these goals of higher energy efficiency and reduced greenhouse gases production (along
with other toxic gases), one of the most reliable and abundant forms of energy, is solar/photovoltaic energy. This
type of renewable energy has more widely used all over the world with costs associated with it decreasing as it is
shown on figures 1.1 and 1.2.
Figure 1.1 - Cost per Watt produced variation since 1985 [1]
2
Figure 1.2 - Solar power global production growth since 2000 [2]
While photovoltaic energy can make little difference when applied to certain means of transportation that already
use electric power (which produce far less emissions per Joule than oil-sourced power, for example), in other
areas of public/private transportation pollution produced per unit of energy is far greater. One such area is
transportation using diesel powered vehicles.
Diesel engines are reliable, fuel efficient, durable, easy to repair and generally inexpensive to operate.
Furthermore, these engines can power buses (which are comparable in weight to a train like the one shown in
figure 1.3) for over 15 to 20 years while having 10-20% [3] lower global-warming emissions and very low
emissions of carbon monoxide and hydrocarbons due to their higher fuel saving, today there are filters capable of
reducing the amount of NOx emissions by 90% [4].
Still these engines, due to their particle emissions, contribute to serious public health problems like respiratory
and cardiovascular [5], incidence of asthma, acute respiratory difficulties, and chronic bronchitis [6], degraded
mental functioning [7] among other diesel exhaust negative impacts is also very likely to be a human carcinogen
by inhalation [8]
Diesel engines also contribute to the greenhouse effect, with the average car producing around 4 tons of annual
CO2 emissions [9].
As an example, one type of diesel transportation that is highly polluting and is widely used near leisure spots
(beaches for instances) and historic city centres is the tourist, or beach trains.
3
These train-like vehicles, akin to the one shown in figure 1.3, while being very useful to carry people to
interesting places such as beaches, museums, parks and others, produce copious amounts of pollution due to
their diesel fuelled engines.
Figure 1.3 - Trainspraia passenger mini-train transport.
Touristic trains are a very good target to incorporate clean, environmental friendly photovoltaic energy
generation due to their operation characteristics (besides of all the diesel engine problems stated above):
They operate on touristic sites where pollution is almost forbidden or considered to be extremely
unfitting, e.g. near historic monuments and buildings, natural parks, recreational, leisure and
amusement parks, city historic centres or near beaches;
These trains are usually quite slow; they do not aim for velocity but for convenience, thus they do not
necessarily need a powerful petrol engine;
Generically speaking, beach trackless trains possess wide roof racks for their size in order to sunshade
the people inside on hot summer days, which enables the allocation of wider still photovoltaic panels to
generate moving power;
Recreational trains are light enough to successfully use photovoltaic power;
The fact that the panels are built and programmed to be always facing the sun (seen figure 1.5) turns
out to be really useful to actually shade customers from it more effectively than a common train
rooftop;
This type of trains, specifically beach trains, are mostly used during the summer season which is when
photovoltaic power is more effective to use.
The Helianto project [10] was designed to overcome the sustainability concerns of this type of transportation.
The aim of the project is to build a lightweight train to operate on a pre-existent train line traditionally used by
diesel powered beach trains alongside some of the sunny beaches of Portugal’s coast line.
A usual solution for a photovoltaic train is to equip the train station ceiling with photovoltaic panels, as it is
shown on figure 1.4:
4
Figure 1.4 - Railway station equipped with solar panels
The solution applied in the Helianto project case was neither of the above, in this case the power is only solar
sourced and the panels are projected to be installed on top of the train carriage. This solution was only made
possible due to the fact that Helianto is a light-weight train (figure 1.5) and hence its friction force is low. Since
it produces little friction force and its speed is also reduced, it does not need more than 3kW of peak power input
[10].
Since the power input required is low, the panels placed on top will generate enough electric power to effectively
propel the vehicle [11].
Figure 1.5 - Helianto, country version [10].
There are several advantages with this type of panel configuration for photovoltaic recreational trains when
comparing with the former:
5
The ceiling of this type of train is usually larger than the ceiling of the train station where passengers
wait;
There are no need for some kind of overhead contact line (like a catenary for normal trains), since the
energy is produced in the train itself, instead of somewhere else;
The fact that there are no cables transmitting the power, from the power source to the train, substantially
reduces the amount of energy loss by cable resistance;
For this project to succeed it is extremely important that it fulfils all the safety requirements. The safety
requirements that this work thesis focus on are fundamentally linked to the accelerations felt on several parts of
the vehicle. This type of research is utterly important for the project itself since the carriage is entirely new. All
the inherent dynamics of the whole vehicle will be quite different from the one in existing train, thus, there’s a
need to make sure if the vehicle will comply with the comfort and safety requirements.
This kind of railway vehicle will substitute the old polluting transpraia and praia do barril trains, usually used
during summer months, to transport bathers to the beaches.
Furthermore, the Helianto’s carriage will be operating in railways placed in a particularly harsh environment
(from machinery standpoint) since it is meant to function, geographically, in parts of Portugal’s coastline.
The quick deterioration of the railway track materials in the targeted environment reinforces the need for proper
means of evaluating the interactions established between the bogie of the vehicle and the railway track.
The objective of this thesis is to analyse a reliable vibrational assessment system and evaluate the case study.
The testing operations of the developed assessment system will be carried out using a prototype of the real
carriage. The reason behind the usage of a prototype, instead of a real-size train carriage, sticks with the fact that
nowadays there are strict regulations for railway and train experimentation on vehicles that travel on those lines
due to understandable concerns regarding passenger and line safety. Furthermore the prototype can be extremely
helpful in other types of tests and there is no prototype available as of today. This prototype allows further
testing of several key features of the functioning of a train.
Another objective is to use the model to forecast what the real train’s behaviour will be, demonstrating the
relationship between the prototype and the real train, which aids to extrapolate the results from the 1/8 scale
model to the real life carriage. This relation will enable further testing while providing a reasonable
understanding of what the results mean for the bigger picture – the real train.
The data obtained from the assessment system is useful to understand the dynamics of the vehicle as well as to
predict if the vehicle will be reliable in terms of passenger comfort and safety, which, as was already been said,
is of most importance from a commercial point of view as well as from a regulation stand point.
1.2. Objectives
Research about the imperative safety requirements for passenger trains and acknowledge some of the
mathematical formulations inherent to those requirements;
6
Analyse and compare results from piezoelectric accelerometers with the analogic accelerometers to
validate the latter in terms of reliability for usage on the subsequent testing;
Analyse and compare the natural frequencies of one of the model’s railway track obtained using
accelerometers with two other lists of results obtained from ANSYS. This will permit to assess with
precision the dynamic behaviour of a part of railway track and validate the sensors and data collection
system;
Experimental setup planning and arrangement;
Selection of proper instruments alongside with the instrumentation of the vehicle itself.
Programming of data collection and data treatment systems;
Analyse and compare the results obtained with the accelerometers and strain gauges attached to the
railway and to the train prototype with, the purpose of understanding as well as possible the dynamic
behaviour of the system railway-train model;
Finally, extrapolate some of the results obtained from the model into the real-size train.
1.3. Contributions
The first contribution of the present work is a better understanding of what vibrations are actually significant
when considering a railway vehicle. This will allow further behavioural study on scaled railways and carriages.
Knowing what kind of vibrations are more likely to be found in a certain system, with specific conditions, is an
effective way of enhancing the analysis of results.
The research of some safety requirement formulas and relations of proportion between a real train and the scaled
carriage is another contribution. These tests will permit a thoughtful understanding of what safety measures
could be tested in a scaled model and what is their relation to a fully operational photovoltaic train.
1.4. Framework of the thesis
The thesis is structured in five main chapters
Chapter one presents a brief introduction, and discusses the motivations, objectives and purposes of this
work. Furthermore it introduces the project main characteristics as well as some basic requirements.
Chapter two describes the acknowledgements required to outline and show a better understanding of
what category would the vehicle fall into as well as some relevant variables to consider, prototype
explanations, safety and comfort regulations and requirements and instruments choice. This chapter
ends up with the comparison of results evaluating the reliability of the accelerometers chosen.
Chapter three is focused on the experimental approach. From the positioning of the accelerometers, to
the actual vibration and acceleration tests.
Chapter four hold all the respective analysis and comparison of the results attained.
Chapter five closes the thesis, providing a few conclusions and discussing possible future improvements
to the work.
During this chapter the project main aspects were summarily explained, all the objectives that will be required
along the work were set and some possible direct contributions that the work will be able to offer were named.
7
The next chapter will show and explain what international standards need to be achieved to reach the assigned
aims.
2. Standards and vehicle parameters
In this chapter a brief description of some relevant safety features to comply with, in train-like vehicles is
outlined. This will also include mathematical formulae that help compare and understand the behaviour of
railway vehicles.
The chapter ahead will only contain information from published standards, documents and papers, and not any
type of result or conclusion of the present work. The objective of the chapter is just to show some borderlines of
thought that have been developed previously with the aim of assessing the safety of a railway vehicle.
2.1. Vehicle dynamics parameters
One of the most important parameters to consider safety-wise are the forces and accelerations measured by the
vehicle in various parts of its structure, therefore UIC (International Union of Railways) carefully lists all of
these accelerations and forces, along with its own nomenclature. For the purpose of ease of understanding and
memorization this work will follow the same nomenclature as UIC’s.
Wheel-rail interaction is one broad portion of the entire picture of how railway vehicle dynamics work. With this
in mind, the forces on the wheel-rail contact surface on each wheel are designated Y if they point towards the
lateral direction and Q if they point towards the vertical axis as shown on figure 2.1
Figure 2.1 - Forces Q and Y directions [12] [13].
Q force
R reaction
force
β angle
8
Another relevant dynamic variable is the H force, which is the lateral force measured on the axle-boxes (figure
2.2).
H forces are transmitted along the axle-boxes into the frame of the vehicle. H forces combine all the rotational
resistances, including the inertial forces caused by the vehicle’s change of direction. These force, while acting
above the wheel-rail contact area (since it is only considered H force when measured in the axle, as seen in
figure 2.2), creates a tilting torque of the axle. The tilting that the axle suffers adds a supplementary load to one
of the wheels of the wheel-set which is directly dependent on their own radius by the following expression [14]:
∆𝑄𝐻 =𝐻𝑟
2𝑒 (2.1)
Where 2e represents the distance between two rails, also known as gauge.
However, the total effect of this load transfer is actually diminished by the elastic behaviour of the rail and the
suspension of the vehicle. Thus, the genuine load transference is [14]:
∆𝑄𝐻 =𝑓𝐻𝑟
2𝑒 (2.2)
Where the diminishing coefficient f is considered to be around 0.85 for regular vehicle wheels with outer shafts.
Figure 2.2 - H forces direction
As was mentioned before, linear accelerations are vital to evaluate. As the UIC’s document shows, the linear
acceleration felt by the wheelset in the lateral direction is named �̈�+, and in the vertical axis �̈�+ and �̈�+ for
acceleration on the railway axis. These accelerations, along with the accelerations felt on the body, above the
bogie, are used to assess the average acceleration felt across the entire vehicle.
The accelerations suffered by the body are named �̈�∗, if in the direction of movement (railway axis), �̈�∗ if the
acceleration pulls towards the side of the vehicle, and �̈�∗ if the acceleration is felt in the vertical axis. Finally, the
H force H force
9
average acceleration felt on the body above the bogie will be named �̈�𝑚, �̈�𝑚 and �̈�𝑚 and can be approximately
determined using both the accelerations named above.
The following image (figure 2.3) shows the direction and positioning of all the accelerations:
Figure 2.3 - Accelerations felt in vehicle bogie and bottom of body.
2.2. Load conditions
The tests performed during this work took into account two different load conditions. One of these conditions,
with less mass, is used to resemble working order and another, with additional mass, to match the functioning of
the vehicle under normal payload conditions.
The working order is typically defined by the mass of the vehicle equiped with all the consumables and occupied
by all the staff which it requires in order to fulfil its function but without any payload.
The normal payload mass is described as being the designed mass of the vehicle in working order plus the
normal design payload. The normal design payload is determined by the type of rolling stock and the level of
comfort associated with the type of service being provided. Since in this thesis there is just the need to simulate
the additional weight, this will be accomplished simply by distributing mass throughout the model vehicle.
The distribution and amount of weight varies according to 3 different categories:
- Passenger vehicles;
�̈�∗
�̈�∗
�̈�∗
�̈�∗
�̈�𝑚
�̈�𝑚
�̈�𝑚
�̈�+
�̈�+
�̈�+
�̈�+
�̈�∗
�̈�+
�̈�+
�̈�∗
10
- Freight wagons;
- Special transport vehicles.
The loading for assessment of the real case must be representative of the loads in regular service in terms of
amount of mass, distribution of mass and location of the centre of gravity, although in some cases of highly
unpredictable mass distribution this test may lose importance to other tests.
The definitions presented come from document prEN15663 [15] dated from November 2006.
2.3. General principles of railway vehicle testing
The objective of this work is to provide some insight on how the vehicle testing works and contribute to obtain
approval for the Helianto project . Any approval of a railway vehicle from a dynamic behaviour point of view
should be based on either on-line running test or a numerical simulation. The contribution towards the Helianto
project, future approval done by this work will be achieved basically through on-track testing.
The testing of the vehicle should be done in several distinct types of tracks shown below [16]:
On tangent track;
In large radius curves;
In medium radius curves;
In small radius curves;
In very small radius curves.
As it was mentioned on the previous topic all the tests to the candidate must be done with two different
conditions, one empty loaded and one fully loaded.
Also, according to the nature of the approval procedure, which may only be an extension to the authorization, the
procedure to be applied can also have two variants termed as follows:
Full approval, considering that the tests take into account all possible running and vehicle conditions.
Partial approval, if only part of these conditions are taken into consideration;
In order to carry out these procedures there is a need to apply one, or more, of three possible methods:
The “normal” method in which the individual wheel-rail interaction forces Y and Q can be measured
and, therefore, the Y/Q ratio calculated, as well as the overturning criterion η for category IV vehicles;
The “simplified” method, if only H forces and/or accelerations on the wheelsets, bogie frame and body
are to be measured;
And lastly, the numerical simulation method using the variables of the “normal” method.
NOTE: Category IV vehicles – vehicles equiped with a cant deficiency compensation system and/or for which a
greater cant deficiency than that required for the other categories may be applied.
11
2.3.1. Choice of the method to be applied
The approval of a vehicle is requested in one of two different situations:
Either the vehicle concerned is new, in which case it corresponds to the first ever approval;
Or, the vehicle has been modified or is to be operated somewhat differently, in which case it only needs
an widening to the approval.
Railway vehicles may also fall into one of the next three categories depending on what type of vehicles they are
[16]:
“Conventional” vehicles if they are of conventional design and subject to usual operating conditions.
“New-technology” vehicles;
“Special” vehicles which are either unique or very few and belonging to either the two following sub-
categories:
a) Track-maintenance vehicles, including rerailing vehicles,
b) And special transport stock.
If the railway vehicle to be approved is actually new it should be assessed via the full procedure as well as the
“normal” measuring method explained before. However, if the vehicle complies with the requirements for an
approval extension (explained below) the simplified method can be applied, except for the new-technology
vehicle in which case the first, complete, method should be applied.
The candidate is considered as only needing an extension to the approval, when the railway vehicle actually
consists of a previously approved vehicle but will be operated differently, without increasing the permissible
cant deficiency ladm. Also, the other possible case is when the candidate vehicle includes revised design features.
A scheme was created by the UIC in order to show the global question one may ask when understanding which
methods should be applied to approve a new railway vehicle. That same scheme is presented on the following
topic, on figure 2.4, along with the path taken by the Helianto project in it.
2.3.2. Helianto case study
The Helianto project will have to overcome some of these tests, thus it is relevant to think in what category(ies)
it will fit in.
Due to the fact that it uses normal bogies one would think that it should be tested according to the simpler
method since it is actually an already existent vehicle which was modified. The problem with this is that the new
designed vehicle uses new technology (photovoltaic energy) to power itself, instead of the normal carbon-
sourced electricity. Also, the photovoltaic panels are mounted on top of the vehicle itself, therefore it is not only
an external modification, indeed it also involves some changes to the train’s structure.
To sum it up, although either category would suit well this project, it is more likely to have Helianto tested under
the conditions of a “new technology” vehicle with a complete analysis.
12
With this in mind, and following the figure 2.4, one can say that the path taken by the Helianto project is quite
straightforward and would be described by:
Figure 2.4 - Method choosing scheme [16].
Hence, one can conclude that the method to be applied in the Helianto case, is the normal method of approval
testing.
Although the tests to be done on the real designed train are complete, the tests to be made on the prototype
throughout this report are simpler and less complete but will, nonetheless, provide some interesting results and
allow some useful assessments.
2.3.3. Helianto standards
Another important issue is the process of evaluating the dynamic behaviour. An effective way of achieve this is
to follow the formulae expressed on some of the railway standards. The most important standards created to
quantify the dynamic behaviour relate to following areas: comfort and safety.
13
Ride Comfort
In any type of passenger transportation and by which one means any kind of transport that deals with passengers
instead of goods, one of the characteristics of utmost importance, and one of the most common design issues, is
the comfort, especially in speed trains.
There are several different contributors to passenger ride comfort attained, the way the ventilation system works,
cabin room temperature, the level of noise, ease of boarding, the amount of space for each passenger is, etc.
However, this study focuses on the effects of the vibrations; in this case, the vibrations felt by the passengers
during their journey. The accelerations felt on the train body are linked to the passenger level of comfort, or
discomfor. Some of the most common formulae employed are shown below.
The accelerations on the carriage body can be measured at different points out, since the accelerations felt will
often be quite similar, depend on how rigid the body is. However the accelerations will be much different if
measured outside the body, due to the layout of springs operating between the body and the bogie of the vehicle.
With this in mind, one effective guidance for ride comfort is the root mean square of the acceleration:
𝑎𝑟𝑚𝑠𝑖 = √
1
𝑡𝑓 − 𝑡𝑖∫ (𝑎𝑖(𝑡))2𝑑𝑡𝑡𝑓
𝑡𝑖
𝑤𝑖𝑡ℎ 𝑖 = 1,2, … ,𝑚 (2.3)
Where m is the total amount of separate measurement one wants to make, ti is the time correspondent to the
initial value and tf is the time correspondent to the final value. In this case, the higher the value determined by
the root mean square of acceleration (RMS) equation above, the more uncomfortable the accelerations of a
vehicle are.
However, the human body is sensitive to vibrations within a more narrow range of frequencies therefore, it is
better to use values of frequency-weighted accelerations for the purpose of evaluating the ride comfort. This can
be achieved using specially designed transfer function’s filters. These special transfer functions can be found in
reference [17].
If considering the root mean square frequency-weighted acceleration, the comfort formula changes to the
following equation:
𝑎𝑤𝑟𝑚𝑠 = √1
𝑡∫ |𝑎𝑤(𝑡)|2𝑑𝑡𝑡
0
(2.4)
Where 𝑎𝑤 is the frequency-weighted acceleration, 𝑎𝑤𝑟𝑚𝑠 the root mean square frequency-weighted acceleration
and the t is the duration of the measurement (usually 5s will be enough) [18].
The ride comfort levels are well presented in the European standards EN 12299 [19] according to ISO 2631,
from which the table 2.1 was taken.
14
Table 2.1 - Comfort levels for different values of the frequency-weighted root mean square acceleration.
Value (-) Description
𝒂𝒘𝒓𝒎𝒔 < 𝟎. 𝟐 Very comfortable
𝟎. 𝟐 ≤ 𝒂𝒘𝒓𝒎𝒔 < Comfortable
𝟎. 𝟑 ≤ 𝒂𝒘𝒓𝒎𝒔 < 𝟎. 𝟒 Medium
𝟎. 𝟒 ≤ 𝒂𝒘𝒓𝒎𝒔 Less comfortable
Wertungszahl criterion
The Wertungszahl criterion, Wz, evaluates the comfort level of a vehicle in vibrational terms. This criterion was
unveiled by Sperling and Betzhold testing in the 40’s and 50’s [20], respectively.
This value is based on the frequency-weighted acceleration, which has to be measured at the floor level of the
carriage body. The equation to determine Wz is [21]:
𝑊𝑧 = 4.42(𝑎𝑤𝑟𝑚𝑠)0.3 (2.5)
Also according to ISO 2631 [19] the human body is most sensitive to lateral and/or vertical excitations within
the range of 3 to 7 Hz, as seen on figure 2.5.
Figure 2.5 - Frequencies to which the human body is most vulnerable.
15
Following the Wz evaluation, the ride comfort levels (either lateral and vertical) can be divided into four
categories described in the table 2.2:
Table 2.2 - Table of comfort with Wz parameter.
Value (-) Description
𝟏 < 𝑾𝒛 < 𝟐 Very comfortable
𝟐 < 𝑾𝒛 < 𝟐. 𝟓 Comfortable
𝟐. 𝟓 < 𝑾𝒛 < 𝟑 Less comfortable
𝟑 < Wz Unpleasant
Safety
One of the most relevant criteria, since it must always be within the permissible range, is safety.
Safety can be described from several stand points, with the most common ones being either track shift force,
running stability and risk of derailment.
Track shift force Y is measured as the difference between the lateral forces acting on outer curve wheels. High
track shift force might affect the track conditions and increase the maintenance cost [22].
From the European standardization [22] it is possible to know that the track shift force limit can be expressed
(with all the units in kN) as:
∑Y20 Hz,99.85%,lim ≤ K1(10 +2𝑄𝑜
3) (2.6)
Where 2Qo is the mean static axle load of the vehicle and can be described as:
2𝑄𝑜 = 𝑚𝑣𝑔
𝑛 (2.7)
Where 𝑚𝑣 is the total mass of the vehicle and n is the number of axles of the vehicle, and K1 = 1 for passenger
trains (which is the case), and with n being the number of axles of the vehicle. The final track shift force is equal
to the 99.85% of the value obtained from the forces and subjected to a 20 Hz low-pass filter. Hence, the track
shift force objective function Γ can be described as (once more, according to EN-14363):
Γtsf = max (∑𝑌20 Hz,99.85%) (2.8)
Where the maximum means the highest force from all the axles, hence Γ is the scalar that results from the
maximum of the filtered track shift force of all the wheelsets of the vehicle.
Running stability
Another relevant criterion of the safety has to do with the running stability of the vehicle, and this takes
particular importance near the critical hunting velocity. Thus, according, once more to the European
standardization [22], the edge condition for a vehicle to operate within a stable range can be expressed as follow:
16
∑𝑌𝑟𝑚𝑠,𝑙𝑖𝑚 =
∑𝑌𝑚𝑎𝑥,𝑙𝑖𝑚2
=𝐾1 (10 +
2𝑄𝑜3)
2
(2.9)
From the above equation the following running stability objective function can be deducted and can be defined
as (following EN nomenclature):
𝛤𝑟𝑠 = max (∑𝑌𝑟𝑚𝑠)𝑖, 𝑖 = 1,2, … 𝑛 (2.10)
As previously, this equation represents the maximum value among all the axles.
Risk of derailment
Once more, based on the European standardization [22], the derailment coefficient is defined, as it was stated
several times along this document, as the ratio between the lateral outwards forces (Y) and the vertical
downwards forces (Q) operating on each wheel of the vehicle. In this case, the safety condition to avoid
derailment is then defined by the following equation:
(𝑌
𝑄)20𝐻𝑧,99.85%
≤ 0.8 (2.11)
And, once more, the risk of the derailment objective function is expressed by:
𝛤𝑟𝑑 = max (𝑌𝑗
𝑄𝑗)20𝐻𝑧,99.85%
, 𝑗 = 1,2, … ,2𝑛 (2.12)
Where j is the wheel number.
2.4. Helianto prototype
In the case of the Helianto project, a prototype was built. This work took several advantages of the existence of
this prototype, when comparing with the alternative of using a real carriage:
Much lower test costing than actually using a real train carriage in an actual railway to assess
vibrations.
Time needed to repeat or prepare a testing series was immensely reduced, while also taking less effort
to assemble all the instruments.
The most important reason is that it is actually generally forbidden to assemble devices on either the
carriages and, above all, on the public railway tracks. It is not impossible to assemble such devices but
the clearance to do so is extremely difficult to obtain. This actually makes a lot of sense, since the
percussions of any kind of damage in the rails could provoke serious consequences, which repair costs,
no student project could pay for.
2.4.1. Prototype variables to assess
A prototype makes testing easier it is necessary to know which variables to assess.
As it was stated in before there are some critical variables that must be assessed. However, besides being
interesting and important, the variables must be present on both the real train and the prototype. The variables
which encompasses all of these requirements are:
17
The lateral, on axle-box force H, which is responsible for the tilting forces in the wheelset axis,
although these forces are not actually fundamental to the study of derailments they are nevertheless
important to understand the forces acting on several parts of the vehicle. As can be seen from figure 2.6
the H force can be approximated to the Y force. In fact, H force < Y force [14] due to the fact that the
axle does not need to endure all of the of the centrifugal force created by the vehicle since their outer
wheels do not contribute for the centrifugal force felt on the vehicle axle. Still, H force can be
approximated by H ≈ Y, since the mass of the outer wheels is negligible when compared with the mass
of the entire vehicle;
The Y forces, which are responsible for the derailment of railway vehicles. The forces are due to
vehicle behaviour caused by running dynamics (hunting phenomena) and centrifugal force and occur
mainly in curves, due to angle of approach and rolling contact equilibrium, being the latter generate by
lateral creepage and centrifugal forces [23];
The Q load, which is the force responsible for maintaining the stability of the vehicle without derailing.
Conversely to the Y forces. Q forces are generated by the own weight of the vehicle making them easier
to quantify. In curves and during possible severe hunting, this force can increase the flanging of the
wheel against the railhead. They are actually quasi-static forces because they vary slightly while the
vehicle is curving due to centrifugal force, which marginally changes the centre of gravity of the vehicle
from the middle of the rail to the outer curve side;
Railway track vibration with the passage of the vehicle;
Derailment coefficient Y/Q, which can be directly calculated by knowing the vertical and load forces.
18
To visualize the direction and positioning/application, on the bogie, of the forces spoken above, the following
image is provided:
Currently there is a growing interest in these types of measurements as a result of new technology operators,
whose vehicles must be carefully evaluated and checked against inbalance, before actually allowing them to
circulate on public transportation railways.
2.5. Measuring devices evaluation
The measurement of train-track interaction force has been handled in numerous different ways as it is critical to
assess potentially harmful situations. In order to measure the variables mentioned above there is a need to choose
the best suitable devices for that matter.
The first three variables are forces which mean that, to get a general understanding of their value, the only
knowledge requirements are the mass of the vehicle and the acceleration felt by it in their directions of
application:
The axle-box force H can be calculated using the mass of the vehicle and the acceleration read in the
axle axis [14] [23];
The lateral force Y can also be obtained by knowing the mass of the vehicle and the sideways
accelerations felt by it [23];
Reaction
Force R
Q Load
Force
β angle
Figure 2.6 - Forces applied on the structure of the Bogie [12] [30].
19
The Q load forces are directly caused by the weight of the vehicle therefore there is no need to measure
accelerations, only the total mass [14]. However, as it was previously stated, this force can change
overtime while curving, due to centre of gravity change, therefore, it might be necessary to calculate Q
force variation using the equation 2.2 in section 2.1;
The longitudinal acceleration felt by the vehicle while cruising the railway.
There is still the need to measure the vibrations on the railway track. An efficient method to read the vibrations
exerted on the rails is to use some device capable of measuring deformations. Those deformations could be
directly translated into vibration levels.
2.5.1. Assessment of accelerations
In order to measure the accelerations mentioned, the device to use is an accelerometer. In this case a three axial
accelerometer with the aim of measuring all the accelerations at the same time. However there are several types
of accelerometers, thus one must choose which one best suits the occasion. Several types are described below
[24] :
Potentiometric accelerometers
This is one of the simplest accelerometers. It measures motion using a spring-mass system which is attached to a
potentiometer. The mass’ change in position is translated into a variation of electrical resistance.
Although they are quite simple their natural frequency is quite low (around 30 Hz or less) which limits their
application to low frequencies. As well as the frequency range, the dynamic range is also low.
Capacitive accelerometers
In these accelerometers, a diaphragm acts as a mass and moves while under the influence of acceleration. The
diaphragm stays between two fixed plates creating two capacitors. The movement of the diaphragm causes a
capacitance shift by altering the distance between the two parallel plates.
The two capacitors form the two arms of the bridge. The output of the bridge varies according to the
acceleration.
This kind of accelerometers is quite common and has a true DC response alike the potentiometric
accelerometers; however it also has a rather limited frequency and dynamic range.
Piezoelectric accelerometers
Piezoelectric accelerometers use material of the same name as an active element. One side of the piezoelectric
material is connected to a rigid base and a mass is attached to the other side. When the device suffer an
acceleration the piezoelectric material deforms, which generates electric charge. The charge is proportional to
the acceleration and finally this charge is converted into voltage.
20
This type of accelerometers possess a wide range of advantages. It has wide dynamic range as well as frequency
range and excellent linearity. They have no moving parts which reduce wear and tear and do not require any
external power equipment.
Peizo-resistive accelerometers
Piezo-resistive accelerometers use material of the same name, which basically consist in strain gauges. The
acceleration applied deforms the gauges which changes the resistance. That change in electric resistance is
monitored to measure the acceleration felt.
The following table summarises the characteristics of the several devices to be used.
Table 2.3 - Qualitative representation of the accelerometer's features [24].
Potentiometric Capacitive Piezoelectric Piezo-resistive
Dynamic
range Average Average
Extremely
wide
Extremely
wide
Response DC DC AC DC
frequency
range Limited Average Wide Wide
Low
frequency
cut-off
~0 ~0 ~0 ~0
Noise level Low Low Very low Low
Sensitivity High High High High
Price Low Low Very High
(>1k€) High
Size Average Small Small Small
Based on the objectives of the project it is possible to identify some desirable and important characteristics of the
accelerometers. They should have a satisfactory dynamic range as well as frequency range, low frequency cut-
off, low noise level, effective sensitivity and small size. Furthermore, the accelerometers must be replaced in
easily replaceable in case of malfunction.
From the characteristics shown on the table 2.3, one can easily conclude that all the accelerometers have
capabilities for the tests intended. However, piezoelectric and piezo-resistive are over expensive for the
experiment, hence the most adequate accelerometers are the potentiometric and capacitive.
21
In conclusion, the capacitive accelerometers (figure 2.7) were the ones chosen after applying a cost-benefit
analysis. However, further testing should to be done in order to assess if these accelerometers produce, in fact,
results close enough to the piezoelectric ones in this testing environment (accelerometers testing section 2.6.6).
Figure 2.7 - Capacitive accelerometer mounted beneath the rail.
2.5.2. Strain gauge configuration
A wire strain gauge can effectively measure strain in only one direction, however, to determine the three
independent components of a strain surface (strain in two dimensions X and Y and rotational strain), three
linearly independent strain measures are needed, i.e., three strain gages positioned in a rosette-shaped layout.
Consider a strain rosette attached onto a surface with an angle from the x-axis. The rosette itself contains three
strain gages with the internal angles β and γ, as illustrated on the figure 2.8:
If one suppose that the strain measured from the strain gauges represented above are Ԑ1, Ԑ2 and Ԑ3, respectively, a
coordinate transformation equation can then be used to convert the longitudinal strain from each strain gauge
into strains in both X and Y Cartesian coordinates.
Ԑ1
Ԑ2
Ԑ3
Figure 2.8 - Strain gauge rosette
22
Applying to each of the three strain gauges, the following system of equations [26] is obtained:
{
Ԑ1 =
Ԑ𝑥 + Ԑ𝑦
2+Ԑ𝑥 − Ԑ𝑦
2cos(2𝛼) + Ԑ𝑥𝑦sin (2𝛼)
Ԑ2 =Ԑ𝑥 + Ԑ𝑦
2+Ԑ𝑥 − Ԑ𝑦
2cos(2(𝛼 + 𝛽)) + Ԑ𝑥𝑦sin (2(𝛼 + 𝛽))
Ԑ3 =Ԑ𝑥 + Ԑ𝑦
2+Ԑ𝑥 − Ԑ𝑦
2cos(2(𝛼 + 𝛽 + 𝛾)) + Ԑ𝑥𝑦sin (2(𝛼 + 𝛽 + 𝛾))
(2.13)
Rearranging the equations for simplicity:
{
Ԑ1 = Ԑ𝑥𝑐𝑜𝑠2(𝜃1) + Ԑ𝑥𝑠𝑖𝑛
2(𝜃1) + 𝛾𝑥𝑦 sin(𝜃1) cos (𝜃1)
Ԑ2 = Ԑ𝑥𝑐𝑜𝑠2(𝜃2) + Ԑ𝑥𝑠𝑖𝑛
2(𝜃2) + 𝛾𝑥𝑦 sin(𝜃2) cos (𝜃2)
Ԑ3 = Ԑ𝑥𝑐𝑜𝑠2(𝜃3) + Ԑ𝑥𝑠𝑖𝑛
2(𝜃3) + 𝛾𝑥𝑦 sin(𝜃3) cos (𝜃3)
(2.14)
Also notice that:
𝛾𝑥𝑦 = 𝑝𝑙𝑎𝑛𝑒 𝑑𝑖𝑠𝑡𝑜𝑟𝑠𝑖𝑜𝑛 = Ԑ𝑥𝑦+Ԑ𝑦𝑥 = 2Ԑ𝑥𝑦 (2.15)
And that:
𝜃1 = 𝛼, 𝜃2 = 𝛼 + 𝛽, 𝜃3 = 𝛼 + 𝛽 + 𝛾 (2.16)
With the three equations above it is possible to solve the three unknown variables, Ԑx, Ԑy and Ԑxy.
The formulae shown above are the general equations for rosette strain gauge transform, however, in this work,
the specific angles used between the strain gauges were θ1=-90o, θ2=+30
o and θ3 =+150
o for the first, vertical
rosette strain gage and, once more, θ4=-90o, θ5=+150
o and θ6=+30
o for the horizontal strain gage system.
This means that the rosette chosen to collect the data was a delta rosette, which means the rosette has an angular
distance between individual strain gauges of 120º. The reason to choose this type of rosette was to reduce errors
to a minimum.
These two structures are illustrated by the figures 2.9 and 2.10 below:
3 2
1
Z
X
Figure 2.9 - Vertical rail rosette reference frames (as seen from the side of the rail).
23
The following solutions were obtained from solving the equations with the angles used (first, second and third
equations belong to the vertical rosette and fourth, fifth and sixth solve the horizontal rosette):
{
Ԑ𝑥 =
−(Ԑ1 − 2(Ԑ2 + Ԑ3))
3Ԑ𝑧 = Ԑ1
𝛾𝑥𝑧 =2 − (Ԑ2 − Ԑ3)√3
3
(2.17)
{
Ԑ𝑥 =
−(Ԑ4 − 2(Ԑ5 + Ԑ6))
3Ԑ𝑦 = Ԑ4
𝛾𝑥𝑦 =2 − (Ԑ5 − Ԑ6)√3
3
(2.18)
Two different strain gauge arrangements, one vertical and another horizontal, are needed in order to assess the
strain on both axis and rotation on the two different planes. This will enable to measure the strain, and therefore,
the vibrations on all of the three-dimensional axis.
2.5.3. Data acquisition systems
Arduino board
The process of conditioning and gathering allows for the correct translation of all that data. Hence, the correct
measurement of any result relies, on both the sensor that acquired it and the collecting board which receives and
interprets the signal, turning it into an understandable result.
The choice landed on the Arduino UNO acquisition board, which is visible in figure 2.11. The Arduino UNO
board is capable of I2C. The Advantage of this acquisition board is the fact that both the hardware and software
required to work with it are totally open source, giving the user all the freedom to alter the board for its specific
purposes. Furthermore, the Arduino is actually the adequate choice in terms of benchmarking, thus fitting
perfectly the purpose of this work.
4
6 5
Y
X
Figure 2.10 - Horizontal rail rosette reference frames (as seen from the bottom side of the rail).
24
Figure 2.11 - Arduino UNO board.
Although the Arduino board works perfectly while receiving analogical impulses from the accelerometers, the
same cannot be said of the strain gauges. The boundary of the strain gauges is especially sensitive due to the
need to transmitting a stress into the Wheatstone bridge and due to its capability to work within the order of the
µV.
Strain gauge acquisition board
In order to correctly read the results from the strain gauges a compatible board was required. The Arduino board
was not equationated, even though that was actually possible but the board had some limitations strain gauges -
reading wise.
The board chosen was one made specifically for strain gauges reading.
This board is from National Instruments which uses acquisition software Labview alongside with a strain gauge
input module which technical specifications.
Technical specifications:
8 simultaneously sampled analog input channels; quarter-, half-, and full-bridge completion;
Programmable excitation (0 to 10 V) per channel;
Programmable gain (1 to 1000) per channel;
Programmable 4-pole Butterworth filter (10 Hz, 100 Hz, 1 kHz, 10 kHz) per channel;
NI-DAQmx measurement services software to simplify configuration and measurements.
2.5.4. Other experimental equipment
Among the above mentioned items, there were other relevant devices and objects used in the instrumentation of
the model. All of these items were chosen due to their ease of access and capacity to withstand harsh conditions,
like the ones occurring during the several tests.
25
Battery specifications
The battery used was a 12V lead acid battery with 30A.h
Fuses
The fuse used, along with its support (shown in images 2.12 and 2.13 respectively) had the capacity to withstand
10A of current and its objective was to protect the accelerometers by disabling the flow of current in case of
excessive discharge, since there is nothing else controlling the discharge from the battery.
Figure 2.12 - 10A fuse [27].
Figure 2.13 - Fuse suport and electric attachment [28].
Switches
Alongside with the LEDs and the electric resistances there were also switches installed, one for each Arduino
board. These switches (like the one shown on figure 2.17) were used to start and stop the recording of
accelerometer data.
Figure 2.14 - Electric switch [29].
26
2.6. Analyse the capacitive accelerometers
As it was previously stated, it is important to know if the capacitive accelerometers offer results close enough to
the results which would be given by the, more expensive and precise piezoelectric accelerometers, for them to be
reliable.
The constraint-free vibration was the test chosen to assess the overall reliability and data collecting error of the
accelerometers due to its effectiveness. This type of test helps to make sure that the accelerometers (as a whole)
are able to collect enough accurate data to assess all the initial modes of vibration of a plate (a railway track part
in this case).
2.6.1. Objective
The aim of this test (in order to assess the quality of results given by the accelerometers) is to compare all the
results with the ones obtained previously with the other more expensive and more accurate accelerometers as
well as with the ones obtained through the ANSYS physics simulation program.
The results collected consist of the frequency of all the first 20 vibration modes. If the frequency modes
calculated using the to-be-tested accelerometers match those from both the piezoelectric accelerometers and the
ANSYS program, than the accelerometers can be considered as useful and reliable.
In order to read all the data from the accelerometers and convert it from a time-amplitude frame into a
frequency-amplitude (FFT) display, a program called sigview was used [31].
Another objective, besides the evaluation of the accelerometers is to better understanding of the behaviour of the
railway track material.
2.6.2. Experimental setup and data acquisition for the vibrational test
In the experimental setup a railway track part miniature was used. This part, while in usage, rests upon rigid
ground, hence the soil-railway interaction can be considered to have a negligible effect.
In order to realize this modal analysis the structure must be constraint-free, without clamps in any of the ends.
This free vibration method relies on the usage of a special hammer to stimulate the structure to oscillate, which
would enable the accelerometers to read the vibrations.
Photos of the named method are presented in the figure 2.18. This image contains the overall arrangement of the
equipment.
27
The free vibration method was chosen due to the difficulty of replicate the effect of a perfectly tied constraint on
an experimental setup (like the ones ANSYS simulate).
Therefore, the chosen object to input force and energy into the system was the hammer for all tests made.
As can be seen in figure 2.16, one should avoid to place the accelerometers right on top of the vibration modes
nodes. Nodes are the points which have a deformation close to zero. Those points should be avoided in order to
enable a clear detection of all the natural frequencies once the readings are combined.
On ANSYS the whole railway was modelled using beam elements, namely BEAM188. This element suits
moderately thin beams. These beams are based on Timoshenko’s Beam Theory, which accounts for shear
deformations.
The structure of the miniature railway is composed by two different materials, the sleepers were made from
some sort of ABS (acrylonitrile butadiene styrene) thermoplastic (in the real scale railways they are actually
made of wood) and the two parallel rails are made out of an aluminium alloy (on a real railway those are actually
made of steel). The aluminium alloy 6061-T6 was the alloy considered since it is one of the most used alloys.
The dimensions of all the parts can be seen in the images of the section 7.4. of the annex.
B) B)
A)
A) Accelerometer’s positions.
B) Rope grabbing two of the sleepers.
Figure 2.15 - Railway vibration mode test layout.
28
The material properties are presented on table 2.4:
Table 2.4 - Material properties of the rails and the sleepers.
Material Aluminium alloy 6061-T6 [30]
[31]
ABS thermoplastic material
[32] [33]
Density [kg/m3] 2710 1060
Young’s Modulus 70 2.5
Poisson’s Coefficient 0.35 0.41
On the ANSYS simulation the connections between the sleepers and the rails are considered as totally rigid
although this is not the case on the real object. Those points dissipate energy and increase friction by wobbling
around therefore changing the direction of the deformation/vibration.
29
2.6.3. Comparison between accelerometer results and ANSYS simulation
The procedure followed while using SIGVIEW is described in figure 2.17:
Figure 2.16 - Vibration modes assesment scheme
Raw data on a
Amplitude Vs
time plane
Application of the
Laplace transform
by the software
Assessment of
potential modes of
vibration
Data in amplitude
Vs frequency
This translates the data from the
amplitude Vs time frame to a
frequency Vs time one.
30
Once all the frequencies were collapsed from a time to a frequency plane, it is possible to evaluate what
frequencies are relevant. These relevant points (viewed as spikes in amplitude on sigview’s graph chart)
correspond to frequencies that stir up a greater amplitude of movement and deformation on the plate tested (a
railway track in this case), therefore being the ones responsible for causing a vibrational mode.
After this procedure, the only thing left to do was to compare the results coming from the ANSYS program with
the frequency collected “manually” through the sigview program (table 2.5).
Table 2.5 - ANSYS Vs experimental vibration modes.
Vibrational
mode
number
Vibrational
modes
(ANSYS)
[Hz]
Experimental
vibrational
modes [Hz]
Absolute
error
between
the
methods
[Hz]
Relative
error
between the
two methods
[%]
Standard
deviation
[Hz]
Number
of
readings
- 1.831 - - - 9
1st 8.507 8.522 0.014 0.169 0.385 20
2nd
9.460 9.387 0.073 0.768 0.355 35
3rd
19.222 19.437 0.214 1.116 0.714 22
4th
26.075 25.794 0.282 1.081 1.115 24
5th
34.968 34.348 0.620 1.774 1.438 21
6th
44.628 44.312 0.316 0.707 0.000 2
7th
51.027 50.859 0.168 0.329 1.923 30
8th
57.615 58.009 0.394 0.683 2.122 15
9th
65.361 68.360 2.999 4.588 4.143 2
10th
84.042 81.421 2.621 3.118 0.180 17
11th
87.566 86.678 0.887 1.014 1.127 17
12th
92.538 92.589 0.051 0.055 1.257 12
13th
113. 821 115.113 1.292 1.135 0.365 3
14th
123.773 120.651 3.122 2.522 0.749 12
15th
124.534 125.283 0.749 0.601 3.121 19
16th
140.989 136.170 4.819 3.418 1.842 4
17th
155.150 151.636 3.514 2.265 2.052 5
18th
170.002 164.866 5.136 3.021 0.365 7
19th
171.398 174.090 2.692 1.571 1.475 11
20th
180.353 179.230 1.123 0.623 0.752 4
21st 183.446 185.420 1.974 1.076 N/A 1
22nd
200.778 200.920 0.142 0.071 3.249 8
31
As it can be deduced from table 2.5, the error between the two readings is minor which confirms that the
methodology explained in figure 2.17 was worthwhile. The maximum error observed was about 4.6%, which,
although high when compared to the other errors detected, it is quite small when considering the fact that it
corresponded only to the 9th
vibrational mode which only had a frequency of about 65.4 Hz, thus only having an
absolute error of 3Hz. Furthermore, the fact that could only be spotted a single amplitude spike close to said
frequency twice, also contributes to increase the probability of reading error. That is supported by the fact that
the standard deviation is high (blue marked), and also due to the same problem, lack of readings.
Although all the readings seem correct, adjusting perfectly to the vibrational modes coming from ANSYS’s
simulation, there were 9 readings that could not be matched up with any of the frequencies. These readings are
shown on the table 2.5 and correspond to a frequency of about 1.8 Hz.
It turns out that this frequency was probably caused by the way the experiment was conducted:
A special short and precise hammer was used in order to stimulate energetically the system (the hanged railway
track), enabling it to vibrate. This method works well as far as making the railway vibrate goes, but, as this
method applies a force to the testing object, and since the railway is not blocked in any direction, a small
remnant frequency is identified. The force applied by the hammer causes the entire railway to oscillate very
slowly and steadily, therefore creating the illusion of another vibration mode corresponding to a frequency of
only 1.8 Hz.
The observed errors are nevertheless originated from the way the real experiment is conducted in comparison to
how ANSYS simulates the problem.
On ANSYS the railway track is considered has perfect, without any flaw in the homogeneity of its building
material (aluminium and ABS). Moreover, ANSYS assumes the material to be without any type of constraints.
This would not be possible to achieve thus the experimental errors must come from (most significant cause to the
least, all of them are able to change the read vibrational modes) one of the following:
Two cables (seen on figure 2.15) were used to sustain the railway track’s weight hence creating more
friction in a kind of minor semi-constraint; this could dissipate energy and slightly change the direction
of vibration;
Figure 2.17 - Thread suspending the rail.
32
The material, either that being aluminium or ABS, is not totally homogeneous, therefore changing the
centre of mass and hence the direction of the vibrations;
The reading error of the accelerometers;
The existence of gravity on the real experiment whereas there’s none in the ANSYS constraint free
vibration analysis. Even given the fact that the railway had its side oriented with the vertical axis (as can
be seen in figure 2.16), reducing the impact of gravity, some rotation modes may be slightly affected;
The fact that the real experiment cannot be conducted in vacuum provoking loss of energy/alteration of
vibration through air friction.
The average error between the two methods is about 1.5%, which can be considered as very low.
2.6.4. Vibration modes
The figures 7.1-7.11 represent all of the vibration modes obtained through the ANSYS’s simulation from the
first to the twentieth second vibration mode (all of the modes belonging to the range of frequencies below
200Hz). The frequency limit of 200Hz since the reading speed was of 1 kHz.
The figures of all of the deformation generated by the vibration modes on the railway track part are shown on the
appendices and annexes.
As shown in the annexes, the 1st, 3
rd, 5
th, 8
th, 11
th, 14
th, 18
th suffer pure torsion while the 2
nd, 4
th, 6
th, 7
th, 10
th, 15
th
and 19th
modes of vibration appear to suffer pure flexion. Usually the first mode of vibration is bending for a one
dimensional plate (a line), however, in this case the object is a plate-like body, therefore it can suffer from
torsion and due to the short width (comparatively to its length) the first vibration mode is actually a torsional one
instead a flexional one.
2.6.5. Accelerometer results and comparison
While still using the capacitive accelerometers, which correspond to the results posted in the table 2.6 but this
time with those results being compared not with results from ANSYS program, but more importantly, with the
results from the piezoelectric accelerometers.
The same methodology of section 2.6.3 was used here: the results from the transferred frequencies obtained on
SIGVIEW are directly compared with results acquired from other previous thorough testing done with the help
of the more accurate accelerometers named before.
The table 2.6 shows all the compared modes of vibration and all the statistically important data to evaluate how
accurate the accelerometers used throughout all of the testing really are.
33
Table 2.6 - Experimental vibration modes measured with capacitive accelerometers Vs piezolelectric accelerometers.
Vibrational
mode
number
Piezoelectric
accelerometers
[Hz]
Vibrational
modes –
Capacitive
accelerometers
[Hz]
Absolute
error
methods
compared
[Hz]
Relative
error
methods
compared
[%]
Standard
deviation
[Hz]
Number
of
readings
1.83 9
1st 8.25 8.52 0.27 3.29 0.38 20
2nd
9.50 9.39 0.11 1.19 0.35 35
3rd
19.50 19.44 0.06 0.33 0.71 22
4th
26.25 25.79 0.46 1.74 1.11 24
5th
35.38 34.35 1.03 2.90 1.44 21
6th
44.31 0.00 2
7th
51.38 50.86 0.52 1.01 1.92 30
8th
58.38 58.01 0.37 0.63 2.12 15
9th
68.36 4.14 2
10th
81.42 0.18 17
11th
84.75 86.68 1.93 2.27 1.13 17
12th
89.75 92.59 2.84 3.16 1.26 12
13th
115.11 0.37 3
14th
120.65 0.75 12
15th
125.88 125.28 0.59 0.47 3.12 19
16th
136.17 1.84 4
17th
151.64 2.05 5
18th
164.87 0.36 7
19th
17.623 174.09 1.47 0.85 1.48 11
20th
179.23 0.75 4
21st 184.50 185.42 0.92 0.50 N/A 1
22nd
200.92 3.25 8
As the comparison above table shows, the margin difference detected between both methodologies is minimal.
This confirms that the usage of capacitive accelerometers will suffice, which is also restated by the table of
comparisons 2.6.
There were several occurrences that should be noted:
Nine readings did not comply with all the other modes of vibration (this was already explained in chap.
2.6.3).
34
The fact that the 15th
mode of vibration presents very low error and was detected in most of the readings
and still has a moderately high standard deviation. This was probably just a statistical coincidence but,
more importantly, the natural frequency matching that vibration mode seems to be correct.
The maximum relative error observed this time was about 3.3% (blue marked). This error can actually
be considered very small, in fact it is even smaller if taken into account the fact that it belongs to the
first mode of vibration, thus corresponding to an absolute error of only 0.27Hz, which is basically
unsound.
There is an absence of several modes of vibration within the column of the high quality accelerometers.
This has to do with the fact that there not enough measurements were made at the time in order to
capture all possible vibration modes. This happens mainly due to 3 reasons:
a) there are several vibration modes that situate themselves too close to one another on the
frequency bandwidth thus one may identify only one of them;
b) Some vibration modes have a much higher spike of amplitude than others making them
almost invisible;
c) Depending on the points chosen the input force and acceleration revealed some modes of
vibration can be undetectable (due to the matching of the nodes location with the points of
acceleration detection).
This time around most of the errors detected are originating from the next causes (from least to most relevant):
Small differences on the position of the strings holding the railway track as well as the spot where the
hammer stimulates the railway. These should be more or less in the same place from one test to the
other but it is impossible to hit the railway exactly in the same spot.
Since the error difference is almost the same as it was in the previous test (the comparison with the
ANSYS results) it is more likely that the errors are induced by the only term constant on these
comparisons: the apparatus.
Either way, the total average relative error is about 1.5% which makes it equal to the error calculated when
making comparisons with the ANSYS’ results. This is a very low error thus confirming that the regular
accelerometers can be used without any problems .The data collecting equipment was therefore tested with
success. Finally, all of these data also mean that the modes of vibration of the railway .
35
Table 2.7 - Railway track part vibration modes.
Vibrational mode number Experimental vibrational
modes [Hz]
1st 8.52
2nd
9.39
3rd
19.44
4th
25.79
5th
34.35
6th
44.31
7th
50.86
8th
58.01
9th
68.36
10th
81.42
11th
86.68
12th
92.59
13th
115.11
14th
120.65
15th
125.28
16th
136.17
17th
151.64
18th
164.87
19th
174.09
20th
179.23
21st 185.42
22nd
200.92
As can be inferred from the results, the general average relative error that the accelerometers have correspond to
1.5% with a maximum error (of the accelerometers actually used) of 0.1G if only one accelerometer is
considered on its most erroneous axis. This magnitude of error is entirely acceptable.
All of this testing needed to be done in order to:
Prove that the accelerometers are on proper working conditions;
Making sure that the data is reliable;
Show that the errors are constant (and do not increase with the increase of acceleration);
Confirm that the data collecting speed is high enough (>1 kHz).
36
2.7. Data acquisition and convertion
2.7.1. Acquisition scheme
The flowchart and explanation is intended to show how the flow of information worked (figure 2.20), until the
actual data treatment.
The entire process was straightforward and enabled the acquisition of data in a fast (around 1 kHz [34]) and
reliable way, without the use of complex linkage between the carriage and the computer.
Figure 2.18 - Data collecting diagram.
a) All starts at the accelerometers, which detect any change of the vehicle acceleration. These magnitudes
of acceleration are sent into the Arduino board when the power is switched ON.
b) When the power source of the Arduino board is switched ON the script in the microprocessor starts
running, thus receiving data from the accelerometers and starting the timer. This information is
transferred into the SD card support board.
c) A micro SD card board was also added to the data acquisition board, in order to be able to store the data
into the actual SD card.
The SD card enables the running of tests and the saving of data without the need for cables between the
vehicle of the PC and/or the usage of a PC on top of the vehicle.
All this data written in the SD card is saved in hexadecimal code to save processing time and therefore
increase the sampling rate (up to about 1000Hz).
d) After a testing series, all the files written inside the SD card are transferred to a PC.
The program inside the microcontroller organizes the data in a specific way, so that the files inside the
SD card are easily read.
The HEX editor software enables the visualization of the entire raw data (including the terminology)
making it possible to immediately identify if the file has become corrupted during the process of testing,
or not, before running it in matlab.
c) SD card
board/card
d) convertion
in Matlab
b) Arduino Board
e) Data treating
a) Accelerometers
End of a testing series
37
e) The next step is to use a matlab script to read and convert all the test files from hexadecimal to decimal.
This step only occurs successfully if the file is correctly structured.
f) and g) After the conversion has been successfully done, the data will be reconverted to the relevant SI
units (m/s2) and used on SIGVIEW to correlate results and test the overall reliability of the equipment.
2.7.2. Data acquisition software and programming
As was mentioned in the section above, the data from the accelerometers had to be read, stored, converted and
treated and, in order to successfully achieve this, it was necessary to elaborate a couple of programs on two
different programming languages.
It can be described as a two-step process, with the first step being the reading and storing of the accelerometer’s
data and the second step being the conversion and treating of that information.
This first program was written in C++ programming language to control the Arduino reading board as well as the
writing of that same data into the micro SD card. This language was chosen because it was the more user-
friendly programming language effectively used on Arduino programming, the other programming languge used
on Arduino being Assembly.
38
Next follows the fluxogram of the program mentioned (figure 2.21) to help understanding the several stages of
the script:
Start
-Define Arduino board�s pins.
-Define variables.
Is the button on
?
YES
-Start the SD card.-Start timer.-Serial port
communication.
Any occuring problems (card, directory, etc.)?
YES
Display error
message
NO
Read raw acceleration measurements from the
devices.
Write the obtained
values
Is the button turned off ?
YES
Close micro SD card
NO
NO
Figure 2.19 - Convertion program fluxogram.
Another important step in the process was the translation of data from hexadecimal to decimal code, as well as
the conversion from normal decimal code to actual significant SI units. This was done by producing another
program, this time around done on Matlab programming language. This language was chosen to do the second
step due to the fact that it is not related to the Arduino and this step is done by the PC and not by an Arduino
board and, simultaneously, due to the fact that Matlab is an extremely easy programming language, making it
39
very effective to work with. The fluxogram of the program mentioned is shown below as a way to summarize
and explain its functioning (next page, figure 2.22):
Start
Set variables:Nr. Of bytes/line
Nr. Of parameters/line-Open raw data
file
Any occuring errors with the
file ?YES
-Quantify file data.
-Store it in a matrix.
Is the doc finished ?
YES
Display - data
reading is finished
Copy data to the matrix
And increment it
Display - starting data conversion
-Create a matriz to deposit the converted data
-Convert all the data from hex to dec
File opened correctly ?
YES
Display –�The TXT file is opened and ready for writing
NO Display –�It was not
possible to open the file
Is the file over yet ?NO
Keep writing the matrix of data in the
txt file
Add to the data file the info retrieved
before:-Access nr.
-Session duration.-Writing time.
-Sample nr.
Close file
Display –�End of file
writing
Stop
Display error
messageNO
YES
NO
Is the reading digit combination correct?
YES
Conveting from binary to decimal:
-Nr of accesses.-Session time.-Writing time.
Close raw data file
NO
Display error
message
Figure 2.20 - Arduino reading program fluxogram.
40
2.8. Damping assumptions and formulae
2.8.1. Damping assumptions
Further calculations were conducted in order to know more accurately (or as accurately as possible) what the
acceleration reduction percentage is, and to know better all the other parameters related with the spring vibration.
However, first, some assumptions must be stated in order to simplify the calculations to be performed:
a) The entire system can be approximated to a mass-spring-damper dynamic system.
b) The force transmitted at the time of the first impulse is significantly higher than the next transmitted
forces, for an interval of, at least, a quarter of a second.
c) For the small displacements observed, the spring considered always remains in the linear deformation
range.
d) Both sides of the vehicle receive similar impulses at the same time.
e) All the results shown are an average, which means that in some specific tests the values may have
varied.
2.8.2. Damping formulae
The equations related to an oscillatory motion are presented next:
𝑑2𝑧(𝑡)
𝑑𝑡2+ 2𝜉𝜔𝑛
𝑑𝑧(𝑡)
𝑑𝑡+ 𝜔𝑛
2𝑧(𝑡) = 0 (2.19)
𝑚𝑑2𝑧(𝑡)
𝑑𝑡2+ 2𝑚𝜉𝜔𝑛
𝑑𝑧(𝑡)
𝑑𝑡+ 𝑚𝜔𝑛
2𝑧(𝑡) = 0 (2.20)
This implies that:
𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = 𝑐 = 2𝑚𝜉𝜔𝑛 (2.21)
𝑆𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝑘 = 𝑚𝜔𝑛2 (2.22)
𝛿 = 𝑙𝑜𝑔𝑎𝑟𝑖𝑡ℎ𝑚𝑖𝑐 𝑑𝑒𝑐𝑟𝑒𝑚𝑒𝑛𝑡 =1
𝑛ln (
𝑧(𝑡)
𝑧(𝑡 + 𝑛𝑇)) (2.23)
Using equations 2.17 and 2.21-25 this results in:
𝜉 = 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜 =
𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑎𝑚𝑝𝑖𝑛𝑔
𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑑𝑎𝑚𝑝𝑖𝑛𝑔=𝑐
𝑐𝑐=
𝑐
2√𝑚𝑘
𝑜𝑟 𝑐𝑐 = 2𝑚𝜔𝑛
(2.24)
𝜉 =
𝛿
√(2𝜋)2 + 𝛿2=
1
√1 + (2𝜋𝛿)2
(2.25)
𝜔𝑑 = 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑑𝑎𝑚𝑝𝑒𝑑 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =2𝜋
𝑇 (2.26)
And using equations 2.17, 2.26 and 2.28 this results in:
41
𝜔𝑛 = 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =𝜔𝑑
√1 − 𝜉2 (2.27)
Finally, the relation between the damping ratio and the acceleration, instead of the displacement, is shown as
follows:
𝑓 =1
𝑇 (2.28)
𝜔 =2𝜋
𝑇= 2𝜋𝑓 (2.29)
𝜉 =1
𝜔𝑇ln (
𝑎(𝑡1)
𝑎(𝑡1 + 𝑇)) =
1
2𝜋ln (
𝑎(𝑡1)
𝑎(𝑡1 + 𝑇)) (2.30)
The equation shown above is quite useful to compare the final results obtained from the integrated displacement
function, in order to assess what the magnitude of error is.
In the last chapter, some relevant features of railway vehicle safety and comfort were summarily described, as
well as their respective standards. This also included some mathematical formulae in order to compare and
understand the behaviour of the model and these types of vehicles. Next chapter will show and explain the
instrumentation of the train prototype.
42
3. Rail/Bogie instrumentation
This chapter contains a brief description of some relevant features of the instrumentation done to the prototype.
This will also include the accelerometer positioning and the explanation of some of the tests done to the
prototype.
3.1. Accelerometer positioning
The first layout shown is the overall arrangement of the bogie with all the parts and measure instruments (figure
3.1).
Figure 3.1 - Overall layout of the carriage.
Figures 3.2, 3.3, and 3.4 show the positioning of all the accelerometers as well as the direction of each of their
axis.
z
x
y
The reference frame on
the left shows which color
belongs to which axis.
On the right is shown a
magnification of the
accelerometer’s�position.
1 7
4
8
3
5
Figure 3.2 - Accelerometer positions.
43
Neither of the two bogies had much space available to place all the required accelerometers, hence, it would be
difficult, nearly impossible, to have all of them facing the same direction on all of their axis. Thus, the only thing
that was possible to do was to try to maintain their x reference frame in the same axis for all the accelerometers.
The number identifying each of the accelerometers is also displayed alongside the coloured reference frames.
The discontinuity on the accelerometer’s identification numbers was due to the failure of accelerometers 6 and 2,
which were replaced by accelerometers 7 and 8 respectively.
The missing 9th
accelerometer was never used, as was previously explained, there was no need for it.
3.2. Instrumentation
In order to make way to an easier vibration assessment and analysis, an instrumentation of the rail was required.
Therefore the research aims to develop some system that could perform the following activities/objectives:
Feed the acquisition system on top of the bogie (the Arduino board placed beneath the railway did not
require feeding, since it was connected to the PC);
The maximum voltage an accelerometer can withstand (while fed with DC) is much lower than an
Arduino board thus the Arduino boards were fed with a voltage of 12V (DC), and they, consequently,
fed the accelerometers with 3.3V of voltage (also DC);
In order to indeed feed the accelerometers remotely the following lead acid battery of 12V was used;
Figure 3.3 - Accelerometers' positions (top view).
Figure 3.4 - Accelerometers' positions (side view).
44
All the equipment needed to be secured in place while the bogie was being used, moving across the
railway. Duct tape was used to fasten all the moving objects (cables mostly);
The accelerometers had to be firmly clutched to the carriage/railway part where they were to be, in
order to obtain the most reliable results possible, eliminating the errors coming from accelerometer
movement instead of vehicle movement;
A type of cyanoacrylate was used to firmly tie the accelerometers’ base to the metallic material;
The condition above had to be satisfied while still having space in the accelerometer’s encircling to
attach both the power and data cable;
While the accelerometers were reading the vibrations, these readings had to be saved somewhere inside
the carriage (using some kind of memory card for instance), enabling its reading to read them later on;
The model weight, after adding the needed components should be reasonable;
The accelerometers had to be strategically placed and directionally oriented in order to receive the right
vibration on the correct axis;
The accelerometers’ positioning is described on section 3.1.
The possibility of having all the accelerometers starting collecting data at the same time made data
analysing and comparing easier. Thus there was a need to add some kind of switch that could control
(start and stop recording information) all the accelerometers at the time. This problem was solved by
using a two stage switch which worked flawlessly.
All electronic components had to be isolated from metallic parts to avoid errors and they had to be
wedged firmly to the carriage/bogie (figure 3.5).
a) Data cable linked to the Arduino board end;
b) Micro SD card. Device where all the data about the acceleration variation is stored;
c) Three stage switch, although only the upper and bottom stages are used, meaning switched on (start
collecting and saving data) and switched off (stop saving data);
d) Cardboard used to isolate the base of the Arduino board from the metallic parts of the vehicle.
a)
b)
c)
d)
Figure 3.5 - Arduino board.
45
3.3. Testing order and objective
After assembling all the needed elements to achieve clear, multiple and flawless readings, several tests were
performed in order to assess the vibrations.
3.3.1. List of tests with their explanation:
The first tests, tests 0 to 3 were made using only the weight of the vehicle without any payload while the tests 4
to 7 were made with extra weight. This would eventually enable to assess the differences in the acceleration felt
between the two cases allowing for some more comparisons.
The light version tests were made with a total load of about 40 Kgs (basically the weight of the bogie metallic
parts). The heavier version of the testing was made with an additional 22-23Kgs of weight. This extra weight
was to account for the percentage of extra weight (+50%) that a train has to carry. This would include all the
people that could board the train plus all of the carriage itself (with the seats, fuel, roof etc.). This could be
considered as the designed mass of the vehicle in working order plus the normal designed payload.
Table summing up all the testing
The table below will sum up the major lines of each test:
Table 3.1 - Test summing table.
No payload
Test nr. Characteristics Objective
0 v = 0 and a = 0. Assess if all the equipment is working
properly.
1
Decelerating movement.
From the non-instrumented rail (rail
1) to the instrumented one (rail 2).
Assess the vibrations (mostly vertical)
felt by rail and model.
Assess the accelerations felt by the rail
(vertical) and the model (vertical and
horizontal, mostly).
2 Accelerating movement.
From rail 2 to rail 1.
Assess the vertical vibrations felt on the
track while accelerating.
Evaluate the accelerations felt both in
the track and model while the vehicle
accelerates.
3 Braking by stopping the wheels.
From rail 1 to 2.
Assess the vibrations and accelerations
felt by the track and vehicle while
braking.
Compare the results with the normal
deceleration (pushing the vehicle to
stop it).
46
Added payload (+50% the original weight)
Test nr. Characteristics Objective
4 Accelerating movement.
Added weight.
Assess the vibrations felt while
accelerating with 50% more weight.
Compare them to the normal
acceleration.
5 Decelerating movement.
Extra weight.
Assess the vibrations felt on the rail
and vehicle with the added weight.
Assess the accelerations felts on rail
and vehicle with extra weight.
Compare them with the normal weight
test.
6 Braking by stopping the wheelset.
Extra weight.
Assess the vibrations and accelerations
felt while braking both in the track and
vehicle.
Compare it with the normal braking.
Compare it with the normal vehicle
stopping.
7
Making the vehicle go from rail 1
to 2 and back from 2 to 1 several
times in the same test.
Making sure that everything keeps
working even with a longer test.
Get more results to eventually complete
any lacking information.
During this last chapter a brief explanation was given about the propose of each of the tests as well as the way
they were concluded. This also includes results about the spring-damper effects on the springs linking the bogie
and wheels, as well as the analysis of the differences between tests.
47
4. Results, tests and comparisons
This chapter presents some of the data collected while running each of the tests described, as well as the
comparisons between the several graphs presented and a complete analysis of all their characteristics along with
reasons for their similarities/differences.
Most of the data was filtered, and, that fact is referred in the underlying figure 4.1 reference.
4.1. Spring-damper effect
When the testing results were analysed, one effect that, although expected, was surprising, was the vibration of
the body of the vehicle caused by the change of rail on the railway track.
This vibrations had the characteristic configuration of a spring-damper system which could be studied more
deeply, to assess if the vibrations are uncomfortable for the passengers as well as what is the spring and damper
constants and how much energy is dissipated by the damper, among others.
Figure 4.1 – Sample of the bogie and axle acceleration variation with time during test 1 (filtered)
48
Figure 4.2 - Vehicle response to vertical vibrations.
From the figures 4.1 and 4.2, several remarkable characteristics, events and patterns can be inferred and
observed in the several charts analysed.
First of all, as can be seen in all the images corresponding to vertical acceleration Vs time graphs (for example
the two images, figures 4.1 and 4.2), there is a spring effect whenever a bump is felt on the vehicle.
This dynamic effect derives from the existence of an actual spring between the axle and the model body (shown
on the figure 4.3 below). Due to the precise information gathered with the accelerometers, all the spring’s
parameters can be calculated with accuracy.
Filtering with a low-pass
20Hz filter:
49
Figure 4.3 - Vehicle suspension.
The spring effect is only noticed in the vertical acceleration due to the existing constraint. This constraint
disables the ability of the body to move on the horizontal axis, whilst allowing it to move considerably on the
vertical axis, since its only constraint is a display of springs. The bogie structure enclosures the movement of the
upper part, therefore it has only two degrees of freedom; the vertical one and the rotation across the x-axis
which, in this case, is not noticed since the vehicle is first being tested in a straight arrangement of rails, hence,
the significant vertical vibrations are felt on both wheels at the same time. These constraints and arrangements
permit to approximate the vehicle suspension to the system described in figure 4.4 a) and b).
Figure 4.4 - Spring-mass-damper system equivalencies for vehicle suspension.
One parameter of particular importance is the damping spring parameter.
This parameter exists due to the fact that this spring is actually also intended as a damper in order to reduce the
vertical displacement felt along the time.
As in any railway vehicle, the accelerations felt on the “carriage” part of the vehicle (the upper zone) must be
reduced in relation to the ones felt on the axle itself (near the wheels of the vehicle). Thus, one sought to confirm
if that is indeed the case in the graphs presented and, in fact, when comparing the scale of the vertical
accelerations felt in the upper part of the bogie (attached to the body) with the ones felt on the axle, right next to
the wheel, it is possible to check that the acceleration felt in the upper zone of the bogie is much lower. Thus the
usefulness of the spring is proven.
≈
a) b)
50
As was explained above, due to all the existing constrains and the reduced lateral vibrations when comparing to
the vertical ones, the following assumptions can be made.
4.1.1. Damping results
It is emphasized once more that the values shown are averages, therefore, different testing may result in slightly
values. The process used to obtain the results consisted of a simple integration (figure 4.5):
Integrating 𝑑𝑧
Integrating 𝑑𝑧
Figure 4.5 – Process of integration to obtain the velocity and displacement graphs.
51
The top image of figure 4.5 is the original oscillatory acceleration detected by the accelerometers installed on the
bogie’s body.
The data from those accelerometers was integrated twice to obtain the displacement of the platform. The first
integration results, as would be expected, translate into the oscillatory behaviour of the platform’s velocity.
The problem with integration is that it accumulates errors from the primitive function, thus, as can be seen
clearly, the graph is now unbalanced; the graph has now much more negative values than positive ones, even
given the fact that the background noise was almost eliminated. In order to eliminate this problem a correction
was applied to the integration.
Finally, the last integration outcome is the function of displacement with time. The graph at the right shows this
function after some error correcting.
From the data presented in this graph it is possible to collect all the information needed to determine all the
variables of equations 2.19-2.26.
Thus, using the mentioned equations and the values from the vertical displacement data the following results
were obtained:
𝛿 = 𝑙𝑜𝑔𝑎𝑟𝑖𝑡ℎ𝑚𝑖𝑐 𝑑𝑒𝑐𝑟𝑒𝑚𝑒𝑛𝑡 =1
3ln (
𝑧(𝑡1)
𝑧(𝑡1 + 3𝑇)) = 0.586 (4.1)
𝜉 =
𝛿
√(2𝜋)2 + 𝛿2=
1
√1 + (2𝜋0.586
)2= 0.0928
(4.2)
𝜔𝑑 = 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑑𝑎𝑚𝑝𝑒𝑑 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =2𝜋
𝑇= 120.83 𝑟𝑎𝑑/𝑠 (4.3)
𝜔𝑛 = 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =𝜔𝑑
√1 − 𝜉2= 121.35𝐻𝑧 (4.4)
Finally the dynamic harmonic equation is:
𝑑2𝑧(𝑡)
𝑑𝑡2+ 22.52
𝑑𝑧(𝑡)
𝑑𝑡+ 14725.8𝑧(𝑡) = 0 (4.5)
In order to perceive the validity of the damping ratio value obtained through the vertical oscillatory
displacement, one should compare it with the same value obtained from the oscillatory acceleration.
This comparison is independent enough to conclude if the values are actually plausible or not.
Hence:
𝜉 =1
𝜔𝑇ln (
𝑎(𝑡1)
𝑎(𝑡1 + 𝑇)) = 0.1109 (4.6)
52
And since Tacceleration = Tdisplacement = 0.052s (this is not only theoretical, it is confirmed by the graphs
shown):
𝜔𝑑 = 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑑𝑎𝑚𝑝𝑒𝑑 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =2𝜋
𝑇= 120.83 𝑟𝑎𝑑/𝑠 (4.7 )
𝜔𝑛 = 121.58 𝑟𝑎𝑑/𝑠 (4.8)
Table 4.1 - Damping ratio and natural frequency.
Values obtained Damping ratio Natural frequency [rad/s]
from displacement data 0.0928 121.35
from acceleration data 0.1109 121.58
Absolut error value 0.0181 0.23
Relative error 19.5% 0.19%
From the errors determined in table 4.1 it is possible to infer that, the results are probably accurate and, therefore,
the error reduction was satisfactory.
Most importantly, all the data calculated from the values obtained from the graph were close to reality. Thus, the
most correct approximation for the damping ratio and the natural frequency is with 𝜉 = 0.1019 and 𝜔𝑛 =
121.465 𝑟𝑎𝑑/𝑠 (which corresponds to the average between the two values).
These are the values which are going to be used to estimate the damper-spring dynamic system equation:
𝑚 = 23.3 𝐾𝑔
8𝑐 = 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑒ℎ𝑖𝑐𝑙𝑒′𝑠 𝑠𝑝𝑟𝑖𝑛𝑔𝑠 = 2𝑚𝜉𝜔𝑛 = 524.7 𝑁𝑠/𝑚
8𝑘 = 𝑚𝜔𝑛2 = 343.11 𝑘𝑁/𝑚
Hence the final oscillating movement equation that describes the movement of the vehicle is:
23.3.𝑑2𝑧(𝑡)
𝑑𝑡2+ 524.7.
𝑑𝑧(𝑡)
𝑑𝑡+ 343110. 𝑧(𝑡) = 0
4.1.2. Acceleration dumping
As stated before, the springs attached to the bogie and the body floor were expected to reduce the accelerations
felt during vehicle movement on the railway track.
53
The amount of acceleration felt during vehicle operation is also an important parameter in what regards
passenger train comfort.
If this was a real size train there criteria would have to be taken into consideration.
Among these criteria, for a train of this type, the maximum acceleration felt on the body floor (acceleration
transmitted to a passenger), must be less than 2.5 m/s2 [35].
As it is understandable, the accelerations felt in this vehicle model far exceed that limit due to its diminute
inertial mass (60 kgs), when comparing with the mass of a life-size railway vehicle.
The result from the maximum passenger level (floor body) vertical acceleration felt on the vehicle model with
added weight across all of the testing was about 15 m/s2 and that the peak of vertical acceleration seems to
happen when the vehicle changes rail track.
Although the peak acceleration seems high, as was stated above, this is mostly due to the difference in mass,
furthermore the vehicle structure and spring system does an efficient job by significantly reducing the raw
acceleration coming from the track level (on the wheel-set).
To obtain an appropriate estimate of the acceleration difference between the wheel-set level and the passenger
level, the mean acceleration attenuation (measured at the spot of peak acceleration felt) throughout all of the
testing was assessed and is shown in table 4.2.
Table 4.2 - Mean acceleration attenuation.
Mean peak acceleration
Wheel-set [g] Body floor [g] Mean acceleration attenuation
2.6 0.88 66 %
4.2. Weight differences and their effects
The following topics are intended to show the comparison between some of the tests made in the different
situations and to establish patterns between measurements by different devices.
Under this topic, a lot of results are omitted due to similarities to results which are or were already described in
the work, previously.
54
4.2.1. Accelerometer results
Test 1 and 2 - deceleration and acceleration
Inside each red square there are some features to take notice, which easily stands out from the rest of the graph.
Afterwards each of those characteristics are explained in greater detail.
Figures 4.6 and 4.7 shown next, illustrate the acceleration variation along the tests
Figure 4.6 - Test 1, body floor and axle x-axis acceleration (movement direction) and body floor vertical axis acceleration
(from rail 1 to 2) - filtered.
a)
c)
b)
a) b)
d)
C
e) f)
e2) f2)
Figure 4.7 – test 2 x-axis body and axle acceleration (filtered).
55
The chosen characteristics are, as mentioned, explained below:
a) The beginning of the graph shows a negative value of the acceleration (on the x-axis) of the vehicle in
both the accelerometers placed on the wheelset and on the body. This negative acceleration felt is due to
the push given to the vehicle in order for it to move along the track;
b) The acceleration peaks during the transition undergone by the vehicle from one railway track part to the
next one which causes severe vibrations on the whole axis;
c) The high acceleration felt at the end of the track has the opposite sign of the one felt at the beginning,
and is, as expected, due to the vehicle braking;
d) This pattern is due to the vibration provoked by the spring-mass-damper system created by the
arrangement of the spring located between the wheelset of the vehicle and its body;
e) and f) Tests 1 and 2 can be considered as equal in terms of accelerometer results, but with opposite
variable signs, as can be seen in e) and f) red rectangles. This happens due to the fact that the vehicle
travels the track in different directions for each test.
Test 3 – braking by stopping wheel
Test 3 was made by actually stopping the rotation of the wheels, instead of gently pushing the vehicle back until
it stops. This increased the overall acceleration felt during the braking and also caused some acceleration spikes
(shown inside the red square), both in the wheelset and in the body of the vehicle itself. Although this is not
totally conclusive it actually makes sense because shows that the type of braking system trains have is effective.
Figures 4.8 and 4.9 show the acceleration variation with time during this test.
Figure 4.8 - test 3 x-axis body and axle acceleration (filtered).
In terms of vertical accelerations, it is very similar to what happened in previous tests.
C
C
56
Test 4 and test 5 - acceleration and deceleration with extra weight
Tests 4 and 5 results were measured exactly the same as tests 1 and 2 but with added weight. The accelerations
felt under these tests are shown in figures 4.9 and 4.10:
Figure 4.9 - Test 5 x-axis, body amd axle acceleration with extra weight (filtered).
As can be observed, in this figure there are still neat acceleration variations arising from the start-and-stopping of
the vehicle motion. However, in this case, the overall accelerations felt while pushing the vehicle into motion or
when trying to stop it, are much lower than in tests 1,2 and 3. This fact is confirmed by the graph in the red
rectangles in the figures 4.8, 4.9 and in the acceleration range at the left of the graph.
The behaviour was as expected, since the vehicle has now more weight, which, due to inertia, reduces the
acceleration felt on the vehicle when applying (approximately) the same force, by following Newton’s law F =
m.a.
The time spent while accelerating or stopping the vehicle is also greater in this test than in any other of the three
first tests (1,2 and 3) even though this greater lenght of time spent transferring energy to the system is not
enough to maintain the velocity constant, as will be explained later on.
Figure 4.10 - Body vertical acceleration with extra weight (filtered).
Another worthwhile conclusion is that the acceleration variation frequency due to the spring-damper system
movement also changed. Due to inertia of the extra body mass, the frequency of acceleration variation (red
square g) also diminished, which was also expected. This can easily be confirmed by comparing the amount of
C
C
C
C
C
g)
57
time spent in order for the spring stabilizes after changing rail on graphs (figures 4.8, 4.9, 4,10) and with the
time taken in figure 4.11.
The comparisons mentioned are valid to both the acceleration and deceleration with extra weight.
Test 6 – Braking by wheel stopping with extra weight
As shown in the other examples mentioned before, the change in mass has several effects in the acceleration.
Figure 4.11 - test 6 x-axis acceleration (filtered).
Taking graphs in figure 4.11, and comparing them with the graphs from test 3, the vehicle is shown to suffer less
acceleration but during a larger period of time. This comes in line with the other effects of an increase of the
inertia mentioned before.
Test 7 – Vehicle circling
The last test had two main objectives;
It was used to complete test information;
It was used to make sure that everything in the vehicle kept working for a long period of time, making it
possible opening up the possibility of using the devices on actual railway vehicles.
This last and more important objective was attained; the arrangement of devices kept working perfectly
throughout the entire test.
4.2.2. Strain gauge results
Another measuring device that is useful and practical, when working and testing in railways is the strain gauges.
In this case the strain gauges were installed without drilling holes inside the rails.
Usually most of the devices used require the drilling of holes in the rails, which makes the process costly, slow
and dangerous, and at the end of the testing the rails must be changed. Naturally, this method requires some
difficult-to-get approvals, in order to do the testing.
58
Thus, in the tests conducted in this work, a less intrusive approach was used, without any drilling or damaging of
the rail, which made the process quicker and inexpensive. However, one must make sure it actually works, hence
the results are going to be studied next to see if they are consistent and if any conclusions can be taken.
Tests 1 to 3 (deceleration, acceleration and braking)
The graphs presented in figures 4.12 and 4.13 show some relevant features regarding the measurement of the
deformation of the rail arising from with the passing vehicle.
Figure 4.12 - Test 1 vertical strain gauge results (Filtered).
The results from both the graphs seem to be consistent with the deformation suffered by the rail.
Figure 4.13 - Test 1 horizontal strain gauge results (filtered).
59
There are several aspects of the strain results shown in the graphs presented above:
The deformation strain is always considerably larger on the x-axis of the horizontal rosette than on the
y-axis. This was expected due to the type of deformation suffered by the rails (shown in figure 4.14
below) and by comparing it with the positioning of the strain gauges in figures 2.10 and 2.11, shown on
chapter 2.5.2;
The base of the rail stretches much more in the x-axis due to the weight of the train wheel-set;
Meanwhile, for the same reason, the upper side of the rails flange also stretches (vertical rosette).
Hence, strain gauges 2, 3, 5 and 6 are the ones detecting a lot of stretching since they are the only ones
with components on the x-axis;
The x-axis suffers a stretch and not a compression hence, by convention, the values of strain are
positive, which is coherent with the values of the graphs;
As expected, the vertical rosette is also detecting a compression on the z-axis, which is also consistent
since that strain gauge is right beneath the point of impact of the vehicle weight (the wheel-set).
Also, as shown in, for example, the red square a) of the first graph, the peaks of the graph correspond to
moments when the wheels of the vehicle are right above the strain gauges;
The unusual double spiked shape of the curve shown inside the red square a) is most probably due to
the way the rail deforms when the wheels are not right above the rosettes. The rail deforms in an odd
way because one of the wheels is already on the other side of the sleeper which pushes the rail a small
bit up while the wheel near the rosette strain gauge is still pushing it down;
Finally, there are some other odd features; for example the existence of distortion on the xy plane (the
base of the rail). At first sight this should not happen since the base of the rail is not supposed to rotate
in any way, however this phenomenon has a simple explanation. The distortion is provoked by the fact
that the rail is slightly bent horizontally and when the vehicle travels over it, it forces the rail to
straighten itself.
60
Test 4 to 6 (same tests but with added weight)
Figure 4.14 - Test 6 vertical strain gauge results (filtered).
In this case, presented in the figure 4.14 above, the strain endured by the rail during one of the several tests done
with extra weight.
The strain increased steeply from the normal vehicle weight to the extra one. This is clearly shown when
comparing the graphs recorded at the same rosette.
From the tests made it can easily be assessed what effect did the weight increase had in the strain measured,
which values are presented in table 4.3:
Table 4.3 - Railway observed strain with and without extra weight.
Von Mises equivalent strain
No added weight 50% more weight
xy (horizontal) plane
[µԐ]
xz (vertical) plane
[µԐ]
xy (horizontal) plane
[µԐ]
xz (vertical) plane
[µԐ]
89.1 68.2 111.8 82.1
Deformation increase +25.5% +20.4%
The effects of the deformations mentioned before is shown in figure 4.15 below in order to be visualize it more
easily.
61
Figure 4.15 - Railway track deformation.
4.3. Velocity results
The velocity graphs/data were obtained by integrating the acceleration data collected with the sole purpose of
assessing what velocities were achieved during the testing. Hence, to every test taken corresponds one of this
time-velocity charts. Some examples of this velocity data are presented in figures 4.16 and 4.17.
Figure 4.16 - Sample graph of the bogie's accelerometer horizontal velocity variation - test 3.
Figure 4.17 - Sample graph of the bogie's accelerometer horizontal velocity variation - test 4.
The velocity charts, although having some small errors, can be seen as quite accurate since both the axle and
bogie results show the same average velocity (which is to be expected since they are part of the same vehicle, in
the same test). Furthermore, the overall pattern of the graphs reflects the usual trend of a velocity graph: one side
with velocity increasing linearly from 0m/s, followed by a semi-stable velocity region and, afterwards, another
side with velocity decreasing linearly until the origin is reached again.
Although the top speed may vary from test to test, in these two different tests, it is safe to say that the maximum
velocity was about 1.2m/s for test 3 and 1m/s for test 4.
62
These results are consistent with the maximum kinetic energies of both systems (kinetic energy before friction
forces start to affect the system):
𝐸𝑐 =1
2𝑚(𝑣)2 (4.9)
𝑣3 = 1.21𝑚/𝑠
𝑣4 = 0.96𝑚/𝑠
𝑚3 = 40𝑘𝑔
𝑚4 = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡 + 𝑎𝑑𝑑𝑒𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 = (40𝑘𝑔 + 22.5𝑘𝑔) = 62.5𝑘𝑔
𝐸𝑐3 =1
240𝑘𝑔 (
1.21𝑚
𝑠)2
= 29.3 𝐽
𝐸𝑐4 =1
262.5𝑘𝑔 (
0.96𝑚
𝑠)2
= 28.8 𝐽
Thus, the error is of about 0.5J, which is not relevant, since it only represents 1.7% of relative error. Hence, the
integration method is capable of achieving accurate and coherent velocity results and all the results obtained are
coherent so far.
The slight slope is proportional to the friction force acting on the vehicle axle while it passes over the railway.
All this energy calculation results confirm that this simple method of evaluating vibrations and accelerations is
sufficient to measure a lot of vehicle variables with a high degree of precision and that all the instrumentation
was correctly applied.
4.4. Friction Coefficient
In this topic an attempt will be made to obtain a close estimate of the actual value of the friction coefficient of
the vehicle which basically means the friction coefficient of the overall interaction of the vehicle parts.
Using the data from the graphs shown, as well as in other similar graphs, all the needed variables to assess the
friction force were determined.
In this case, two different approaches to the calculation of the friction force were used. These two distinct ways
were meant to verify and validate each other’s correctness and accuracy. The first method was the direct force
method, and the second method was the energy method.
Second law method:
𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑎 = 𝑚𝑎 = 𝑚∆𝑣
∆𝑡= 𝑚
𝑣2 − 𝑣1
𝑡2 − 𝑡1 (4.10)
Energy method:
63
𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒 = 𝐹𝑎 = ∆𝐸𝑐
∆𝑥=
12𝑚(𝑣22 − 𝑣12)
𝑥2 − 𝑥1
(4.11)
The results obtained from the calculations are presented in the table 4.4.
Table 4.4 - Friction force results.
Friction
force 1st
method [N]
Friction
force 2nd
method [N]
Abs.
error
Relative
error [%]
Test 1
(Body)
-1.8 -1.8 0.02 0.9
Test 3
(Body)
-2.2 -2.3 0.03 1.3
Test 3
(Axle)
-2.3 -2.4 0.01 0.6
Test 4
(Body)
-2.7 -2.7 0.01 0.5
Test 4
(Axle)
-3.1 -3.3 0.19 6.3
Test 5
(Axle)
-3.7 -3.7 0.02 0.6
Test 6
(Axle)
-3.4 -3.3 0.03 0.9
Test 6
(Body)
-3.4 -3.4 0.04 1. 2
After obtaining all the values it is clear that both methods reached similar results.
The average difference between both methods was about 1.5%. Besides, the results point towards the following
conclusions:
a) The integration process was precise enough;
b) The friction force of the moving parts of the vehicle depends on the weight of the pay load that it has to
carry;
c) Small differences in vehicle speed do not seem to affect the amount of resistance arising from friction;
d) It is hard to assess the initial force responsible for stirring the vehicle into movement;
e) Same tests had similar average friction forces.
Explanation:
a) Since both values, from the two approaches, are similar, and due to the fact that the two methods are not
directly dependent it can be concluded that the direct integration and the results available are quite
realistic and reliable, even taking into consideration that integration tends to increase pre-existent
errors;
64
b) The small opposing forces previously calculated (friction forces) were caused by the contact surfaces of
several moving parts of the vehicle and also due to the energy wasted through vibration of some of the
components of the vehicle tested (e.g. cables).
This movement-opposing force was clearly in proportion to the carried weight/overall weight of the
vehicle. This is confirmed by the calculations presented below:
𝐹𝑎̅̅̅̅ = 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑑𝑑𝑒𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 = −2.04𝑁
𝐹𝑎̅̅̅̅ 𝑤 = 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒 𝑤𝑖𝑡ℎ 𝑎𝑑𝑑𝑒𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 = −3.25𝑁
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑒ℎ𝑖𝑐𝑙𝑒
𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑤𝑒𝑖𝑔ℎ𝑡 𝑤𝑖𝑡ℎ 𝑒𝑥𝑡𝑟𝑎 𝑙𝑜𝑎𝑑=
𝑤
𝑊𝑙= 0.64
𝐹𝑎̅̅̅̅
𝐹𝑎̅̅̅̅ 𝑤=2.04
3.25= 0.63
c) Due to the use of oil-like substances to lubricate places where two different components of the vehicle
have contact to each other, there usually is a non-linear increase in friction force with velocity due to
viscous forces. Nevertheless, this tends to occur only at higher speeds and/or when comparing two very
different velocities (one much higher than other).
The speed at which the vehicle goes do not seem to affect the overall resistance force felt since the
friction force increased linearly with the increase in weight, even though the velocity was lower for the
latter.
This may be because the overall velocity was not high enough, or because the velocity difference
between vehicle weight plus extra load and normal weight was not significant, or just because the
engineering and lubrication behind the vehicle was good enough to prevent such friction increase.
Since the friction force is mostly dependent on the weight of the vehicle it is safe to assume that the
overall friction coefficient of the vehicle is (following Coulomb damping rule):
𝑓𝑎 = 𝐹𝑎
𝑤. 𝑔=
2,04𝑁
40𝑘𝑔. 9.8067𝑚/𝑠2= 0.0052 (4.12)
d) Although the friction force was calculated with ease and precision, other forces are conversely difficult
to assess, namely the input force.
The input force (force that made the object start moving), as well as the braking force, are both artless
to calculate since the equations are straightforward, but due to the short periods of time in which those
forces are actually interacting with the vehicle any indirect attempt to calculate them would generate a
large amount of error.
e) Last interesting occurrence to account for is, that the calculations based on the same test (whether using
the data from the body or the axle of the vehicle) will result in very similar friction forces since the
accelerations and velocities felt are almost equal (on the x-axis).
65
4.5. Curve/derailment tests
The purpose of this topic is to show the data gathered while testing the vehicle in curve and incorporate that data
in the overall context of the standards used to evaluate the safety of a railway vehicle behaviour.
The results include tests in curve at different speeds and with manifold weights with the subsequent comparison
between these tests.
After assembling all the needed elements to achieve clear, multiple and flawless readings, several tests were
conducted in order to assess the accelerations felt in two different parts of the vehicle – On the wheelset, right on
top of the axle box and right beneath the body-frame of the vehicle, near the front bogie.
Some of the test series, 1, 2, 5 and 6 were made using only the weight of the vehicle without any extra load,
while test 3 was conducted with some extra weight, in the same way of what was done with the straight line tests
described on topic 3.3, and test 4 was done with even more extra weight. These differences open up the
possibility for some comparisons related to the lateral acceleration felt in curve.
The first test is solely the debug test, where all the instruments are tested and the accelerometer reading errors
are recorded in order to account for them later on the data processing.
Finally, the last series of tests, test series 5, is meant to test the vehicle in conditions of near derailment and test 6
was meant to assess the accelerations felt during an actual derailment. Both test series were conducted without
extra weight.
The “light” version of the tests, with same weight as in tests of topic 3.3, was done with 40.7 Kgs. The heavier
versions of the testing (test 3 and 4) had an additional weight of 55%, for a total of 63.1 Kgs and 110% more
weight, for a total of 85.5 Kgs, respectively.
The table 4.5 sum up the main aspects of each test.
Table 4.5 - Test summary table.
Vehicle movement assessment on a 7m wide curve
Test nr. Characteristics Objective
0 v = 0 and a = 0. Assess if all the equipment is working
properly.
1 Vehicle movement without any
extra load.
Assess all the accelerations felt while
moving in curve, specifically the lateral
acceleration.
Relate the results with the safety
measures and standards, when possible.
2 Vehicle movement in a curve with
extra weight.
Assess all the accelerations felt while
moving in curve.
66
55% more weight. Compare the accelerations detected
with the accelerations felt with other
different weights.
3
Vehicle movement in curve with
even more weight.
110% more added weight than in
test 1.
Assess all the accelerations generated
while moving along the curve.
Compare the results to the other two
tests done.
4 Close to derailment tests.
No added weight.
Assess all the acceleration felt along
the curve while close to derailment.
5 Derailment test. Assess the accelerations playing a role
in the derailment of the vehicle.
4.6. Curve lateral acceleration
The four accelerometers placed on the vehicle’s body floor and on the axle box of the front axle were able to
assess the accelerations on all the axis. In this section of the work the most important acceleration to be assessed
is the lateral acceleration. The figure 4.18 shown shows the variation of y-axis acceleration with time (felt in the
body floor and in the axle, respectively).
Figure 4.18 - Lateral acceleration variation with time from test in a curve (image filtered at 6Hz low-pass filter).
These images, as can be read in the description, follow the standards of data processing since they were filtered
accordingly.
4.7. Comfort/safety results
One analysis that can also be done is the relation between the accelerations felt on the vehicle and how do they
fit within the safety standards.
It is also relevant to observe if the results acquired and links established originate credible results (of lateral and
vertical force etc.). The fact that the results are reliable, confirms that the array of instruments used is adequate
for this type of testing, even without any invasive testing (e.g. drilling holes on the structures of the railway).
As it was stated on topic 2.3.3., comfort and safety assessment can be done in several ways from several stand
points, with the most common ones being the use of the root mean square frequency-weighted acceleration and
67
Wz criteria for the comfort, measurement and track shift force, running stability and risk of derailment as for the
safety.
In order to assess these topics it is first required to establish some assumptions for the correct approximation of
all the needed variables.
The most relevant variables in the following topics are, by order of appearance the following:
1) The root mean square frequency-weighted acceleration;
2) Lateral vehicle forces Y;
3) Vehicle vertical forces Q.
The assumptions used were the following:
The safety variables are treated by excess to consider always the worst case scenario;
The average acceleration felt on both accelerometers placed on both ends of one of the vehicle’s axle;
box is considered to be close to the acceleration felt by the entire bogie. Although this is not true, it is a
sufficiently satisfactory approximation (by excess);
The measurement of the accelerations on both accelerometers placed on the floor of the vehicle’s body,
is an approximation, by excess, of the acceleration felt on the whole vehicle’s body-frame;
The lateral force generated by the vehicle’s inertia against the rail, responsible for the derailment
process are much larger than the friction force exerted by the inner wheel’s base contact surface on the
rail, hence, the latter can be neglected. This enables to determine an approximation in excess for the Y
force.
o The vertical Q force divides itself approximately equally through all the wheels of the vehicle,
since the slope of the body of the vehicle while in curve is almost inexistent, considering the
weight of the body, the lateral acceleration and the stiffness of the springs.
4.7.1. Track shift force results
The track shift force is determined by the net difference between the lateral forces acting on the outer and inner
wheels of the vehicle. These forces are generated by the inertial centrifugal force and the friction force on the
contact surface of the wheel, respectively.
As stated in topic 4.7., the friction force of the base of inner wheel can be neglected when comparing it with the
centrifugal force.
With this being said and after filtering the data of the accelerations felt and using the track shift force equation in
accordance with the European standardization [19] shown on topic 2.3.3.
𝑚𝑎𝑥 (∑Y20 Hz,99.85%,lim ) =𝑚𝑓𝑟𝑎𝑚𝑒 . �̈�𝑓𝑟𝑎𝑚𝑒 +𝑚𝑏𝑜𝑔𝑖𝑒𝑠 . �̈�𝑏𝑜𝑔𝑖𝑒𝑠
𝑛=
=23.3𝐾𝑔 ∗ 0.64𝑔 + 17.4𝐾𝑔 ∗ 0.53𝑔
4. 9.806𝑚/𝑠2 = 59.5𝑁
(4.13)
However, since the equation for the track shift force safety condition possesses a constant a, with the value of 10
kN, the results hereby will consider using a proportionally smaller constant value in accordance with the smaller
68
area (64 times smaller) and yield stress of the rails used [36], when comparing to the real rails [37], and another
without even using the constant.
𝑎 =
10 𝑘𝑁
𝐴𝑟𝑒𝑎𝑙 . 𝜎𝑐𝑒𝑑_𝑟𝑒𝑎𝑙𝐴𝑚𝑜𝑑𝑒𝑙 . 𝜎𝑐𝑒𝑑_𝑚𝑜𝑑𝑒𝑙
=10000𝑁
64.462𝑀𝑝𝑎276𝑀𝑝𝑎
= 93.3𝑁 (4.14)
2𝑄𝑜 = 𝑚𝑣𝑔
𝑛=40.7 ∗ 9.806
4= 99.8𝑁 (4.15)
K1 (a +2𝑄𝑜
3) = 1. (93.3 +
99.8
3) = 126.6𝑁 (4.16)
Since it is necessary to ensure that the maximum value of the lateral forces result is lower than that of to the
equations above, the equation which will be considered is the objective function for the track shift force and its
limit value (shown below):
max (∑𝑌20 𝐻𝑧,99.85%,𝑙𝑖𝑚 ) = 59.6𝑁 ≤ 126.6𝑁 (4.17)
4.7.2. Running stability results
Another safety standard [19] explained in topic 2.3.3. was related to running stability. Running stability is
measured by calculating the root mean square of the variation of the lateral force or the maximum of the lateral
force value. Either of them are actually straightforward to assess by using the assumptions explained at the
beginning of this section and the lateral acceleration data measured.
The limit for running stability is given by the same equation mentioned before:
𝐾1 (10 +
2𝑄𝑜3)
2= 63.3𝑁
(4.18)
Also, once again, the objective function applied in this equation is the maximum of the root mean square lateral
force between all of the axles (shown below), even though in the case of this work only one axle was measured;
however, as was explained before, the accelerations felt on the front axles and the rear axles are similar.
The mass-weighted root mean square force was calculated:
𝛤𝑟𝑠 = max (∑𝑌𝑟𝑚𝑠) = 0.32 ∗ 9.806 ∗ 40.7/4 = 31.9𝑁 (4.19)
∑𝑌𝑟𝑚𝑠,𝑙𝑖𝑚 = 31.9𝑁 ≤ 63.3𝑁 (4.20)
4.7.3. Risk of derailment results
Another relevant safety result is the value of the risk of derailment coefficient.
69
Since this is a adimensional coefficient one can apply it directly to the model safety, given the fact that the
geometry of the rails used in the model is equal to the geometry of the rails used for a real size carriage.
With this being said the equation is presented below as well as the results of such coefficient, using the values of
the forces measured, once again using the accelerations felt on the vehicle.
𝑚𝑎𝑥 ((𝑌
𝑄)20𝐻𝑧,99.85%
) =59.5𝑁
40.7 ∗ 9.8064
= 0.596 ≤ 0.8 (4.21)
Once more, the target value used correspond to the maximum of the proportion of Y to Q; However Q can be
considered to be constant since there are no bumps on the railway track and, as was explained in the
assumptions, the slope of the vehicle body is negligible, thus, the maximum of the combination of variables
correspond to the maximum of lateral force (or acceleration).
4.8. Real vehicle result estimations and model extrapolations
Several calculations were made with the aim of making sure that the prototype would respect the standards in its
own scale, which it successfully did. However, in this very topic, the objective is to estimate what the values
would be for the life-size vehicle and extrapolate the results obtained from the model to the real railway vehicle.
4.8.1. Vehicle size relation
One of the most fundamental relations to be considered while working with models is the geometric relations
between the real and the model objects. Geometry is important since it defines the directions and, thus, the
relations between the forces. If the relations between the forces are the same, despite their value, the
relationships between results are much clearer.
In this case the model tests were made, as it was previously stated, a 7m wide curve, hence, in order to maintain
the same geometric positions of the vehicle wheels both in the model and in the full-size vehicle, it is would be
required to consider an hypothetical curve 8 times wider (since the real vehicle is 8 times larger).
With that being said, the what is needed left to determine the estimate of the centrifuge acceleration is the speed
at which the vehicle travels as well as its mass. This velocity is stated to be of 30 Km/h and the fully loaded
vehicle weight is 5300 Kg [10].
With the data presented above it is possible to make some rough estimates of the track shift force and risk of
derailment results.
4.8.2. Track shift force result estimation for the real vehicle
Using once more the track shift force equation in accordance with the European standardization shown on topic
2.3.3 the force exerted on the rails can be estimated as follows:
First the centrifuge acceleration must be calculated:
70
𝐶𝑒𝑛𝑡𝑟𝑖𝑓𝑢𝑔𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑣2
𝑟=(30000 𝑚/ℎ3600 𝑠
)2
56 𝑚= 1.24 𝑚/𝑠2
(4.22)
Hence, the maximum force felt on each wheel-set is estimated in the worst case scenario, by considering the
vehicle fully load while curving:
𝑚𝑎𝑥 (∑Y ) =𝑚𝑣𝑒ℎ𝑖𝑐𝑙𝑒 . �̈�𝑣𝑒ℎ𝑖𝑐𝑙𝑒
𝑛=
=5300 𝐾𝑔 ∗ 1.24 𝑚/𝑠2
4= 1643 𝑁
(4.23)
However, since the equation for the track shift force safety condition possesses a constant a, with the value of 10
kN, which is obviously only possible to apply to full sized trains and not to models, the results hereby shown
will consider using a proportionally smaller constant value in accordance with the smaller area (64 times
smaller) and yield stress of the rails used [36], when comparing to the real rails [37], and another without even
using the constant.
𝑎 = 10 𝑘𝑁 (4.24)
2𝑄𝑜 = 𝑚𝑣𝑔
𝑛=5300 𝐾𝑔 ∗ 9.806 𝑚/𝑠2
4= 12993𝑁 (4.25)
K1 (a +2𝑄𝑜
3) = 1. (10 𝑘𝑁 +
13 𝑘𝑁
3) = 14.33 𝑘𝑁 (4.26)
Since it is necessary to make sure that the maximum value of the lateral forces result is inferior to the value of
the equations above, the equation which will be considered as the objective function for the track shift force and
its limit value is the following:
max (∑𝑌 ) = 1.64 𝑘𝑁 ≤ 14.33 𝑘𝑁 (4.27)
From the results shown above, one can clearly assess that the Helianto train is well within the permitted limits,
even taking into account the worst case scenario. However one must keep in mind that all the values obtained
under section 4.8. are only estimates and were not measured in any concrete way.
4.8.3. Risk of derailment results
The results from the estimates of the parameter of running stability for the real Helianto train were omitted due
to the lack of experimental results to calculate the root mean square. The root mean square could be determined
with a constant value but it is not advisable.
Once again it the equation for the derailment coefficient using the estimated values is shown:
𝑚𝑎𝑥 ((𝑌
𝑄) ) =
1643 𝑁
12993 𝑁= 0.1265 ≤ 0.8 (4.28)
71
As could be seen on both topics, the Helianto train is well within the acceptable boundaries for either the
maximum acceptable force exerted on the rails’ side and for the coefficient between the lateral and vertical
forces acting upon each wheel.
4.8.4. Model extrapolations
Even though the real Helianto train has all its parameters, as estimated, within the, this estimation didn’t take
into account the accentuated acceleration variation in a real railway track caused by imperfections on either the
train and/or the rail track.
Derailment coefficient extrapolation
Let us take for example the case of the modelled train (with its results presented on section 4.7.): in this case the
values used to measure the safety and comfort parameters were the peak ones (after applying the appropriate
filter etc.), which results on a value of lateral acceleration far higher than the average lateral acceleration felt
while running the curve section of the railway. The peak lateral acceleration considered was of 0,64g and 0,53g,
for the body and bogies respectively, while the average lateral acceleration felt by the whole model while
curving was of 0,144g, or 1,41 𝑚/𝑠2 (considering the moment at which the model starts curving up until the
moment it finishes curving, which only happens at the end of the track).
This means that the lateral acceleration corresponds to a speed of:
1.41𝑚/𝑠2 =𝑣2
𝑟=> 𝑣 = 3.14 𝑚/𝑠
Since the derailment coefficient is dependent on the lateral acceleration, the mean derailment coefficient is of
Y/Q = 0.144.
However, considering the mean derailment coefficient determined for the real vehicle in order to obtain the
correspondent model in-curve speed have the following:
1.24𝑚/𝑠2 =𝑣2
𝑟=> 𝑣 = 2.95 𝑚/𝑠
With this being said it is valid to state that a model traveling along a 7 m wide curve at roughly 3 m/s is
equivalent in terms of derailment safety to a real, 8 times larger, carriage traveling through a 56 m wide curve at
roughly 30 Km/h (8.3 m/s).
Track shift force extrapolation
However, the relation applied to the track shift force cannot be the same when extrapolated. In order to simulate,
in the model railway track and vehicle, the effect of the real carriage traveling in curve through the real steel rails
the model must be travelling at a much lower speed.
72
The factor of safety in the case of the real carriage in terms of track shift force was of 14.33/1.64 = 8.74.
However, it must be taken into account that the peak acceleration is roughly 4 times larger than the mean lateral
acceleration felt, hence the factor of safety for track shift force will be estimated at 2.1, or a maximum reaction
force on each wheel-set of 59.7 N, which is almost exactly the force exerted by the vehicle model on the
aluminium rails while curving.
This means that, a model train travelling at roughly 3 m/s in a 7 m wide curve on proportionally smaller
aluminium rails will bring about the same kind of effects of a real Helianto carriage, 8 times larger than the
model, traveling at 30 Km/h on a 56 m wide curve.
These extrapolations establish a connection between both scales which may make testing cheaper and faster,
from now on.
During this last chapter all results obtained from the tests using the Helianto model were presented with the
respective comparisons and analysis between them. This includes all the value results from the spring-damper
effect of the model’s body frame, the variations that a weight difference induces, as well as the speed of the
vehicle, the friction force and the lateral acceleration and derailment tests. This chapter concludes itself with the
relation between those same results and the standards used in these types of railway vehicles.
73
5. Conclusions
This chapter summarizes the main points of each previous chapter in terms of results and outcomes of this work.
Many results shown across the document will not be mentioned, only the fundamental ones will be discussed
herein.
5.1. Accelerometer results comparison In section 2.6 several results were shown regarding the comparison between the capacitive accelerometers, the
piezoelectric accelerometers and the ANSYS results. The objective was to prove that the capacitive
accelerometers had results almost as accurate as the more expensive accelerometers (the piezoelectric ones) for
the range of frequencies measured. This was positively verified, since the mean relative error measured between
the capacitive accelerometers and the values obtained through the p
rogram ANSYS was only 1,4%, while the error measured between the former and the piezoelectric
accelerometers was 1,5%.
These error percentages can be considered as irrelevant, hence can be assuredly concluded that the capacitive
accelerometers are efficient alternatives to it for the piezoelectric accelerometers for the range of frequencies
from 5 to 200 Hz.
5.2. Spring-damper parameters Using the accelerations felt by the body frame of the vehicle, while knowing its mass, made possible to
approximate, in section 4.1., the value of the parameters of the model’s springs using the formulae from
vibration analysis. From the experimental results and the calculations done, it was estimated that the spring’s
constant k had a value of k = 43 N/mm, while the damping coefficient was valued at 65 Ns/m. However, one
should take notice that the suspension arrangement of one Bogie contains 8 springs.
Another relevant result obtained from the suspension system was the fact that the amount of acceleration felt was
effectively reduced by 66% in the model. However, the acceleration felt in the passenger floor was still high but
if one considers the difference in inertia between the model and the real carriage, the acceleration would
probably have an acceptable level, even taking into account the fact that the real vehicle travels at a higher speed
than the model.
5.3. Accelerometer and strain gauge use for vibration assessment on rails As explained in section 4.2., one problem when trying to obtain vibration measurements on railway tracks is the
fact that, due to safety measures it is not possible to alter or damage the rails in any way, which is fundamental to
ensure passenger safety. However, most vibration detection arrangements require the drilling of holes on the
rails, which is highly invasive. Fortunately, using the strain gauge and accelerometer placement shown on
figures 2.10, 2.11 and 3.2 – 3.4, respectively, it is possible to obtain most of the relevant information regarding
the measurement of vibrations/deformations and accelerations felt both in the vehicle and on the track. Examples
of these types of information can be the deformation level depending on the distance of the wheel-set from the
strain gauges, the accelerations felt on the track while the train is running on the railway and extension direction
of each part of the rail material when deformed by the passing of the vehicle. Finally, all information can be
74
acquired without any need for invasive, expensive, lenghty or dangerous methods; with this type of experimental
arrangement there is no need to affect the railway condition.
5.4. Friction coefficient By using the accelerometers in the vehicle model it was possible to integrate those values and obtain an accurate
estimate of the vehicle speed variation with time. As explained in section 4.4., the slowing of vehicle speed was
due to loss of energy through friction between the model’s mechanical moving parts. The fact that, the loss of
energy was strictly proportional to the weight of the vehicle, and by knowing the distance along which that
energy was lost it was possible to accurately determine that the average friction coefficient between all
mechanical moving parts of the model involved on traveling was of about fa = 0.0052, which corresponds to a
friction force of Fa = 2.04 N.
5.5. Model and real vehicle standards comparisons and extrapolations As outlined in sections 4.6. to 4.8., there are several relevant comfort and safety-related standards that must be
respected in order for a railway vehicle to be approved. Some of the main variables in terms of safety standards
are track shift force value, running stability values, and risk of derailment, based on the derailment coefficient.
The objective of this section was to make sure that both the model and the real train were within the limits of
these standards for all the categories tested. In fact this was confirmed with both the model and the real vehicle
having their values well within the standards’ boundaries (however the real vehicle values were theoretical
estimations).
The model exerted a track shift force of 59.6 N, when the maximum allowed would be 126.6 N (this value was
estimated using the size and materials of the model rails when comparing with the real ones); in terms of running
stability, the model surpassed the assessment with 31.9 N for a maximum of 63.3 N; and finally, in terms of
derailment safety the derailment coefficient for the model was 0.6 while the danger zone starts at 0.8 hence, it is
within the safety limit.
The theoretical estimates made for the real size Helianto train were also within the boundaries, with the track
shift force being at 1.64 kN to a maximum of 14.3 kN, however these values do not take into account the
acceleration peaks if taken into account the factor of safety for the track shift force of the real vehicle is almost
exactly the same as for the model. In terms of risk of derailment, theoretically the real vehicle would be way
within the limits of the derailment standard, since Y/Q = 0.13 < 0.8, however if there is a peak acceleration of 4x
the average lateral acceleration (which seems to be the case for the model in the worst case scenario) this value
would be 4 times higher, even so still within the limits, Y/Q = 0.5 < 0.8.
Finally some extrapolations taken from the model into the real vehicle are shown, all of them are presented in
topic 4.8.4.; By taking into account all of the variables and values intervening in the standards it is possible to
estimate that, in terms of derailment coefficient assessment, a model of 40 Kgs, travelling at roughly 3 m/s in a 7
m wide curve is equivalent to the real vehicle (8 times larger and with 5300 Kgs of weight) travelling at 30 Km/h
(8.3 m/s) through a 56 m wide curve.
75
Furthermore, a model travelling at roughly 3 m/s through a 7 m curve on proportionally smaller aluminium rails
will exert the same kind of effects/damage of a real Helianto carriage 8 times larger than the model and traveling
at 30 Km/h on a 56 m wide curve.
5.6. Review and future work The first improvement that comes to mind is the integration of an engine in the modelled vehicle, which
would enable further testing with as less human interference as possible.
Another possibly relevant modification would be the testing of the model in more types of railway
tracks to get a larger sample of the model’s behaviour.
Additionally, an important adjustment would be the integration of an automated braking system which
would enable a more accurate study of accelerations, vibrations and deformations due to train braking.
76
6. References [1. 1985 - 2010 data from Paula Mints, Principal Analyst, Solar Services Program, Navigant. 2011
numbers based on market data.
2. 2014., "Global Market Outlook for Photovoltaics 2014-2018". http://www.epia.org. EPIA -
European Photovoltaic Industry Association. Archived from the original on 12 June 2014. Retrieved
12 June.
3. 2005., "Emission Facts: Average Carbon Dioxide Emissions Resulting from Gasoline and Diesel
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4. Guan, B, et al. Review of state of the art technologies of selective catalytic reduction of NOx from
diesel engine exhaust Review Article Applied Thermal Engineering. 2014. Vol. 66, 1-2, pp. 395-414.
5. A. BLOMBERG, H. TÖRNQVIST, L. DESMYTER, V. DENEYS, C. HERMANS. Exposure to diesel
exhaust nanoparticles does not induce blood hypercoagulability in an at-risk population. s.l. : Journal
of Thrombosis and Haemostasis, 11 AUG 2005. Vol. 3, 9, pp. 2103-2105.
6. Nawrot, Perez, Künzli, Munters, Nemery Public health importance of triggers of myocardial
infarction: comparative risk assessment The Lancet Volume 377, Issue 9767, Pages 732 - 740, 26
February 2011.
7. Power, et al. Traffic-related air pollution and cognitive function in a cohort of older men. Vol. 119,
5, pp. 682-7.
8. International Agency for Research on Cancer: DIESEL ENGINE EXHAUST CARCINOGENIC. 12 June
2012.
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Vehicle. http://www.epa.gov/otaq/climate/documents/420f14040.pdf s.l. : Office of Transportation
and Air Quality, May 2014.
10. “Helianto project, ” Instituto Superior Tecnico, TU Lisbon. [Online]. Available:
http://helianto.ist.utl.pt.
11. Maria Féria, Msc., Electrotecnical Engineering. Decision and control system of a solar powered
train. Lisbon, Lisbon, Portugal : Instituto Superior Técnico, Abril 2012.
12. Railway Trucks for Continuous Measurement of Derailment Coeffiicient and Observation Systems
Using Such Trucks on In-serve Trains. M. Shimizu, H. Ohmo, Y. Sato, M. Tanimoto, A. Matsumoto. 10
2005, The Japan Society of Mechanical Engineers.
13. Iwnicki, Simon. Handbook of Railway Vehicle Dynamics. [ed.] Taylor and Francis. Boca Raton :
CRC Press, 2006. pp. 435-440. ISBN-13: 978-0-8493-3321-7.
14. EXPERIMENTAL VERIFICATION OF THE LATERAL ACCELERATIONS MEASURING METHOD FOR
GUIDING FORCES SUM DETERMINATION OF A TWO AXLE WAGON. Daniel-Marius MIHAI, Nicolae
ENESCU. 2, 2012, UPB Scientific Bulletin, Vol. 74.
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15. Railway applications - Definition of vehicle reference masses. STANDARDIZATION, EUROPEAN
COMMITTEE FOR, [ed.]. Brussels : s.n., 2006. EN 15663.
16. Railway Applications - Testing and approval of railway vehicles from the point of view of their
dynamic behaviour – Safety - Track fatigue - Running behaviour. CEN. Brussels, European Committee
for Standardization : s.n., August 2007. UIC 518.
17. IMPACK Documentation, Version 8903, X–PF:5 Ride Index VDI and ISO.
18. ORVNAS, ANNELI. On Active Secondary Suspension in Rail Vehicles to Improve Ride Comfort. KTH
Engineering Sciences. Stockholm, Sweden : s.n., 2011. Doctoral Thesis in Railway Tchnology.
19. CEN, EN 12299. Railway Applications – Ride Comfort for Passengers – Measurement and
Evaluation. Brussels : European Comittee for Standardization (CEN), 2009.
20. Verfahren zur Beurteilung der Laufeigenschaften von. Sperling, E. s.l. : Organ f.d. Fortschritte des
Eisenbahnwesens, Vol. 12, pp. 176-187.
21. Ride comfort for passengers - Measurement and evaluation. Andersson, E., Berg, M., and Stichel,
S. Brussels : European Committee for Standardization, 1999.
22. Numerical studies of the influence of laterally deteriorated track geometry on track shift forces
and RCF in freight operations. Kalle Karttunen, Elena Kabo & Anders Ekberg. [ed.] Chalmers
university of technology. Sweden : s.n. 17th Nordic Seminar on Railway Technology. p. 3.
23. Railway applications - Ride comfort for passengers - Measurement and evaluation. CEN. Brussels :
European Committee for Standardization, 1999.
24. Tuzik, Bob. http://interfacejournal.com/archives/409. [Online] July 2014.
25. The estimation method of wheel load and lateral force using the axlebox acceleration. H. Tanaka,
A. Furukawa. Tokyo : Railway Technical Research Institute.
26. http://www.engineersgarage.com/articles/accelerometer?page=2.
http://www.engineersgarage.com. [Online]
27. efunda.
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/strain_gage_rosette.cfm.
http://www.efunda.com/home.cfm. [Online]
28. http://www.jameco.com/1/1/39011-mdl-3-r-fuses-electric-fuse-time-delay-3a-250vac-100a-ir-
inline-holder.html. http://www.jameco.com. [Online] Jameco Electronics.
29. http://shop.rabtron.co.za/catalog/fuse-holder-5x20-p-
211.html?osCsid=0lch7q50fi3954sj4mnkn9df64. http://www.shop.rabtron.co.za. [Online] RABTRON.
30. http://www.rapidonline.com/electronic-components/sub-miniature-toggle-switches-79431.
http://www.rapidonline.com/. [Online] Rapid Electronics.
31. Signal Lab. Sigview. http://www.sigview.com/. [Online]
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32. http://www.alumicopper.com.br/pdf/aluminio/info-tec-alumi_aluminio_6351.pdf.
http://www.alumicopper.com.br. [Online]
33. http://www.engineeringtoolbox.com/poissons-ratio-d_1224.html.
http://www.engineeringtoolbox.com. [Online] The Engineering ToolBox.
34. http://www.matbase.com/material-categories/natural-and-synthetic-polymers/commodity-
polymers/material-properties-of-acrylonitrile-butadiene-styrene-general-purpose-gp-
abs.html#properties. http://www.matbase.com. [Online] MATBASE.
35. http://www.makeitfrom.com/material-data/?for=Acrylonitrile-Butadiene-Styrene-ABS.
http://www.makeitfrom.com. [Online] MakeItFrom.
36. Real-Time Monitoring of Railway Traffic UsingFiber Bragg Grating Sensors. Massimo Leonardo
Filograno, Pedro Corredera Guillén, Alberto Rodríguez-Barrios, Sonia Martín-López,Miguel
Rodríguez-Plaza, Álvaro Andrés-Alguacil, and Miguel González-Herráez. Madrid : s.n., 1 January
2012, IEEE SENSORS JOURNA, Vol. 12.
37. Railway applications - Testing for the acceptance of running characteristics of railway vehicles -
Testing of running behaviour and stationary tests. Brussels : CEN - European Committee for
Standardization, 2005. EN 14363:2005: E.
38. ASM Aerospace Specification Metals, Inc.
http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6.
http://www.aerospacemetals.com. [Online]
39. Jersey Shore Steel. http://www.jssteel.com/content/rail-steel-vs-mild-steel.
http://www.jssteel.com. [Online]
40. 2008-03-13, "Greenhouse Gas Reductions". Diesel Technology Forum. Archived from the
original on 2008-03-02. Retrieved.
41. (Abstract), Exposure to Diesel Nanoparticles Does Not Induce Blood Hypercoagulability in an at-
Risk Population.
42. Garg, V.K. and Dukkipati, R.V. Dynamics of Railway Vehicle Systems. s.l. : Academic Press, 1984.
43. Ramon, John G. Webster. Sensors and Signal Conditioning. 2nd. s.l. : John Wiley Sons INC., 2001.
79
7. Appendices
7.1. Deformation generated by the vibration modes on the railway track
part
The first 22 modes of vibration and their respective natural frequencies are shown below:
Figure 7.1 - 1st and 2nd rail vibrational modes.
Figure 7.2 - 3rd and 4th rail vibrational modes
80
Figure 7.3 - 5th and 6th rail vibrational modes
Figure 7.4 - 7th and 8th rail vibrational modes
Figure 7.5 - 9th and 10th rail vibrational modes
81
Figure 7.6 - 11th and 12th rail vibrational modes
Figure 7.7 - 13th and 14th rail vibrational modes.
Figure 7.8 - 15th and 16th rail vibrational modes.
82
Figure 7.9 - 17th and 18th rail vibrational modes.
Figure 7.10 - 19th and 20th rail vibrational modes.
Figure 7.11 - 21th and 22th rail vibrational modes.
83
7.2. Arduino C++ data collecting and storing code
//#define DEBUG //descomentar esta linha para usar o modo debug com a porta série
//define pin configuration on arduino mega
const int x_axis1=0;
const int y_axis1=1;
const int z_axis1=2;
const int x_axis2=3;
int y_axis2=0;
int z_axis2=0;
int x_axis3=0;
int y_axis3=0;
int z_axis3=0;
int p_throttle=0;
int p_steer=0;
const int Logled_on_off=6;
//initialize all variables and their values
int xx1 = 0;
int yy1 = 0;
int zz1 = 0;
int xx2 = 0;
int yy2 = 0;
int zz2 = 0;
int xx3 = 0;
84
int yy3 = 0;
int zz3 = 0;
int throttle=0;
int steer=0;
//unsigned long t_abs=0;
unsigned long t_absolute=0; //time since the power up of the arduino board
volatile int state = LOW; //logging switch on or off, using interrupts allows on less analog read during
the loop, saving execution time, speeding other readings
volatile int finish = LOW; //variable for controlling the end of each log session
int apont = 0;
unsigned long numWrites = 0;
int inicio=0;
int erro = 0; //variavel que controla o tipo de erro detectado e assim permite controlar o led
correctamente
//inicializa variaveis necessarias ao cartao SD
uint32_t t = 0;
uint16_t maxWriteTime = 0;
uint32_t tw = 0;
uint32_t bgnBlock, endBlock;
#include "Wire.h"
// I2Cdev and ADXL345 must be installed as libraries, or else the .cpp/.h files
// for both classes must be in the include path of your project
#include "I2Cdev.h"
85
#include "ADXL345.h"
#include "ADXL333.h"
#include <stdlib.h>
#include <SdFat.h>
#include <SdFatUtil.h>
// number of blocks in the contiguous file
#define BLOCK_COUNT 30000UL //ficheiro de 100mb é com 20000 blocos deve dar para + de 4
horas (2.4mins)
//ficheiro de 500Kb é com 1000 blocos e dá para 80 segundos +/- estava ca 2000
#define num_bytes_bloco 512 //corresponde a blocos de 512 bytes cada
Sd2Card card;
SdVolume volume;
SdFile root;
SdFile file;
char str_t[100], str_max[100], str_num[100];
ADXL345 accel1;
ADXL333 accel2;
int16_t ax1, ay1, az1;
int16_t ax2, ay2, az2;
// store error strings in flash to save RAM
86
#define error(s) error_P(PSTR(s))
void error_P(const char *str)
{
#ifdef DEBUG //se o modo debug está a ser utilizado, caso contrário nao usa a porta série
PgmPrint("error: ");
SerialPrintln_P(str);
if (card.errorCode()) {
PgmPrint("SD error: ");
Serial.print(card.errorCode(), HEX);
Serial.print(',');
Serial.println(card.errorData(), HEX);
}
#endif
digitalWrite(Logled_on_off,LOW);
}
uint8_t *pCache = volume.cacheClear();
void setup() {
Wire.begin();
// digitalWrite(10, HIGH);
pinMode(Logled_on_off, OUTPUT);
interrupts();
attachInterrupt(0, botao_on_off, RISING); //assign the button to corresponding interrupt pin (18)
with interrupts triggered by RISING in pin value (LOW to HIGH)
////
#ifdef DEBUG //se o modo debug está a ser utilizado, caso contrário nao usa a porta série
87
Serial.begin(115200);
Serial.println("Debug mode ligado!");
Serial.println("Atencao: a frequencia de amostragem obtida no modo debug sera significativamente
mais lenta que com o programa autonomo!");
Serial.println("");
#endif
// #ifdef DEBUG
// // initialize device
// Serial.println("Initializing I2C devices...");
// #endif
//
accel1.initialize();
accel2.initialize();
//
//// #ifdef DEBUG
//// // verify connection
//// Serial.println("Testing device connections...");
// Serial.println(accel1.testConnection() ? "ADXL345 connection successful" : "ADXL345 connection
failed");
//Serial.println(accel2.testConnection() ? "ADXL333 connection successful" : "ADXL333 connection
failed");
//// #endif
accel1.setRange(0x00);
accel1.setFullResolution(1);
accel1.setRate(0x0f);
accel2.setRange(0x00);
accel2.setFullResolution(1);
accel2.setRate(0x0f);
88
#ifdef DEBUG
//
Serial.println("Ready");
#endif
}
void loop() {
t_absolute=millis();
if ((inicio==0) && (state==HIGH)){// initialize the SD card
t = millis();
if (!card.init()) {
error("card.init");
}
// initialize a FAT volume
if (!volume.init(card)) {
error("volume.init");
}
// open the root directory
if (!root.openRoot(volume)) {
error("openRoot");
}
89
//verificação do nome do ficheiro para nao haver ficheiros sobrepostos
char name[] = "RAW00.DAT";
char nome[] = "RAW00.DAT";
for (uint8_t i = 0; i < 100; i++) {
name[3] = i/10 + '0';
nome[3] = i/10 + '0';
name[4] = i%10 + '0';
nome[4] = i%10 + '0';
// only create new file for write
if (file.open(root, name, O_CREAT | O_EXCL | O_WRITE)) break;//tenta abrir um ficheiro com o
nome e apenas tem sucesso quando o ficheiro nao existe
}
if (!file.isOpen()) {
error ("duplicateverification.fileopen");
}
if (!file.close()) {
error ("duplicateverification.fileclose");
}
// delete possible existing file
SdFile::remove(root, name); //apos verificação do nome a usar para não haver sobreposiçoes,
remove o ficheiro para o abrir em modo de blocos contiguos.
// create a contiguous file
if (!file.createContiguous(root, nome, 512UL*BLOCK_COUNT)) {
error("createfile");
}
// get the location of the file's blocks
90
if (!file.contiguousRange(bgnBlock, endBlock)) {
error("contiguousRange");
}
// tell card to setup for multiple block write with pre-erase
if (!card.erase(bgnBlock, endBlock)) {
error("erase");
}
if (!card.writeStart(bgnBlock, BLOCK_COUNT)) {
error("writeStart");
}
#ifdef DEBUG
Serial.println("Card setup complete");
#endif
inicio=1;
} //if ((inicio==0) && (state==HIGH)){// initialize the SD card
if ((state==HIGH) && (inicio==1)){
//leitura de parametros
// // read raw accel measurements from device
accel1.getAcceleration(&ax1, &ay1, &az1);
91
accel2.getAcceleration(&ax2, &ay2, &az2);
// // display tab-separated accel x/y/z values
ax1=ax1+2048;
ay1=ay1+2048;
az1=az1+2048;
ax2=ax2+2048;
ay2=ay2+2048;
az2=az2+2048;
#ifdef DEBUG
Serial.print(ax1);
Serial.print(" ");
Serial.print(ay1);
Serial.print(" ");
Serial.print(az1);
Serial.print(" ");
Serial.print(ax2);
Serial.print(" ");
Serial.print(ay2);
Serial.print(" ");
Serial.print(az2);
Serial.print(" ");
Serial.print(xx3);
Serial.print(" ");
Serial.print(yy3);
Serial.print(" ");
Serial.print(zz3);
92
Serial.print(" ");
Serial.print(throttle);
Serial.print(" ");
Serial.print(steer);
Serial.print(" ");
Serial.println(t_absolute);
#endif
if (apont==0){
// clear the cache and use it as a num_bytes_bloco byte buffer
memset(pCache, ' ', num_bytes_bloco);
}
//guarda na cache os valores dos parametros medidos
pCache[0+apont]=0xff; //primeiro valor a escrever: byte de sincronismo
//
pCache[1+apont]=(ax1 >> 16) & 0xff;
pCache[2+apont]=(ax1 >> 8) & 0xff;
pCache[3+apont]=(ax1) &0xff;
//
pCache[4+apont]=(ay1 >> 16) & 0xff;
pCache[5+apont]=(ay1 >> 8) & 0xff;
pCache[6+apont]=(ay1) &0xff;
//
93
pCache[7+apont]=(az1 >> 16) & 0xff;
pCache[8+apont]=(az1 >> 8) & 0xff;
pCache[9+apont]=(az1) &0xff;
pCache[10+apont]=(ax2 >> 16) & 0xff;
pCache[11+apont]=(ax2 >> 8) & 0xff;
pCache[12+apont]=(ax2) &0xff;
//
pCache[13+apont]=(ay2 >> 16) & 0xff;
pCache[14+apont]=(ay2 >> 8) & 0xff;
pCache[15+apont]=(ay2) &0xff;
////
pCache[16+apont]=(az2 >> 16) & 0xff;
pCache[17+apont]=(az2 >> 8) & 0xff;
pCache[18+apont]=(az2) &0xff;
pCache[19+apont]=(az2 >> 16) & 0xff;
pCache[20+apont]=(az2 >> 8) & 0xff;
pCache[21+apont]=(az2) &0xff;
pCache[22+apont]=(t_absolute >> 16) & 0xff;
pCache[23+apont]=(t_absolute >> 8) & 0xff;
pCache[24+apont]=(t_absolute) &0xff;
apont+=25; //avança o apontador para que no proximo loop nao haja sobreposição
//verificar se a cache ainda tem espaço para mais uma gravação completa. Se nao, entao gravar
para o cartão
94
if (apont+25>num_bytes_bloco){
//escrita para cartao SD
// write a num_bytes_bloco byte block
tw = millis();
if (!card.writeData(pCache)) {
erro=3;
error("writeData");
}
tw = millis() - tw;
// check for max write time
if (tw > maxWriteTime) {
maxWriteTime = tw;
}
numWrites++;
//fim da escrita
apont=0;
//verificação de capacidade restante no ficheiro
if (numWrites > BLOCK_COUNT-2){
#ifdef DEBUG
Serial.println("Atencao: o ficheiro de dados atingiu o limite da capacidade!");
Serial.print("Capacidade actual: ");
Serial.print(BLOCK_COUNT);
Serial.println(" blocos");
Serial.println("A sessao sera terminada");
#endif
95
state=LOW;
finish=HIGH;
}
} //if
} //if ((state==HIGH) && (inicio==1))
else
{
if (finish == HIGH){
//escreve o que ainda está na cache mesmo que não tenha 512 bytes
tw = millis();
if (!card.writeData(pCache)) {
erro=3;
error("writeData");
}
tw = millis() - tw;
// check for max write time
if (tw > maxWriteTime) {
maxWriteTime = tw;
} //if
numWrites++;
// total write time
t = millis() - t;
96
// clear the cache and use it as a num_bytes_bloco byte buffer
memset(pCache, ' ', num_bytes_bloco);
//write stats to memory buffer
pCache[0]=0xff;
pCache[1]=0xff;
pCache[2]=0x40;
pCache[3]=0xff;
pCache[4]=0xff;
pCache[5]=(numWrites >> 40) & 0xff;
pCache[6]=(numWrites >> 32) & 0xff;
pCache[7]=(numWrites >> 24) & 0xff;
pCache[8]=(numWrites >> 16) & 0xff;
pCache[9]=(numWrites >> 8) & 0xff;
pCache[10]=(numWrites) &0xff;
pCache[11]=0xff;
pCache[12]=(t >> 40) & 0xff;
pCache[13]=(t >> 32) & 0xff;
pCache[14]=(t >> 24) & 0xff;
pCache[15]=(t >> 16) & 0xff;
pCache[16]=(t >> 8) & 0xff;
pCache[17]=(t) &0xff;
pCache[18]=0xff;
pCache[19]=(maxWriteTime >> 24) & 0xff;
pCache[20]=(maxWriteTime >> 16) & 0xff;
pCache[21]=(maxWriteTime >> 8) & 0xff;
97
pCache[22]=(maxWriteTime) &0xff;
pCache[23]=0xff;
pCache[24]=0xff;
pCache[25]=0x40;
pCache[26]=0xff;
pCache[27]=0xff;
//write session statistical data to the SD card
if (!card.writeData(pCache)) {
erro=3;
error("writeData");
}
//
// // end multiple block write mode
if (!card.writeStop()) {
erro=3;
error("writeStop");
}
// close files
root.close();
file.close();
#ifdef DEBUG
Serial.println(" ");
Serial.println("Log Stop");
Serial.println(" ");
sprintf(str_num,"Numero de acessos: %lu ",numWrites);
98
sprintf(str_t,"Duracao da sessao: %lu milisegundos ",t);
sprintf(str_max,"Tempo maximo de escrita: %d milisegundos\r\n",maxWriteTime);
Serial.println(str_num);
Serial.println(str_t);
Serial.println(str_max);
Serial.println("done");
#endif
digitalWrite(Logled_on_off,state);
finish=LOW;
}//if (finish == HIGH)
} //else
}
void botao_on_off() {
//debouncing the interrupt button
static unsigned long last_interrupt_time = 0;
unsigned long interrupt_time = millis();
// // If interrupts comes faster than 500ms, assume it's a bounce and ignore
if (interrupt_time - last_interrupt_time > 500) {
state = !state;
if (state==HIGH){
#ifdef DEBUG
99
Serial.println(" ");
Serial.println("Log Start");
#endif
inicio=0;
digitalWrite(Logled_on_off,state);
}
else{
finish=HIGH;
}
}
last_interrupt_time = interrupt_time;
}
100
7.3. Matlab data conversion code
%opens the logging file and imports its content to the matlab workspace %separating the calibration data and statitics from logging data clear all clc
bytes_linha=25; %numero de bytes entre cada caracter de sincronização (ver % o sketch do arduino e procurar pela variavel apont. verificar qual o % incremento de bloco em bloco) npar_linha=8; %numero de parametros em cada linha de dados (ver sketch do % arduino e contar) tic error=0; disp(' '); disp('CONVERT DATA FROM HEXADECIMAL FILE TO DECIMAL FILE'); disp(' '); nome_ficheiro='RAW01'; filename=strcat('logs_bruto/',nome_ficheiro,'.dat');
fid=fopen(filename,'r'); if fid~=-1 fprintf(1,'Log file %s openned sucessfully\n',nome_ficheiro); % make sure the file is not empty finfo = dir(filename); fsize = finfo.bytes;
if fsize > 0 %read the whole file content=fread(fid); %place the file content in a vector to be
analysed later
i=0; j=0; data=zeros(round(size(content,1)/bytes_linha),bytes_linha);
for aux=1:size(content,1)
if (content(aux)==hex2dec('FF') && j>=bytes_linha) % se chegou ao fim da linha, passar para a linha abaixo e % repor o contador da coluna a 0 i=i+1; j=0; end j=j+1; %coluna seguinte
if (j<bytes_linha+1 && i>0) %se ainda estamos dentro da linha válida, copiar conteúdo %para a tabela %serve para evitar que em caso de erro de escrita, haja %linhas maiores que outras data(i,j)=content(aux); end
if i>1 %garantir que nao executa na primeira passagem para nao
dar erros de memória (aux-3=-2 => fora do vector % 0xFF=hex2dec('FF')=255 e 0x40=hex2dec('40')=64
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if (content(aux)==255 && content(aux-1)==255 &&
content(aux-2)==64 && content(aux-3)==255 && content(aux-4)==255) %if the character combinarion 'sinc sinc @ sinc sinc '
is %found and we have more read than one file line, then
the %data part of the file is finished. from know on, its
only %statistical data written at the end of the log session
%numero de acessos do arduino ao cartao SD para gravar %blocos de 512bytes
num_acessos=content(aux+1)*2^40+content(aux+2)*2^32+content(aux+3)*2^24+con
tent(aux+4)*2^16+content(aux+5)*2^8+content(aux+6);
%duração da sessão de data_log em milisegundos
duracao_sessao=content(aux+8)*2^40+content(aux+9)*2^32+content(aux+10)*2^24
+content(aux+11)*2^16+content(aux+12)*2^8+content(aux+13);
%tempo máximo de escrita de 512bytes no cartao SD.
Serve %para ver se existiram atrasos ou erros de gravação
tempo_escrita=content(aux+15)*2^24+content(aux+16)*2^16+content(aux+17)*2^8
+content(aux+18);
%numero estimado de amostras lidas pelo arduino e
gravdas %no cartão SD npar_calculado=num_acessos*17; disp('aqui'); if (content(aux+7)~=255 || content(aux+14)~=255 ||
content(aux+19)~=255 || content(aux+20)~=255 || content(aux+21)~=64 ||
content(aux+22)~=255 || content(aux+23)~=255) disp('CAUTION: Failed format verification at end of
session information.'); disp('Some data lines integrety may have been
compromised!'); error=1; end
data_raw=data(1:i-1,2:bytes_linha); %ignore the statistical information just read and save %logging data only as data_raw variable ignoring the
sincronims character break
end
end end
disp('Data reading finished\Starting statistics reading');
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else disp('File is empty'); %the file is empty and there is nothing to
read error=1; end
fclose(fid);
disp('End of log file reading'); else disp('Could not open specified file'); error=1; %fopen operation failed, put error flag to 1 end
clear aux i j content data
%the files are know read and closed because no longer needed %moving on to converting data if error~=1 %convert the data that comes in BYTES to numeric data and save it to a %readble txt log file disp('Starting data conversion'); data_dec=zeros(size(data_raw,1),npar_linha); %number of lines=number of parameters, %number of columns=npar_linha
i=1:size(data_raw,1); j=1:3:size(data_raw,2)-6;%ignore the last 6 colums l=1:1:size(j,2); data_dec(i,l)=data_raw(i,j).*2^16+data_raw(i,j+1).*2^8+data_raw(i,j+2)-
2048; %convert
j=size(data_raw,2)-5:3:size(data_raw,2); %ignore the other columns
because all we want is and time parameters
colunas_destino=[npar_linha-1,npar_linha]; % set destination columns
(last 2)
data_dec(i,colunas_destino)=data_raw(i,j).*2^16+data_raw(i,j+1).*2^8+data_r
aw(i,j+2); %convert
clear i j colunas_destino
disp('End of BYTE-DEC conversion\Starting file openning and writing');
filename=strcat('logs_decimal/',nome_ficheiro,'_dec.txt'); fid=fopen(filename,'w'); if fid~=-1 disp('File for output writing openned sucessfully'); fprintf(fid,'ACEL X1|ACEL Y1|ACEL Z1|ACEL X2|ACEL Y2|ACEL
Z2|INTERVAL|TIME\r\n'); for i=1:size(data_dec,1) %print to file fprintf(fid,'%d,%d,%d,%d,%d,%d,%d,%d\r\n',data_dec(i,:)); end
npar_fich=size(data_dec,1); fprintf(fid,'\r\n\r\nNúmero de acessos ao cartão SD:
%d\r\n',num_acessos);
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fprintf(fid,'Duração da Sessão: %d
milisegundos\r\n',duracao_sessao); fprintf(fid,'Tempo máximo de escrita: %d
milisegundos\r\n',tempo_escrita); fprintf(fid,'Número máximo de amostras lidas pelo Arduino
(estimativa): %d \r\n',npar_calculado); fprintf(fid,'Número de amostras lidas do ficheiro: %d
\r\n',npar_fich);
fclose(fid);
disp('End of file writing\File closed');
else disp('Could not open specified file'); error=1; %fopen operation failed
end toc end
7.4. Railway track part dimensions
Figure 7.12 - Railway dimensions and sleeve dimensions.
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Figure 7.13 - Railway and sleepers dimensions
Figure 7.14 - Rail section dimensions.
