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Lecture Notes in Networks and Systems 305
Daniela Doina Cioboată Editor
International
Conference on Reliable
Systems Engineering
(ICoRSE) - 2021
Lecture Notes in Networks and Systems
Volume 305
Series Editor
Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,
Warsaw, Poland
Advisory Editors
Fernando Gomide, Department of Computer Engineering and Automation—DCA,
School of Electrical and Computer Engineering—FEEC, University of Campinas—
UNICAMP, São Paulo, Brazil
Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici
University, Istanbul, Turkey
Derong Liu, Department of Electrical and Computer Engineering, University of
Illinois at Chicago, Chicago, USA, Institute of Automation, Chinese Academy of
Sciences, Beijing, China
Witold Pedrycz, Department of Electrical and Computer Engineering, University of
Alberta, Alberta, Canada, Systems Research Institute, Polish Academy of Sciences,
Warsaw, Poland
Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS
Research Center for Intelligent Systems and Networks, University of Cyprus,
Nicosia, Cyprus
Imre J. Rudas, Óbuda University, Budapest, Hungary
Jun Wang, Department of Computer Science, City University of Hong Kong,
Kowloon, Hong Kong
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Daniela Doina Cioboată
Editor
International Conference
on Reliable Systems
Engineering (ICoRSE) - 2021
123
Editor
Daniela Doina Cioboată
Bucharest, Romania
ISSN 2367-3370 ISSN 2367-3389 (electronic)

Lecture Notes in Networks and Systems
ISBN 978-3-030-83367-1 ISBN 978-3-030-83368-8 (eBook)
https://doi.org/10.1007/978-3-030-83368-8
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2022
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Foreword
During the last two years, we have witnessed unprecedented challenges. But human
beings’ ingenuity is endless, and we were able to find solutions to all the threats we
deal with. In this context, organizing a scientific event is not an easy task. This is
why I am very proud to be able to coordinate a conference during the pandemic that
seems–hopefully–to be coming to an end.
And it is due to the degree of excellence that science has attained–in terms of
medicine–that we can now say that we stand firm against the threat of COVID-19.
And, more than ever, the impact that science has–on the long run–on the well-being
of society is easier than ever to spot.
The evolution of science and technology, so fast paced, is obvious especially in
the fields of electronics and microelectronics, automation and digitization. These
have resulted in a shift in focus, from precision mechanics to mechatronics, inte-
gronics, adaptronics and currently claytronics and cyber-mix-mechatronics. This is
why the National Institute of Research and Development in Mechatronics and
Measurement Technique (INCDMTM), which is the main organizer of our con-
ference, and that is an organization that has been writing the history of
Mechatronics in Romania for 40 years, has strived to keep up with the trends and
developments in the field. Consequently, we have changed the concept and the
structure of former International Conference of Mechatronics and
Cyber-Mix-Mechatronics (ICOMECYME), and we have established ICoRSE—The
International Conference on Reliable Systems Engineering.
As of this year, ICOMECYME, which used to have a rich tradition behind (it
derives from MECAHITECH International Symposium too), aims to adapt to the
challenges of the field of mechatronics and that of related engineering fields, thus
becoming ICoRSE.
The conference that my team and I are coordinating aims to promote scientific
research results and technological developments in reliable systems engineering,
cyber-physical systems, mechatronics, applied mechanics and complementary
fields, by facilitating the interaction and exchange of experience and good practice
between experts in universities, research institutes and private companies.
v
vi Foreword
I would like to take the chance to thank all the authors for their valuable
contributions. Given the reasons mentioned in the first lines, I appreciate their effort
more than ever. This is the first year that I am coordinating an international con-
ference, and it is a great honour to benefit from such valuable works. I am also very
proud to say that the papers we have reunited in the form of these proceedings come
from all major parts of the world. The collected papers are from Europe, Asia,
North and South America, and the fact that the country of origin of the authors of
papers is so diverse, along with the rich scientific contents debated in the papers,
makes me able to strongly stress out the importance of this event and to express my
belief that ICoRSE 2021 is–indeed–a conference that can render the current state
of the art of mechatronics.
To conclude, I would like to thank the organizing team members for their
support in all areas. An international event is a matter of team work above anything,
and it is important to acknowledge the efforts of my colleagues too. Also, the
excellent collaboration with Springer is to be pointed out, and I am highly thankful
for the support offered by Mr. Holger Schaepe and Mr. Thomas Ditzinger in the
development of the work herein.
I genuinely hope that the readers of the proceedings will find the current book
interesting and useful.
Doina-Daniela Cioboată
Contents
Study of a Test Stand for Determining the Oil Density

in Hydraulic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mihai Avram, Valerian-Emanuel Sârbu,
and Mariana-Florentina Ştefănescu
The Absorbents Nanoporous Structures Regeneration for Industrial
Dryers by Microwave Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Sergey Dobrotvorskiy, Aleksenko Borys, Vitalii Yepifanov,
Yevheniia Basova, Ludmila Dobrovolska, and Viktor Popov
Lifetime of Optical Fibers Submitted to Thermo-
Mechanical Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
R. El Abdi, R. Leite Pinto, G. Guérard, and C. Capena
Design of a Mobile Robot to Work in Hospitals and Trajectory
Planning Using Proposed Neural Networks Predictors . . . . . . . . . . . . . . 32
Şahin Yıldırım and Sertaç Savaş
Design and Measurement of the Peltier Cell Thermal Actuator
for Fine Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Jan Hošek
S-Shape Feedrate Scheduling Method with Smoothly-Limited Jerk
in Cyber-Physical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Volodymyr Kombarov, Volodymyr Sorokin, Yevgen Tsegelnyk,
Sergiy Plankovskyy, Yevhen Aksonov, and Olena Fojtů
Selecting the Method for Pre-tightening Threaded Connections
of Heavy Engineering Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Anatoliy Gaydamaka, Yuriy Muzikin, Volodymyr Klitnoi,
Yevheniia Basova, and Sergey Dobrotvorskiy
vii
viii Contents
Production Scheduling of Semiconductor Wafer Fabrication Facilities

Using Real-Time Combinatorial Dispatching Rule . . . . . . . . . . . . . . . . . 78
Suraj Panigrahi, Srijeta Agrahari, José Machado, and V. K. Manupati
Microindentation Hardness Testing of D – gun Sprayed Coatings . . . . . 91
Oleksiy Romanchenko, Oleksandr Lohunov, Yuriy Kharlamov,
Volodymyr Sokolov, and Oleg Krol
Application of Magnetic Field on Lubricating Cooling Technological
Condition in Metal Cutting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Umarov Erkin, Mardonov Umidjon, and Shaozimova Umida
Rapid Prototyping of a Lower-Body Exoskeleton
for Paraplegia Patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Filip-Alexandru Harmon and Patricia-Isabela Brăileanu
Methods for Testing the Strength of Layers for Different
Optical Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Ciprian Ion Rizescu, Ionela Ghita, and Dana Rizescu
Force Simulation of Bird Strike Issues of Aircraft Turbojet Engine
Fan Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Vyacheslav Merculov, Mykola Kostin, Gennadii Martynenko,
Natalia Smetankina, and Volodymyr Martynenko
ROBO-PVAFM Proper Software Platform . . . . . . . . . . . . . . . . . . . . . . 142
Adrian Olaru, Tiberiu Dobrescu, and Serban Olaru
Hardening, High-Speed Steel R6M5, Using a Combined Heat
Treatment Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Umarov Tolibjon
Increasing the Abrasive Wear Resistance of Steels by Heat
Treatment with Preliminary Preparation of the Structure . . . . . . . . . . . 162
Darob Berdiev, Botir Saydumarov, and Nargiza Makhmudova
Biodegradable Starch-Based Polyvinyl Alcohol Films with
Zinc-Oxide Particles for Wound Dressing Applications . . . . . . . . . . . . . 171
Mohammad Mohsen Delavari and Ion Stiharu
Compliant Positioning System with 6 DOF for High Precision Medical
Standing Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Mihai Tutoveanu, Nichita Larisa Milodin, Nicoleta Mirela Popa,
Flavia-Petruța-Georgiana Artimon, and Constantin-Daniel Comeagă
Formation Structure of Cement Systems Under the Influence
of Chemical Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Makhmudova Naima
Contents ix
Increasing the Accuracy of Calibration Device for Measuring

the Moisture of Bulk Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Erkin Uljaev, Shohrukh Narzullayev, Ubaydullayev Utkir,
and Sulaymonova Shoira
Device for Processing Micro-bores by Electrical
Discharge Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Aurel Mihail Țîțu and Alina Bianca Pop
Communication and Control Algorithms for a Heterogenous
Multi-agent System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Andrei Cristian Dinu, Paul-Nicolae Ancuța, and Victor-Marin Zafiu
Development of Measurement Scales for Measuring Performance
Value in the Market of Research, Development, and Innovation
in Technical Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Nina Antičić
Mathematical Model for Calculating Heat Exchange . . . . . . . . . . . . . . . 243
Turakhodjaev Nodir, Tursunbaev Sarvar, Jeltukhin Andrey,
and Meliboyev Yahyojon
Technologies for Thin Layers on Ceramics Substrate . . . . . . . . . . . . . . 250
Georgeta Ionascu, Elena Manea, Raluca Gavrila, and Edgar Moraru
Flexural Test of 3D Printed Mecanum Rollers . . . . . . . . . . . . . . . . . . . . 266
Victor-Marin Zafiu, Diana-Maria Cotorobai, Ana Maria Eulampia Rolea,
and Andrei Cristian Dinu
Predictive Motor Speed Control for an Industrial Robot.
A Dead-Beat Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Iulia Clitan, Cristina Stancioi, and Vlad Muresan
Mathematical Model of the Stress State of the Antenna Radome
Joint with the Load-Bearing Edging of the Skin Cutout . . . . . . . . . . . . 287
Sergei Kurennov, Natalia Smetankina, Vladimir Pavlikov,
Darya Dvoretskaya, and Vladyslava Radchenko
Intelligent Network for Measuring Natural
Environment Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Paul-Nicolae Ancuţa and Sorin Sorea
Compression Testing of PA2200 Additive Manufactured
Lattice Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Nichita-Larisa Milodin, Nicoleta-Mirela Popa, Mihai Tutoveanu,
and Flavia-Petruta-Georgiana Artimon
The Use of CPS for Assistive Technologies . . . . . . . . . . . . . . . . . . . . . . . 316
Pierluigi Rea, Erika Ottaviano, and Maurizio Ruggiu
x Contents
Mathematical Modeling and Simulation in Sheet Hydroforming

Process for the Parts of Space Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Manh Tien Nguyen and Truong An Nguyen
Approach to Product Quality Requirements in the Context
of Aeronautical Domain Process Modeling . . . . . . . . . . . . . . . . . . . . . . . 337
Aurel Mihail Țîțu and Gheorghe Ioan Pop
Pulsed Fiber Laser Surfaces Micro-processing - Optimization
and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Daniela Doina Cioboata, Mircea Udrea, Mihai Selagea,
Danut Iulian Stanciu, Silvia Savencu, Radu Mihail Udrea,
and Cristian Logofatu
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Study of a Test Stand for Determining the Oil
Density in Hydraulic Systems
Mihai Avram1 , Valerian-Emanuel Sârbu2(B) , and Mariana-Florentina Ştefănescu2

1 Faculty of Mechatronics and Mechanical Engineering, Mechatronics and Precision
Engineering Department, University Politehnica of Bucharest, Bucharest, Romania
2 University POLITEHNICA of Bucharest, Bucharest, Romania
Abstract. The purpose of this paper is to document the development of a test

stand that enables experimentally determining the viscosity of the fluid used in
a hydraulic system. This test stand also doubles as a method for determining the
influence of the temperature and pressure on this parameter.
The resulting setup allows full control of the system while also measuring
and processing the measured data. For the core of this type of system a microcon-
troller was selected. High performance transducers are used for ensuring accurate
measurements, they provide a proportional electrical output. The microcontroller
firmware mostly runs as a command processor, a Lab View program is responsible
for communicating with it in order to acquire data and control the system variables
in a predefined sequence.
Keywords: Hydraulic oil · Density · Hydraulic drive system · The theoretical

and experimental analysis
1 Introduction
Hydraulic systems use pressurized fluid to transfer the energy from the pump to the
desired system. At first, hydraulics appeared and rapidly evolved in applications that
require the control of high power, high inertia and forces with relatively high accuracy;
furthermore, they also facilitate full control of the position and speed. The method
by which the delivery of hydraulic power is adjusted gives hydraulic transmissions
advantages compared to electrical and mechanical transmission systems [1, 2].
In order to determine the performances of this type of system, static or dynamic, there
are two methods available depending on the circumstances: theoretical and experimental.
In practice we generally encounter two scenarios:
When the real system is available.
When it needs to be designed and then manufactured.
In both cases the system needs to be mathematically defined [6]. Mathematical
models of systems that use a liquid transport medium include several equations that
describe its movement if the following parameters are known: fluid density - ρ, Elasticity
modulus - E, Dynamic viscosity - η and cinematic viscosity - μ.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

D. D. Cioboatǎ (Ed.): ICoRSE 2021, LNNS 305, pp. 1–7, 2022.
https://doi.org/10.1007/978-3-030-83368-8_1
2 M. Avram et al.
Mathematical models are used for describing existing machines and for designing
new ones. The first case is used in attempts to determine optimum functional parameters
of the system in order to improve its overall performance. Thus, it requires knowing
these parameters and the way they vary in time. This can be accomplished with an
experimental test stand that is designed specifically for this purpose. In order to ensure
that valid values are measured the system must be designed with accuracy in mind, the
transducers need to be of high quality along with the acquisition system. Temperature,
pressure and flow sensors are necessary in this setup. The control and data acquisition
are done with a control unit built around a microcontroller [3–5].
Designing of this system was done with some targets in mind, some are considered
general practice while others are application specific:
• Rapid deployment of the equipment and its components

• Being able to measure both static and dynamic variables
• Lightweight, robust and compact design
• The usage of standard and readily available components
• Can adapt to different sensors
• Needs to be designed with current easily available technology
• Be able to easily acquire the components in due time
Following these guidelines results in: high cost for designing and measurements,
complex test setups, expensive equipment, and poor time usage.
Up next, the experimental test stand that enables the measurement of the fluid density
and the test procedures will be described.
2 Methodology and Experimental Details
To be able to experimentally determine the density of a mineral oil, used as work medium
in a hydraulic drive system, a stand has been designed and built with the corresponding
functional scheme presented in Fig. 1A.
The proposed stand contains the following equipment:
– the hydraulic power generation group GGE, group containing the fixed flow pump P
and safety valve Ssig ;
– proportional valve SP;
– classic hydraulic valve 3/2, with a preferential position and electrical control DHC;
– proportionate butterfly valve DrP;
– flow transducer Tq ;
– pressure transducers TPav s, i TPam ;
– temperature transducer TT ;
– electronic acquisition and control block BEAC.
Observation: The proportionate butterfly valve DrP used is a proportional hydraulic

distributor, model 4 WREE 6 EA08-2X/G24K31/A1V, manufactured by Rexroth Bosch,
to which the holes A and T are plugged (Fig. 1B).
Study of a Test Stand for Determining the Oil Density 3
Fig. 1. Functional scheme of the experimental stand (A); Proportional hydraulic valve (B)
Proportional equipment used, proportional valve SP and the proportional butterfly

valve DrP are served by proportional amplifiers AESP and AEDrP .
Figure 2 presents two images of the experimental stand designed and realized by us,
where A represents the electronic control block and B represents the hydraulic power
generation group.
Fig. 2. Main components of experimental setup, with the electronic control block (A) and
hydraulic power generation group
The presentation will be clear and concise, and the symbols used therein will be spec-
ified in a symbol list (if necessary). In the paper the International System measurement
units will be used. There will however be no apparatus or installation descriptions.
The initial condition of the system is defined as follows:
u0 = 0 V, uc1 = 0 V and uc2 = 0 V

4 M. Avram et al.
In this situation the distributor DHC assumes the position (0), the flow section through
the proportional hydraulic butterfly valve DrP is zero, and the proportional valve SP is
open (no flow resistance).
From this moment experimental determinations can start, which involve the
following steps:
Start the hydraulic power generator unit and apply a control voltage (u0 = 24 V) to the
GGE, the distributor electromagnet DHP will engage and the distributor will materialize
the position (1));
At the input of the amplifier AESPis a voltage is installed uc2 ∈ [0,10] V which pro-
vides the desired hydraulic pressure to the hydraulic system; this pressure will be con-
stantly maintained during the experiment, as in the memory of the microcontroller that
is integrated in the electronic acquisition and control block BEAC there is an algorithm
specifically designed for this purpose;
First the electronic amplifier AEDrP is supplied with a voltage of uc1 = 1 V;
Measurement is done using the system transducers: Pam , Pav , q, x and t;
Finally, there is the increasing of the voltage uc1 by uc1 ; previous steps are repeated
until target voltage uc1 = 10 V is reached.
Same pattern but in reverse (from 10 V to 1 V) is then applied;
3 Experimental Determination of Mineral Oil Density
Fig. 3. Experimental results
Figure 3 shows the results obtained for two set feed pressure values Pam , i.e.25 bar
and 30 bar.
For a set of experimentally determined values, the density of the oil can be calculated
with the relationship [6]:
2
ρ= · S 2 (uc ) · (Pam − Pav ) (1)
q2 c
The law of variation of the flow section is not known, the only certain thing is the maxi-
mum stroke of the drawer xmax = 1,25 mm as this value is specified by the manufacturer
in the catalog tab of this equipment.
For this reason, we have attempted at the theoretical determination of the variation
law of the flow section. For the drawer geometry indicated by the manufacturer in the
documentation of this equipment, the following expression of the flow section has been
determined:

b 2 2 b
S(x) = n · · arccos 1 − · (x − la ) − − (x − la ) · x − la · b − (x − la )
2 b 2
(2)
where:
n – the number of channels processed on the drawer in the control area;
b – the width of the channel;
la – cover length.
This expression is valid for x ∈ [la , l a + b/2]. In the range [0, la ) the flow section is
null.
Figure 4 shows the variation of the flow section according to the spool position for
different situations.
Below we consider that the flow section through the butterfly valve corresponds to
the variant (*) on the graph (see 4). In this case, the maximum value of the flow section
is obtained for xmax = 1.25 mm and is Sc,max = 5,8 mm2 .
Following the measurements, for a maximum control voltage were obtained the
following values:
p = Pam − Pav = 20, 469 bar

q = 23, 61 l/ min
Oil density can be now calculated with the relation (1) as follows:
2
ρ = 360 · · 5, 82 · 20, 469 = 889, 39 kg/m3
23, 612
The stand allows determination of density variance with pressure and temperature.
Because the connections between the stand equipment are made with metal inserts rubber
hoses, the maximum system pressure must be limited to 80 bar. Within this scope, density
variance with pressure is insignificant and most of the times the density is assumed to
be constant. Keeping the same stand structure and making couplings of the equipment
with metal ducts, the working pressure may be increased to 320 bar a situation where
the determination of density variation with temperature makes sense.
6 M. Avram et al.
Fig. 4. Variation of flow section depending on the position of the drawer
4 Conclusions
Determination of the density of a mineral oil used as a working medium in a hydraulic
drive system under certain working conditions, as well as the dependence of the density
with temperature and pressure is an important issue for which a solution is still being
sought.
The experimental stand designed and made by the authors is an effective solution
to solve the above-mentioned issues. This stand represents, through its hardware and
software structure, a complex system of experimentation and testing, where all activities
are computer assisted.
One of the advantages of the system consist in that the experimental results obtained
can be both directly viewed on the computing system monitor, during the measurement,
which is a great advantage in experimental research, and stored in memory in the form
of csv files, for further data processing and their printing as test /experimental bulletins,
without human operator intervention.
References
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displacement controlled system. IEEE Access 99, 1–1 (2007)
3. Valer, D.: Proiectarea Sistemelor Mecatronice. Editura Politehnica, Timisoara (2007)
4. Ilie, I., Blejan, M.: Distributed Hardware and Software Architecture for Monitoring and Control
of Hydraulic Drives, “HIDRAULICA” (No. 4/2017) Magazine of Hydraulics, Pneumatics,
Tribology, Ecology, Sensorics, Mechatronics
5. Hristea, A., Radoi, R., Tudor, B., Balan, I.: Electronic Module for Data Acquisition and Trans-
mitting for Portable Power Steering Test Equipment, “HIDRAULICA” (No. 4/2017) Magazine
of Hydraulics, Pneumatics, Tribology, Ecology, Sensorics, Mechatronics
6. Avram, M., S, tefănescu, M.F., Sârbu, V.E., Năstase, V.: Theoretical analysis of a hydraulic
drive system. The influence of the work environment on the performance of the system. Int. J.
Mechatron. Appl. Mech. 7, 152–157 (2020)
The Absorbents Nanoporous Structures
Regeneration for Industrial Dryers
by Microwave Energy
Sergey Dobrotvorskiy1(B) , Aleksenko Borys1 , Vitalii Yepifanov1 ,

Yevheniia Basova1 , Ludmila Dobrovolska1 , and Viktor Popov2
1 National Technical University “Kharkiv Polytechnic Institute”,
2, Kyrpychova street, Kharkiv 61002, Ukraine
sergiy.dobrotvorskyy@khpi.edu.ua
2 Joint Stock Company “FED”, 132 Sumska Street, Kharkiv 61023, Ukraine
Abstract. The presented work is devoted to solving the problem of energy con-
servation in industrial production. Modern industrial equipment and technological
processes use compressed air energy. Wherein deep drying of compressed air is
often required. The air preparation process is an expensive and energy-intensive
process. Reducing useless energy losses, in this case, is possible through the use
of innovative technologies that are technically feasible and economically justified.
The adsorption air dryer’s efficiency feasibly increased by using microwave energy
to regenerate the adsorbent by deporising water molecules from its nanoporous
structure. This paper explores the application of this regeneration technology in
air dryers wich have high throughput. The scientific novelty of this submitted
research lies in this study of the regularities of the spatial distribution of thermal
and electromagnetic energy and their uniform distribution in the adsorbent volume
if the proposed innovative technology is applying. Also, it was establishing the
dependence of the intensity of exposure to microwave energy depending on the
frequency, voltage level, and design features of the adsorption tower. The prac-
tical significance lies in the proposition of a new technological process for the
regeneration of the adsorbent in adsorption dryers with high performance.
Keywords: Nanopores · Air dryer · Regeneration · Microwave energy
1 Introduction
Nanotechnology is used intensively in modern industrial [1–4], agricultural [5], and food
[6, 7] production. In particular, the use of nanostructures has become widespread in the
technological process of drying compressed air using adsorption technologies. Today,
adsorption dryers are the main type of equipment that can provide modern technology
processes with high-quality compressed air.
The problem of increasing the efficiency of adsorption dryers is to reduce energy
costs and increase the intensity of the process of periodic desorption of accumulated
moisture from the nanoporous structure of the adsorbent.

https://doi.org/10.1007/978-3-030-83368-8_2
The Absorbents Nanoporous Structures Regeneration 9
Today the conventional adsorbent regeneration technology uses heated purge air
for drying the adsorbent [8–11]. Air dryers with hot regeneration of the adsorbent are
currently the most economical means of producing dried air and the development of the
design of this type of equipment is the most important direction to improve the energy
efficiency of industrial production.
In this case, energy is transferred from the electric heater to the purge air, then from
the heated air to the adsorbent material, and only then to the water molecules in the
pores. At the same time, at the stages of energy transfer, its non-productive losses occur.
It is possible to qualitatively increase the efficiency of adsorption dehumidifiers by
applying new technology for removing moisture from the nanoporous structure of the
adsorbent, which will make it possible to act directly on water molecules.
We have proposed a regeneration technology using the energy of microwave radi-
ation. The electromagnetic field created in the cavity of the adsorption column causes
accelerated movement of water molecules in micro-pores, which leads to deporization of
moisture and its subsequent evaporation from the surface of the adsorbent granules. The
impact of microwave energy on an adsorbent saturated with water leads to an increase
in its temperature. This makes it possible to purge the adsorbent volume with a stream
of unheated air.
Studies show that the use of microwave radiation reduces the energy loss, which is
spent during the regeneration of the adsorbent [12, 13]. Microwave energy acts directly on
water molecules. This avoids unproductive convective and conductive heat losses, which
is inevitable in the case of using classical regeneration technology [14, 15]. Under the
influence of microwave radiation, the drying of the adsorbent occurs more intensively,
faster [16–29], and at a lower temperature [30]. This makes it possible to reduce the
energy consumption for the regeneration of the adsorbent and the consumption of dried
air for the subsequent cooling of the adsorbent.
The presented article examines the use of high-frequency exposure to adsorbent
adsorption dryers with high throughput.
2 Research Problem
The process of regenerating serves to remove moisture desorbed from the porous
structure of the adsorbent.
The completeness of regeneration depends on the uniformity of energy distribution
in the volume of the adsorbent [31–37]. All areas of the adsorbent volume must be
energized. This eliminates the occurrence of residual zones with high moisture content
in the porous structure. Also, the design of the adsorption tower must ensure a uniform
laminar flow of purge air through the entire volume of the adsorbent. Stagnant zones
with a low flow rate of purge air prevent complete moisture removal, which reduces the
quality of regeneration.
Our earlier studies [38–42] have shown the possibility of using a magnetron with
a wave-guide system for the action of microwave energy on a small volume of the
adsorbent. The low price of this design makes it advisable to use microwave regeneration
in dryers with a productivity of 1.5 m3 /min and less [43]. The problem of using one or
10 S. Dobrotvorskiy et al.
a group of magnetrons to regenerate a large volume of adsorbent is the limited depth of

wave energy penetration into the bulk of the material.
It should be taken into account that silica gel loses its useful properties when it
overheats above 200 °C. From this, it follows that an increase in temperature above this
limit to intensify the process of regeneration of the adsorbent is unacceptable. Thus,
an unlimited increase in the parameter is not possible to increase the intensity of the
regeneration process.
In a column with a diameter of 100 mm, it is possible to achieve a uniform distribution
of energy without the appearance of peripheral overheating zones due to heat exchange
in the horizontal section of the column. In this case, the microwave energy does not
intensively affect the inner layers of the adsorbent (Fig. 1, pos.5).
Fig. 1. Design of adsorption columns with pole plates and waveguide system and energy
distribution in the adsorbent volume.
An increase in the number and power of magnetrons leads to the appearance of local
overheating zones on the outer layers of the adsorbent volume without increasing the
total intensity of regeneration. Dehumidifiers with a productivity of 5 m3 /min and more
have an ad-sorption tower diameter of more than 250 mm and cannot use microwave
radiation effectively enough due to the limited penetration depth. Meanwhile, high-
capacity dehumidifiers are widely used in production. Also, in the chemical and gas
industry, adsorption plants are used in which the diameter of the adsorption columns is
several meters. In this case, exposure to radiation from the outside does not affect even
if the energy is uniformly distributed over the outer surface of the adsorbent volume.
To solve this problem, it is proposed to use concentric pole plates, which are located
in the volume of the adsorbent (Fig. 1, pos.1).
Pole plates are made in some form:
1) several nested cylinders (Fig. 2, pos. 1), the axes of which coincide with the axis of
the column;
2) two nested spirals (Fig. 2, pos. 2);
3) a set of parallel planes (Fig. 2, pos. 3) inscribed in the cylindrical volume of the
adsorption column.
Fig. 2. Variants of the pole plates placement in the adsorption column cavity (column horizontal
section, top view).
The presented study is devoted to the study of the effect of microwave energy on the
adsorbent in a dryer with columns having cylindrical pole plates.
3 Materials and Methods
The research is carried out using several mathematical multiphysics computer models
of adsorption column. The models are constructed to study the movement of the purge
airflow through the adsorbent, the intensity of the high-frequency effect on the adsorbent,
and to evaluate the uniformity of temperature distribution in its volume. Simulation is
performed using the Komsol Multiphysicstm software environment.
The calculation is carried out using the mathematical model of a desiccant adsorption
tower with a capacity of 50 m3 /min. The adsorption tower model is a hollow cylindrical
body. The cylinder is closed from two ends with elliptical bottoms. The body material is
steel. Concentric pole plates are located inside the column body. An adsorbent is placed
in the spaces between the pole plates (Fig. 1, pos. 2,4). Thus, the adsorbent volume is
divided by plates into separate concentric cylindrical volumes.
The purge air blowing is carried out in the vertical direction, with the blowing air
moving through the adsorbent bed endlong the pole plates.
The purge air moves from the top-down direction, (Fig. 4) along the axis of the
adsorption column.
Adsorbents have a different porosity at a scale of a separate granule. This defines
the adsorption capacity and affects the intensity of the regeneration process.
The gas-dynamic process, considered at a scale of the adsorption column, will be
determined by the size and shape of the adsorbent granules. This defines the bulk density
of the adsorbent volume. The adsorbents, used in dryers, have the same characteristics:
adsorbent granules have a spherical shape and a diameter of 3 to 7 mm. The normal
range of porosities in granular systems is 5% to 35%. A hexagonal or cubic close pattern
is assumed with the calculated packing density is 0.7045, gives a porosity void fraction
of 0.2955, provided that all the balls are the same size. The difference in grain size will
create a lower porosity. But adsorbent retaining grids of modern dryers can remove small
granules and products of their shredding. Due to this the spread in the diameters of the
granules is small. This makes it possible to use in the model the value of porosity of
the adsorbent volume to be 20%. Granules will not give closed pores, so the effective
porosity is considered equal to 100%. The physical properties of silica gel are shown in
the table (Table 1). The properties of silica gel [44] are corrected taking into account the
moisture content and the bulk density of wet silica gel.
Table 1. Silica gel physical properties.
Parameter Dimension Value

Density kg/m3 2900
Bulk density kg/m3 780
Heat capacity j/(kg*K) 730
Relative permeability 1 16
Relative permittivity 1 4,1
Electric conduction S/m 0
Heat conduction W/m 0,2
Linear dimensions of the model (Fig. 3) are given in the table (Table 2). The model
uses steel material for the column and walls.
Since the flow rate of the purge air in the column throughout the entire path does not
exceed 1.2 m/s, the flow is calculated as laminar flow using equation [45, 46].
Fig. 3. Linear dimensions of the adsorbent volume and the distance between the pole plates.
Table 2. Linear dimensions of the adsorption column.
Index Size Dimension, mm

H Column height 1000
D Column diameter 760
a Distance between the pole plates 32/40/64
The impact on the adsorbent of high-frequency energy is carried out by applying an

alternating voltage to the pole plates. The process is modeled as inductive heating. An
alternating voltage across the pole plates is generated using a sinusoidal function with a
given angular frequency. The voltage is determined by the amplitude of the function.
The stationary problem of the air medium’s motion was calculated by the equation:
2
ρ(u · ∇)u = ∇ −pl + μ ∇u + (∇u) − μ(∇ · u)l + F
T
(1)
3
∇ · (ρu) = 0 (2)
where: u - is the velocity, p - is the pressure, and μ - is the dynamic viscosity.

Fig. 4. The movement of the purge air in the adsorbtion column cavity and also through the
adsorbent layer.
The movement of air in the volume of the adsorbent was modeled as a motion in a
porous medium and was calculated by the equation:

1 1 1 2 1
ρ(u · ∇)u = ∇ −pl + μ ∇u + (∇u)T − μ (∇ · u)l
∈p ∈p ∈p 3 ∈p

θm
− μk −1 + βF |u| 2 u + F (3)
∈p
∇ · (ρu) = Qm (4)
where: θm - the value of porosity of the material.

The dynamic heat transfer problem was calculated by the equation:
ρCp u · ∇T + ∇ · q = Q + Qvd (5)
q = −keff ∇T (6)
where: Cp - heat capacity value, T - temperature, Q - quantity of heat.

Heat transfer in a porous medium was calculated as:

keff = θp kp + 1 − θp k + kdisp (7)
where: θρ - is the volume fraction of the material, kρ - is the thermal conductivity.

The influence of purge air flow on thermal processes in the column is calculated as
dynamic heat transfer model through the following equations:
∂T
ρCp + ρCp vtrans · ∇T + ∇ · q = Q + Qted (8)
∂t
where ρ is the density, Cp – heat capacity, q – heat flux, T – temperature, Qe – heat
sources and sinks.
The initial temperature of the adsorbent is the same at all points in the volume of the
adsorbent and is 20 °C. The purge air also has an initial temperature of 20 °C. The same
temperature is conventionally considered the adsorption temperature.
The electric field generated in adsorbent volume is calculated with equations:
jσ
∇ × (μ−1
γ ∇ × E) − k0 εγ −
2
E=0 (9)
ωε0
∇ · J = Qj,v (10)
J = σ E + jωD + Je (11)
ω = 2π f (12)
where μγ is the complex relative permeability; E – complex amplitude representing

an oscillating electric field; εγ – complex relative permittivity; ω – circular (angular)
frequency, k0 – phase constant of free space, σ – electrical conductivity, j – is an imag-
inary unit, J – externally generated current density, D – electric displacement, Qj,v
– charge, f – frequency (Fig. 5).
Fig. 5. Variable electrical potential in the space between the pole plates.
The heating of the adsorbent due to the effect of alternating voltage is calculated as:
ρCp u · ∇T = ∇ · (k∇T ) + Qe (13)
Qe = J · E (14)
The force, which is effects on the water molecule is calculated as:
F =ρ·E (15)
∂E
F= i ρi (16)
∂xi
U
E= (17)
d
E = −∇V (18)
where F is the electric displacement, ρ – dipole moment, U – potential difference, d

– distance between the pole plates, V – electric potential.
The calculations were carried out in the time interval from 0 to 180 min, with step
5 min.
4 Results and Discussion

The calculation of the computer model shows that the high-frequency action can be used
to increase the temperature in the adsorbent volume for regeneration (Fig. 6).
Neglecting the change in the absorption coefficient of water as the frequency changes
and also taking into account that the dipole moment of water (1.84 Debye) is a constant
value, we can influence the efficiency of exposure to microwave energy by changing the
frequency of exposure (9), the voltage between the pole plates and the distance between
them (17).
The calculation of the comparative model shows the positive effect of increasing the
frequency on the dynamics of the growth of the average temperature of the adsorbent
volume (Fig. 7).
It should be noted that obtaining a high polarization frequency is a technically dif-
ficult task and requires specialized equipment. This is because most general-purpose
semiconducting elements operate effectively in the frequency range up to 20 MHz. In
this case, the problem of high voltages commutation is solved relatively easier and
cheaper.
The performed calculation shows a positive effect of an increase in the voltage which
is supplied to the pole plates on the dynamics of an increase in the average temperature
of the adsorbent volume (Fig. 8).
Fig. 6. Dynamics of temperature rise in the volume of the adsorption column under the influence
of microwave energy.
The disadvantage of this method is the danger of high voltage electric shock. There-
fore, increasing the voltage on the pole plates to the level of hazardous ones (over 60 V)
will require complicating the design of the adsorption column. This is due to the need
to ensure the safety of the operating personnel and will entail an increase in the cost of
the dryer design (Fig. 9).
Also, the dynamics of the growth of the average temperature of the volume of the
adsorbent (Fig. 8) are positively affected by a decrease in the distance a between the
pole plates (Fig. 3).
Fig. 7. A figure Dynamics of growth of the average temperature in the volume of the adsorbent
depending on the frequency. Voltage (peak) = 4 V, distance between pole plates = 4 mm.
Fig. 8. The dynamics of the growth of the average temperature in the volume of the adsorbent
depending on the (peak) voltage on the pole plates. Frequency = 2.45 GHz, distance between pole
plates = 4 mm.
Fig. 9. Dynamics of the average temperature growth in the adsorbent volume depending on the
distance between the pole plates. Frequency = 2.45 GHz, Voltage = 4 V.
It should be noted that the specified distance cannot be reduced to a size less than
10 mm, which corresponds to the minimum diameter of the adsorbent granule used in
dryers. Also, reducing the distance between the pole plates will require an increase in
their quantity. This, in turn, will complicate the design of the equipment and entail an
increase in its cost.
5 Conclusions
The presented work shows the possibility of using the energy of microwave radiation
during the regeneration of adsorbents applied in compressed air dryers with high pro-
ductivity, more than 50 m3 /min. It is shown that the impact on the adsorbent using pole
plates makes it possible to uniformly distribute energy in a large volume of the adsorbent.
The influence on the intensity of exposure to microwave energy of such factors
as frequency and voltage on the pole plates, as well as the distance between them is
considered.
The economic effect of the use of microwave energy in the process of regeneration of
nanoporous structures is achieved due to the intensification of drying in comparison with
blowing with preheated air. Research shows the applicability of the described technology
in high throughput adsorption dryers. This opens up opportunities for increasing the
efficiency of this type of industrial equipment.
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tro.5.1.htm
Lifetime of Optical Fibers Submitted
to Thermo-Mechanical Stresses
R. El Abdi1(B) , R. Leite Pinto1 , G. Guérard2 , and C. Capena2

1 Univ. Rennes-CNRS, Institut de Physique de Rennes, UMR 6251, 35000 Rennes, France
relabdi@univ-rennes1.fr
2 Entreprise Acome-Usines de Mortain, 50140 Mortain, France
Abstract. The reliability and the expected lifetime of optical fibers used in
telecommunication technologies are closely related to the thermo-mechanical and
chemical environment actions on silica network. To ensure the long-term mechan-
ical strength of the optical fibers, a polymer coating is applied onto fibre surface
during fiber fabrication. The coating protective action includes several functions,
such as: to protect glass fiber from any external damage, to limit chemical attack,
in particular those of water and temperature.
This paper presents the results of new silica optical fibers aged in hot water
between 20 °C and 70 °C and subjected to mechanical static bending stresses from
2.5 GPa to 3.2 GPa. The mechanical strength of optical fibers aged in distilled water
at different temperatures was studied. Optical fibers were then wound around
ceramic mandrels with different diameters in order to evaluate the influence of
the static bending stresses on the lifetime of the fiber. Dependence of the time
to failure on temperature was observed and different fatigue parameters such as
activation energy, fiber lifetime and stress corrosion parameter can be analyzed
and a behavior law can be proposed.
Keywords: Optical fibers · Thermo-mechanical stresses · Lifetime · Bending

tests · Stress corrosion parameter
1 Introduction
Optical fibers are key components in telecommunication technologies. Apart from opti-
cal specifications, optical fibers are expected to keep most of their physical properties
for 10 to 20 years in current operating conditions. Fiber failure makes an irreversible
accident which may occur when an external stress is applied on a defect located on fiber
surface. While intrinsic defects, referred to as Griffith flaws, lead to failure only for large
applied stresses, other heterogeneous defects make a far more serious concern as they
lead to the fiber failure of the aged fibers under moderate stress. The fabrication process
includes a proof test that eliminates the largest defects. However, the chemical action of
water is likely to induce stress corrosion in the long term and to promote fiber aging.

https://doi.org/10.1007/978-3-030-83368-8_3
24 R. El Abdi et al.
Polymer coatings are currently applied to optical fibers to prevent the formation of
surface defects through scratches and abrasion and to minimize the influence of the pre-
existing defects. They also act as a diffusion barrier against the surrounding humidity
reaching the glass surface. Water is known to be one major factor of the propagation of
cracks at fiber glass surface because it makes much easier the breaking of the Si-O bonds
which build the vitreous network [1]. Accordingly, fiber strength is closely related to the
water concentration at the glass surface [2]. It is well known that flaws in glass subject
to stress in humid conditions grow subcritically. Crack velocity is related to applied
stress and also to relative humidity [3]. It has also been reported that the kinetics of the
reaction between silica and water changes at very low water concentration [4, 5]. On the
other hand, the temperature effects accentuate the damage when fibers were submitted
to combined thermo-mechanical stresses.
In this work, optical fibers were wound around ceramic mandrels and aged in distilled
water at different temperatures to evaluate the influence of the static bending stresses
and the temperature on the fiber lifetime.
Change of different physical fiber parameters were analyzed with temperature
variations.
2 Used Test Bench
The used single mode silica optical fibers with thick dual acrylate coating have
242 μm (±5 μm) in diameter, a cladding with 125 μm (±0.7 μm) in diameter and
a zero dispersion wavelength from 1300 nm to 1324 nm (zero dispersion slope ≤
0.092 ps/nm2 .km).
Optical fiber was wound onto a ceramic mandrel of 2.8, 3, 3.2 and 3.4 mm in diameter
(Fig. 1). The winding of each fiber was automated and the same applied stress was
obtained for each fiber. The real deformation for each fiber depends on the mandrel
diameter and each fiber has taken on the exact shape of the mandrel (Fig. 1).
Once the fiber was wound around the mandrel, it was placed between a transmitter
T and a light receiver R (Fig. 1). The light beam cannot reach the receiver and from then
on the time of fiber loading is triggered. The mean time to failure is recorded, and this
corresponds to the time required for the fiber strength to degrade until it equals the stress
applied through winding round the mandrel. The time to failure is measured by optical
detection when the ceramic mandrel moves out of the special holder. When fiber breaks,
the mandrel rocks from its vertical static position, the light beam can reach the receiver
and the time to failure is directly recorded with an accuracy of ±1 s. The testing setup
consists of a large number of vats containing 16 holders each. The fibers (wound around
a mandrel) are aged in water at different temperatures.
Lifetime of Optical Fibers Submitted to Thermo-Mechanical Stresses 25
Fig. 1. Ceramic mandrel with wound fibers
3 Theoretical Background
The Weibull theory is one of the most used methods to characterize the failure of optical
fibers [6]. The statistical Weibull law gives a relationship between the probability F of
fiber rupture with a length L and the applied stress σ:

1 1
Ln Ln = m[Ln(σ ) − Ln(σo )] (1)
L 1−F
where m is a size parameter and σ o is a scale parameter.
The evolution of Ln L1 Ln 1−F 1
according to Ln(σ ) is called Weibull diagram.
This diagram enabled us to calculate m and σ o which respectively correspond to the
curve slope and to the curve intersection with the stress axis.
The m parameter characterizes the defect size dispersion [7]. A high m value indicates
that along the fiber the defects sizes are averaged. A low m value reveals that the defects
found at the fiber surface have varying sizes, which results in different values of the
failure stress. As to the σ o parameter, it represents the stress for which the cumulated
rupture probability of the fiber F is equal to 50%.
To plot the Weibull diagram, which corresponds to a fiber thus characterizing a defect
population, a series of mechanical tests were carried out on a great number of samples
of this fibre (in practice about thirty samples were tested). All the samples were the same
length L. Once the tests were carried out, by ascending order:
σ1 ≤ σ2 ≤ . . . ≤ σι ≤ σι+1 ≤ . . . ≤ σN (2)
(N is the total number of tested samples).

The obtained breaking stresses were classified. For each breaking stress σ i, a rupture
probability Fi is affected using the following estimator.
i − 0.5
Fi = (3)
N
If the rupture is characterized by a single defect category, Ln [(1/L) {Ln (1/(1−F))}]

varies in a linear way with Ln (σ ) and Weibull modulus is given by the slope of this
curve. But when the tests are carried out with large fibers lengths, one observes a slope
break indicating the passage of a defect distribution to another.
On the other hand, the stress-strain relation of optical fibers was first examined by
Mallinder and Proctor [8]. They found that the applied stress σ (GPa) for an optical fiber
is related nonlinearly to the strain ε (where both σ and ε are positive in the tensile region),
according to:

α .ε
σ = E0 .ε 1 + (4)
2
where E 0 is the Young modulus (= 72 GPa for the silica); α’ = 0,75 α. A value for the
non-linearity constant α of 6 can be used [9].
One can note that a wound fiber was subjected to compressive stresses on its internal
part (fiber surface close to the curvature center) and a tensile stress on its external part
(fiber surface furthest away from the curvature center).
A tensile stress is experienced by the outer surface of the fiber. The bending stress
must first be calculated from the mandrel diameter φ. This can be performed with (4)
and the simple expression for the maximum strain ε [10]:
dglass
ε = (5)
φ + dfiber
φ is the mandrel diameter (in μm); d glace is the glass fiber diameter (125 μm); d fiber is
the fiber diameter (242 μm), including the layer polymer coating. This leads, in the case
of a usual fiber, to the corresponding stresses of 3.13 GPa for the calibrated diameter
mandrel of 2.8 mm.
4 Results and Discussion
4.1 Environment Influence
For different mandrel diameters, fibers were aged in air and distilled water at 20 °C.
Figure 2 shows that the water weakens the fibers and a significant number of water
molecules diffused on the cladding leading to reaction between silica network and water
molecules. The ratio between times to failure for aging in the air and in the water was
about 4.
Fig. 2. Time to failure for fibers aged in air and in distilled water at 20 °C
4.2 Temperature Dependence of Failure Time
Fibers rolled around different mandrel diameters (2.8 mm; 3.0 mm; 3.2 mm and 3.4 mm)
were aged in hot water for different temperatures (20 °C, 30 °C, 40 °C, 50 °C, 60 °C
and 70 °C). Weibull plot curves for water temperature of 20 °C and 70 °C are given in
Figs. 3 and 4.
Fig. 3. Weibull’s diagram for fibers aged in distilled water at 20 °C
Temperature plays an essential role in fiber strength weakening. One can note for
example for the mandrel diameter of 3.0 mm, the median time to failure was equal to
30 h when water temperature was 20 °C and 0.5 h when water temperature was 70 °C.
Matthewson and Kurkjian [11] found that the time to failure is therefore inverse
Arrhenius:

Q
tf = C. exp (6)
RT
where Q is the apparent activation energy and R is the perfect gas constant (R =
8.314 J mol−1 K−1 ). Equation (6) shows the high sensitivity of the silica fiber strength
resistance as a function of the temperature change.
Fig. 4. Weibull’s diagram for fibers aged in distilled water at 70 °C
On the other hand, using experimental results, we can obtain the time to failure
change according to the temperature (Fig. 5). For each value, the standard deviation was
about 8%.
Whatever the mandrel diameter, the logarithm of time to failure increases linearly
according to the inverse of temperature as following:

1000
ln(tf ) = a . + b (7)
T

1000. a
tf = C . exp (8)
T
Using Eq. (6), Q values can be obtained (Q = 1000 a. R). Table 1 summarizes C and
Q values. The strain slowly decreases but remains around 3.7%. The activation energy
increases when stress increases from 61 kJ/mol to 82 kJ/mol.
Fig. 5. Time to failure in inverse proportion to temperature for different diameters
4.3 Change of Failure Time According to Applied Stress

The fatigue curves according to the temperature were given in Fig. 6. Two remarks can
be made:
Table 1. Q and C values versus applied stresses.
Mandrel Applied stress (GPa) Deformation Q (kJ/mol) C (h)

diameter (mm) ε (%)
2.8 3.13 4.1 61.16 2.09.10–11
3 2.93 3.8 63.19 2.28 10–11
3.2 2.75 3.6 67.71 1.96 10–11
3.4 2.59 3.4 82.62 3.15 10–13
1/ The fiber lifetime roughly decreases when temperature increases: for an applied
stress σ of 3.13 GPa (Ln (σ ) = 1.14 GPa), the lifetime decreases from 103 min to 2 min
when the aging temperature increases from 20 °C to 70 °C.
2/ All the fatigue curves can be described using straight lines. This linear behaviour
was not obtained when the temperature was greater than 80 °C. Cuellar et al. [12]
observed a change in the curve slope for fibers aged at 85 °C under a stress of 2.7 GPa.
But for a temperature lower than 70 °C and during all the other aging tests, the coating
doesn’t undergo significant damage and the optical behaviour remains linear.
Fig. 6. Time to failure according to applied stress for different temperatures
4.4 Stress Corrosion Parameter Versus Temperature
Stress corrosion parameter n is one of important values which characterize the fiber
reliability.
The generally accepted corrosion parameter, n, is ~20 for high strength fiber [13].
Equation (9) gives the stress corrosion parameter [6] which is the opposite of the
curve slope:

ln tf = −n. ln σ + a (9)
The n values were determined through experimental results. Figure 7 shows a decreasing
behaviour according to temperature. This parameter (n) can be expressed as a linear
function of the inverse of temperature (1/T ):
ao
n(T ) = + bo (10)
T
where ao = 9371.5 K and bo = −8.03.
A high stress parameter n involves a great sensibility to applied stresses.
Fig. 7. Stress corrosion parameter n versus inverse temperature
5 Conclusion
A linear dependence of time to failure was observed for the fatigue of silica optical
fibers as predicted by the exponential law. The apparent activation energy and the others
fiber parameters as the stress corrosion parameter were summarized for all temperature-
dependent fatigue data. This survey illustrates the temperature-dependent fatigue data
for optical fibers aged in hot water and under bending stresses; these data are critical
because they are a standard for all other studies.
References
1. Adams, R., McMillan, P.W.: Review static fatigue in glass. J. Mat. Sci. 12, 643–657 (1977)
2. Gurney, C.: Delayed fracture in glass, Proc. Phys. Soc., London, 59, 169–185 (1947).
3. Wiederhorn, S.M.: Influence of water vapor on crack propagation in soda-lime glass. J. Am.
Ceram. Soc. 50, 407–414 (1967)
4. Duncan, W.J., France, P.W., Craig, S.P.: Strength of inorganic glass. In: Kurkjian, C.R. (ed.)
The Effect of Environment on the Strength of Optical Fiber, p. 351. Plenum Press, New-York
(1985)
5. Mrotek, J.L., Matthewson, M.J., Kurkjian, C.R.: Diffusion of moisture through optical fiber
coatings. J. Lightwave Tech. 19(7), 988–993 (2001)
6. Pinto Leite, R.: Caractérisation physique et thermo-mécanique et analyse de la fiabilité des
fibres optiques à base de silice, Thèse de doctorat de l’Université de Rennes1, Rennes, Juin
(2019)
7. Zhao, F.M., Okabe, T., Takeda, N.: The estimation of the statistical fiber strength by
fragmentation tests of single-fiber composites. Comput. Sci. Tech. 60, 1965–1974 (2000)
8. Mallinder, F.P., Proctor, B.A.: Elastic constants of fused silica as a function of large tensile
strain. Phys. Chem. Glass 5, 91–103 (1964)
9. Glaesemann, G.S., Gulati, S.T., Helfinstine, J.D.: Effect of strain and surface composition on
Young’s modulus of optical fibers. Techn. Digest, 11th OFC, TUG5, 26 (1988)
10. Griffioen, W.: Optical fiber reliability. Thesis edited by Royal PTT Netherlands NV, PTT
Research, Leidschendam (1994)
11. Matthewson, M.J., Kurkjian, C.R.: Environmental effects on the static fatigue of silica optical
fiber. J. Am. Ceram. Soc. 71(33), 177–183 (1988)
12. Cuellar, E., Kennedy, M.T., Roberts, D.R., Ritter, J.E.: Zero stress aging and the static fatigue
transition in optical fibers. In: Proceeding of the Society of Photo-Optical Instrumentation
Engineers, vol. 1791, pp. 7–17 (1992)
13. Matthewson, M.J.: Optical fiber reliability models, Fiber optics reliability and testing. SPIE
Critical Reviews of Optical Science and Technology, CR50, 3–31 (1993)
Design of a Mobile Robot to Work in Hospitals
and Trajectory Planning Using Proposed Neural
Networks Predictors
Şahin Yıldırım(B) and Sertaç Savaş
Mechatronics Engineering Department, Engineering Faculty, Erciyes University,

38039 Kayseri, Turkey
{sahiny,sertacsavas}@erciyes.edu.tr
Abstract. Considering the intense and tiring working conditions in hospitals,

healthcare personnel’s performance decreases during prolonged working times,
and patients are directly affected by this decrease in performance. This study aims
to design and implement a mobile robot that can help healthcare professionals
improve the healthcare industry conditions. In this context, the focus is on the
mobile robot performing two main tasks. The first task is dispensing medication
to patients with an eight-chamber mechanical feeding unit. Thus, patients can take
only their medicines from the defined reservoir by selecting their names or photos
on the touch screen. The second task is to interact with patients to give moral
support with phrases such as “good morning”, “you look great today”. Also, drug
delivery activity is recorded in a database, and the health status of the patients
can be kept under surveillance with the camera on the mobile robot. The designed
mobile robot goes to the patient rooms with magnetic strip tracking. For this
purpose, a controller is designed for the omni-drive robot using MATLAB, and
its performance is simulated. Also, the control velocities that enable tracking the
trajectories are taught to artificial neural networks (ANN), and the requirement
magnetic strip for trajectory tracking is eliminated. In this direction, two artificial
neural networks are compared in terms of their learning performance.
Keywords: Mobile hospital robot · Omni-drive · Controller design · Trajectory

tracking · Neural networks
1 Introduction
Developing technology has brought robotic systems from factories to our daily lives.
Mobile robots, which find many application areas, especially with their mobility fea-
tures, are among the most important research topics of recent years. Until today, many
types of mobile robots have been used to solve different problems. Also, robots used in
mobile applications have very different motion systems [1], and the movement patterns
of animals generally inspire them in their designs. Although the existence of a wheel or
similar system in the animal kingdom is not complete, the wheel design is inspired by
the rolling motion of some insects [2].

https://doi.org/10.1007/978-3-030-83368-8_4
Design of a Mobile Robot to Work in Hospitals and Trajectory Planning 33
Omni-directional wheels are used in many studies on mobile robots due to their driv-
ing flexibility. Kosuge et al. [3] developed a mobile robot called Ms. Dancer. This mobile
robot was designed for dance partnership, using omni-directional wheels in the motion
system. Human-robot physical interaction and coordination were investigated based on
ball dances with the developed robot. This study is an excellent example of mobile robot
applications’ breadth and the flexibility of omni-directional capability. Many studies have
also been done on the control and trajectory tracking of omni-directional mobile robots.
Wang et al. [4] used a model predictive control strategy to control an omni-directional
mobile robot’s trajectory tracking. Liu et al. [5] developed a non-linear controller con-
sisting of a two-stage structure. While the kinematic control approach is applied in the
controller’s outer loop, the Trajectory Linearization Control (TLC) method is used in
the inner loop, which is based on the robot’s dynamic model. Karras and Fourlas [6]
designed a fault-tolerant control scheme to control an omni-directional mobile robot and
accordingly developed a non-linear model predictive controller.
Studies have also been carried out for different configurations of omni-directional
mobile robots. Wang et al. [7] performed trajectory tracking control with the robust
model predictive control (MPC) strategy for a four-mecanum-wheeled omni-directional
mobile robot (FM-OMR). Cooney et al. [8] also designed a four-mecanum-wheeled
omni-directional mobile robot and performed path tracking. They used an optical
mouse to navigate the mobile robot with a dead-reckoning approach. Hashemi et al.
[9] also designed a controller for a four-wheeled omni-directional mobile robot. In
their work, they designed a model-based PI-fuzzy controller. They used the mobile
robot’s linear discrete dynamic model to determine the optimum inputs. Mishra et al.
[10] used the behavioral fault-tolerant-control approach for a four-mecanum-wheeled
omni-directional mobile robot.
Mobile robots are frequently used in the healthcare field. Tan et al. [11] developed
a robotic system for transporting surgical tools in hospitals. They proposed a robust
integrated system for enabling mobile robots to autonomously perform manipulation
of assets. Wang et al. [12] designed a smart robotic hospital bed to transport critical
patients in crowded hospital corridors safely. Again, due to their driving ability, omni-
directional wheels are frequently preferred in mobile robot designs to be used in a hospital
environment. Takahashi et al. [13] designed an omni-directional mobile robot to be used
in transport applications in the hospital domain. They used a four-wheel configuration in
the driving system of the robot they designed. Saekow et al. [14] designed an autonomous
rehabilitation robot and implemented external force/velocity control.
This paper is organized into six sections. In Sect. 2, mechanical, electronic, and
software designs of the mobile robot are explained. In Sect. 3, kinematics of the mobile
robot is given. In Sect. 4, controller design for trajectory tracking, and in Sect. 5, ANN
training of control velocities that will track the determined trajectories is mentioned,
study results and findings are given. In the last section, the 6th section, the results, and
suggestions are emphasized.
2 Mobile Robot Design

The mobile robot will dispense medicine to patients with an eight-chamber mechanical
feeding unit controlled through the interface of a touch screen. Thus, patients will be
34 Ş. Yıldırım and S. Savaş
enabled to take only their medication from the defined reservoir by selecting their names
or photos on the screen. Also, the mobile robot will interact with the patients with words
such as “good morning”, “you look great today” to give moral support to the patients. In
addition to these basic tasks, drug delivery activity will be recorded in a database, and
the general health status of the patients will be recorded with a camera on the mobile
robot to ensure that the healthcare personnel keep the patients under surveillance. In
this direction, the design process of the study consists of three main parts: mechanic,
electronic, and software.
The mechanical parts of the mobile robot consist of;
• Drive system that enables navigation

• A mechanism for drug delivery
• The general construction of the robot
The mobile robot is driven by three omni-directional wheels to be placed at 120°

angles and three different servo motors for each wheel. These wheels provide the robot
omni-drive. Also, these wheels are specially designed and manufactured to increase the
ground grip and increase the carrying capacity of the mobile robot. Omni-directional
wheels and servo motors manufactured to be used in the mobile robot’s driving system
are shown in Fig. 1.
Fig. 1. Omni-directional wheels and servo motors used in mobile robot driving system.
Also, a rotating mechanism with eight chambers that can deliver drugs to eight
different patients is designed. After the patient selection is made on the robot screen, the
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had hitherto done little, came to her, with a contralto voice, and a
request for assistance. After hearing her sing, Grassini exclaimed,
“You have no contralto voice, and need small help. You will have,
with care, one of the finest mezzo-sopranos in the world. Your throat
will be to you a mine of gold, and you may be both rich and
renowned, my dear Giulietta Grisi.” The niece has excelled the aunt.
Knights of the shire are but sham knights now, and they originally
sprung from a revolutionary movement. Previous to the reign of
Henry III. the people had no voice in the selection of their legislators.
In that king’s reign, however, the legislators were at loggerheads.
Simon de Montfort, the aristocratic head of a popular party, was
opposed to the king; and the great earl and his friends being fearful
of being outvoted in the next parliament, succeeded in procuring the
issue of a writ in the name of the king, who was then their prisoner,
directing the sheriffs of each county to send two knights, and the
authorities in cities and boroughs to send citizens and burgesses, to
represent them in parliament. This was a fundamental change of a
long-established usage. It was, in fact, a revolution; and the
foundation at least of that form of a constitution on which our present
constitutional substantiality has been erected.
When the king became emancipated, however, although he
continued to summon “barons and great men,” he never during his
reign issued a writ for the election of knights of the shire. His son,
Edward I., summoned the greater and lesser barons, or his tenants
in chief, according to the old usage. This he did during, at least,
seven years of his reign. The last were not barons, but they were
summoned as “barons’ peers, and all these attended in their own
persons,” and not as representatives of the people. In the reign of
John, indeed, the people’s voice had been heard, but it may be
stated generally, that until the forty-ninth of Henry III., the constituent
parts of the great council of the nation was composed solely of the
archbishops and bishops, the earls, barons, and tenants in capite.
It is a singular fact that, in the early elections, the knights of the shire
were elected by universal suffrage; and so, indeed, they are now, in
a certain way, as I shall explain, after citing the following passage
from Hallam’s State of Europe during the Middle Ages: “Whoever
may have been the original voters for county representatives, the
first statute that regulates their election, so far from limiting the
privilege to tenants in capite, appears to place it upon a very large
and democratical foundation. For (as I rather conceive, though not
without much hesitation) not only all freeholders, but all persons
whatever present at the county court, were declared, or rendered,
capable of voting for the knight of their shire. Such at least seems to
be the inference from the expressions of 7 Henry IV., c. 15, ‘all who
are there present, as well suitors duly summoned for that cause, as
others.’ And this acquires some degree of confirmation from the later
statute 8 Henry VI., c. 7, which, reciting that ‘elections of knights of
shires have now, of late, been made by very great, outrageous, and
excessive number of people dwelling within the same counties, of
the which most were people of small substance and of no value,’
confines the elective franchise to freeholders of lands or tenements
to the value of forty shillings.”
The original summons to freeholders was, without doubt, by general
proclamation, so that, as Mr. Hallam remarks, “it is not easy to see
what difference there could be between summoned and
unsummoned suitors. And if the words are supposed to glance at the
private summonses to a few friends, by means of which the sheriffs
were accustomed to procure a clandestine election, one can hardly
imagine that such persons would be styled ‘duly summoned.’ It is not
unlikely, however,” adds Mr. Hallam, “that these large expressions
were inadvertently used, and that they led to that inundation of
voters without property which rendered the subsequent act of Henry
VI. necessary. That of Henry IV. had itself been occasioned by an
opposite evil, the close election of knights by a few persons in the
name of the county.”
The same writer proceeds to observe that the consequence of the
statute of Henry IV. was not to let in too many voters, or to render
election tumultuous in the largest of English counties, whatever it
might be in others. Prynne, it appears, published some singular
indentures for the county of York, proceeding from the sheriffs,
during the intervals between the acts of the fourth and sixth Henry.
These “are selected by a few persons calling themselves the
attorneys of some peers and ladies, who, as far as it appears, had
solely returned the knights of that shire. What degree of weight,”
says Mr. Hallam, “these anomalous returns ought to possess, I leave
to the reader.”
I have said that the universal suffrage system in the election of these
knights (and indeed of others) as far as it can be carried out, in
allowing all persons present to have a voice, is still strictly in force.
Appeal is made to the popular assembly as to the choice of a
candidate. The decision is duly announced by the highest authority
present, and then the rejected candidate may, if he thinks proper,
appeal from the people present to those who are legally qualified to
vote. The first ceremony is now a very unnecessary one, but it is,
without doubt, the relic of a time when observation of it bore
therewith a serious meaning.
From parliament to the university is no very wide step. Sir Hugh
Evans and Sir Oliver Martext were individuals who, with their titles,
are very familiar to the most of us. The knightly title thus given to
clergymen, was not so much by way of courtesy, as for the sake of
distinction. It was “worn” by Bachelors of Arts, otherwise “Domini,” to
distinguish them from the Masters of Arts, or “Magistri.” Properly
speaking, the title was a local one, and ought not to have been used
beyond the bounds of the University: but as now-a-days with the
case of “captains” of packet-boats, they are also captains at home;
so, in old times, the “Sir” of the University was Sir Something
Somebody, everywhere.
We laugh at the French for so often describing our knights only by
their surnames, as “Sir Jones.” This, however, is the old English form
as it was used at Cambridge. The Cambridge “Sirs” were addressed
by Christian and surname in their livings, and in documents
connected therewith. This practice continued till the title itself was
abandoned some time after the Reformation. The old custom was
occasionally revived by the elderly stagers, much to the
astonishment of younger hearers. Thus when Bishop Mawson of
Llandaff was on one occasion at court, he encountered there a
reverend Bachelor of Arts, Fellow of Bene’t College, and
subsequently Dean of Salisbury. His name was Greene. The bishop,
as soon as he saw the “bachelor” enter the drawing-room, accosted
him loudly in this manner: “How do you do, Sir Greene? When did
you leave college, Sir Greene?” Mr. Greene observing the
astonishment of those around him, took upon himself to explain that
the bishop was only using an obsolete formula of bygone times. The
most recent courtesy title that I can remember, was one given to a
blind beggar who was very well known in the vicinity of Trinity
College, Dublin, where, indeed, he had been a student some five-
and-thirty years ago. He was invariably styled “Domine John,” and
he could return a suitable answer in good Latin, to the query, Quo
modo vales?—or to any other query.
“Vale!” is indeed what I ought to utter to the courteous reader; nor
will I detain him longer—supposing he has kindly borne with me thus
far—than with one brief chapter more, which, being miscellaneous, I
may not inaptly call “Pieces of Armor.”
PIECES OF ARMOR.
The word Pieces reminds me of a curious theatrical illustration of
Macedonian chivalry. When Barry used to play Alexander the Great,
he made a grand spectacle of his chariot entry. But it was highly
absurd, nevertheless. When he descended from the vehicle, his
attendant knights, bareheaded and unarmed, placed their hands
upon it, and in an instant it went to pieces, like a trick in a
pantomime, and left in every warrior’s possession, swords, javelins,
shields, and helmets, supplied by the spokes of the wheels, the
poles, the body of the car and its ornaments. This feat was very
highly applauded by our intellectual sires.
This act, however, was hardly more unnatural than the sayings of
some real chevaliers, particularly those of Spain.
Among the Spanish Rhodomontades chronicled by Brantome, we
find none that have not reference to personal valor. There is the
choleric swordsman who walks the street without his weapon, for the
good reason that his hand is so ready to fly to his sword, if the wind
but blow on him too roughly, he is never able to walk out armed
without taking two or three lives. “I will hoist you so high,” says
another Spanish cavalier to his antagonist, “that you will die before
you can reach the earth again.” It was a fellow of the same kidney
who used not only to decapitate dozens of Moorish heads every
morning, but was wont afterward to fling them so high into the air,
that they were half-devoured by flies before they came down again.
Another, boasting of his feats in a naval battle, quietly remarked, that
making a thrust downward with his sword, it passed through the sea,
penetrated the infernal region, and sliced off a portion of the
moustache of Pluto! “If that man be a friend of yours,” said a cavalier
to a companion, referring at the same time to a swordsman with
whom the cavalier had had angry words, “pray for his soul, for he
has quarrelled with me.” The self-complacency also of the following
is not amiss. A Spanish captain in Paris, saw the haughty chevalier
d’Ambres pass by him. “Is he,” said the Spaniard, “as valiant as he is
proud?” The reply was in the affirmative. “Then,” remarked the
Iberian, “he is almost as good a man as myself.” We hear of another,
less gallant, perhaps, than brave, who made it a great favor to ladies
when he put off a combat at their request, and passed a pleasant
hour with them, in place of knocking out brains upon the field. It was
a knight of similar notions who cudgelled his page for boasting of the
knight’s valor. “If thou dost such foolish things, Sir Knave,” said the
doughty gentleman, “the whole female sex will perish of love for me,
and I shall have no leisure left to take towns and rout armies.” This
was a full-developed knight. It was probably his youthful squire who
remarked, when some one expressed surprise that one so young
had mustaches of such unusual length. “They sprung up,” said the
young soldier, “under the smoke of cannon; they grew thus quickly
under the same influences.”
Some of the old Spanish cavaliers used to maintain that their very
beauty dazzled their enemies. However this may have been, it is a
fact that the beauty of Galeozo Maria, Duke of Milan, was sufficiently
striking to save him for a while, against the daggers of conspirators.
One of these, named Lampugnano, longed to slay him, but did not
dare. He was, nevertheless, resolved; and he employed a singular
means for giving himself courage. He procured a faithful portrait of
the handsome duke, and every time he passed it, he looked
steadfastly at the brilliant eyes, and graceful features, and then
plunged his dagger into the canvass. He continued this practice until
he found himself enabled to look the living duke in the face without
being dazzled by his beauty; and this done, he dealt his blow
steadily, and destroyed his great and graceful foe.
It has often been asserted that there have been few cavaliers who
have carried on war with more indifference and cruelty than the
Spanish knights. But war in all times and in all ages has induced the
first, at least, if not the last. I may cite among what may be called the
more recent instances, one that would hardly have occurred, even at
Sebastopol. It is in reference to Schomberg’s army at Dundalk. “The
survivors,” says Leland, “used the bodies of their dead comrades for
seats or shelter; and when these were carried to interment,
murmured at being deprived of their conveniences.” While touching
upon Irish matters, I will avail myself of the opportunity to notice that
Irish knights were sometimes called “iron knee,” “eagle knee,” and
“black knee,” from the armor which was especially needed for that
part of the body, the Irish with their dreadful battle-axes making the
sorest stroke on the thigh of the horseman. The Irish appellation of
the White Knight, was given to the heir of a family wherein gray hairs
were hereditary. The Irish knights, it may be observed, were
generally more religious than the Spanish. The latter were too ready
to ascribe every success to their own might, and not to a greater
hand. Even in the case of St. Lawrence, calmly roasting to death on
his gridiron, the proud Spaniards would not have this patience
ascribed to the grace of God, but only to the true Spanish valor.
While speaking of the burning of St. Lawrence, I will add that St.
Pierre quotes Plutarch in stating, that when the Roman burners had
to reduce to ashes the bodies of several knights and ladies, they
used to place one female body among eight or ten males, fancying
that with this amalgamation they would burn better. The author of the
“Harmonies of Nature” makes upon this the truly characteristic
comment, that the Roman fashion was founded on the notion, that
“the fire of love still burned within us after death.”
Reverting, for a moment, to the Spaniards, I may notice a fashion
among them which is worth mentioning. When a Spanish cavalier
entered the presence of a Spanish queen, accompanied by his lady,
he did not unbonnet to his sovereign. He was supposed to be so
engrossed by his mistress as to forget even the courtesies of loyalty.
Brantome, on the other hand, notices kingly courtesy toward a
subject. When describing the battle-acts of the famous M. de
Thorannes, he states that the King in acknowledgment that the battle
of Rentz had been gained chiefly through his courage, took the collar
of his own order from his neck, and placed it on that of the gallant
soldier. This was a most unusual act, according to the showing of
Brantome, but probably not the first time of a similar occurrence. The
author just named complains in piteous terms that, in his time and
previously, the honors of chivalry had been bestowed for anything
but knightly deeds. They were gained by favor, influence, or money.
Some set their wives to exert their fascination over the Christian
sovereign, and purchase the honor at any cost. M. de Chateaubriand
gave a house and an estate for the order of St. Michael. Ultimately, it
was conferred on single captains of infantry, to the great disgust of
the better-born gentlemen who had paid dearly for the honor.
Brantome declares that he knew many who had never been half a
dozen leagues from their houses, who wore the insignia of the order,
and who talked of the taking of Loches, as if they had really been
present. He angrily adds, that even lawyers were made knights,
stripping themselves of their gowns, and clapping swords on their
thighs. He appears especially annoyed that the celebrated
Montaigne should have followed a similar example: and he adds with
a malicious exultation, that the sword did not become him half so
well as the pen.
One French Marquis was persecuted by his neighbors to get orders
for them, as if they were applying for orders for the theatre. He
obtained them with such facility, that he even made a knight of his
house-steward, and forced the poor man to go to market in his collar,
to the infinite wounding of his modesty. It was, however, one rule of
the order that the collar should never, under any pretence whatever,
be taken from the neck. The Court had very unsavory names for
these mushroom-knights; and Brantome gives us some idea of the
aristocratic feeling when he recounts, with a horror he does not seek
to disguise, that the order was sold to an old Huguenot gentleman,
for the small sum of five hundred crowns. A cheap bargain for the
new knight, seeing that membership in the order carried with it
exemption from taxation. Luckily for the Huguenot he died just in
time to save himself from being disgraced. Some gentlemanly
ruffians had agreed to attack this “homme de peu,” as Brantome
calls him, to pull the order from his neck, to give him a cudgelling,
and to threaten him with another, whenever he dared to wear the
knightly insignia.
Brantome wonders the more at what he calls the abuse of the order
as it had been instituted by Louis XI., on the ground that the old
order of the Star founded by King John, in memory of the star which
guided the Kings to the Cradle of Divinity, had become so common,
that the silver star of the order was to be seen in the hat and on the
mantle of half the men in France. Louis XI., in abolishing the order,
conferred its insignia as an ornament of dress, upon the Chevaliers
de Guet, or gentlemen of the watch, who looked to the safety of
Paris when the stars were shining, or that it was the hour for them to
do so. It was an understood thing with all these orders that if a knight
went into the service of an enemy to the sovereign head of the order,
the knight was bound to divest himself of the insignia and transmit
the same directly to the King.
Before the dignity of the order was humbled, the members took pride
in displaying it even in battle; although they were put to high ransom,
if captured. Some prudent knights, of as much discretion as valor,
would occasionally conceal the insignia before going into fight; but
they were mercilessly ridiculed, when the absence of the decoration
testified to the presence of their discretion. In the earlier years of its
formation, a man could with more facility obtain a nomination to be
captain of the body-guard than the collar of the order of St. Michael.
Louis XI. himself showed a wise reluctance to making the order
common, and although he fixed the number of knights at six-and-
thirty, he would only, at first, appoint fifteen. Under succeeding kings
the order swelled to limitless numbers, until at last, no one would
accept it, even when forced upon them. One great personage,
indeed, sought and obtained it. He was severely rallied for his bad
ambition; but as he remarked, the emblems of the order would look
well, engraved upon his plate, and the embroidered mantle would
make an admirable covering for his mule.
This sort of satire upon chivalry reminds me that a knight could
unknight himself, when so inclined. An instance occurs in a case
connected with Jeanne Darc. The chevaliers of the Dauphin’s army
had no belief in the inspiration of the Maid of Orleans, until success
crowned her early efforts. The female knight, if one may so speak,
on the other hand, had no measure whatever of respect, either for
knight or friar, who appeared to doubt her heavenly mission. I may
just notice, by the way, that a “board” of seven theologians
assembled to consider her claims, and examine the maiden herself.
One of the members, a “brother Seguin,” a Limousin, who spoke with
the strong and disagreeable accent of his birthplace, asked Jeanne
in what sort of idiom she had been addressed by the divine voice, by
which she professed to be guided: “In a much better idiom than you
use yourself,” answered the pert young lady, “or I should have put no
trust in it.” Here, by the way, we have, perhaps, the origin of the old
story of the stammering gentleman who asked the boy if his m—m—
magpie could speak? “Better than you,” said the boy, “or I would
wring his neck off.” But to resume. Jeanne was quite as nonchalante
to the knights, as she was flippant to the friars. She expressly
exhibits this characteristic, in the first council held in her presence
within Orleans, when she urged immediate offensive measures,
contrary to the opinion of the knights themselves. One of the latter,
the Sire de Gamache, was so chafed by the pertinacity of the
Pucelle, that, at last, springing to his feet, he exclaimed:—“Since
noble princes listen for a moment to the nonsense of a low-bred
hussy like this, rather than to the arguments of a chevalier such as I
am, I will not trouble myself to give any more opinions. In proper time
and place, my good sword will speak, and perchance I may prevail;
but the king and my honor so will it. Henceforward, I furl and pull
down my banner; from this moment I am only a simple ’squire; but I
would much rather have a noble man for master, than serve under a
wench who, perhaps, has been a—one really does not know what!”
and with these words, he rolled up his banner, placed the same in
the hands of Dunois, and walked out of the tent, not Sir John de
Gamache, but plain John Gamache, Esquire.
A curious result followed. The first attack on the bastion of Tourelles
failed, and Jeanne was slightly wounded and unhorsed. Gamache
was near, and he dismounted and offered her his steed. “Jump up,”
cried the good fellow, “you are a gallant lass, and I was wrong in
calling you ugly names. I will serve and obey you right willingly.” “And
you,” said Jeanne, “are as hearty a knight as ever thwacked men or
helped a maid.” And so were they reconciled, and remained good
friends to the end;—which was not long in coming.
Knights, irregularly made so, were unknighted with little ceremony.
Although each duly dubbed knight could confer the same honor on
any deserving such distinction, it was necessary that the individual
about to be so honored should be a gentleman. In France, if this rule
was infringed, the unlucky knight had his spurs hacked off, on a
dunghill. Occasionally the unknighted person was fined. It may be
observed, however, that the king might make a knight of a villain, if
the sovereign were so minded. That is, a king could raise any of his
own subjects to the rank, if he thought proper. Not so with
sovereigns and persons not their subjects. The Emperor Sigismund,
for instance, when visiting Paris, in 1415, knighted a person who was
below the rank of gentleman. The French people were indignant at
this, as an act of sovereignty in another monarch’s dominions. If this
chevalier was not unknighted, the reason, probably, was that the
Emperor might not be offended. It is said, that in Naples it has never
been necessary for a man to be noble, a gentleman in fact, in order
to be a knight. This may readily be credited. In Naples the fact of a
man being a brute beast does not incapacitate him from exercising
the office even of a king.
After all, there appears to have been some uncertainty in the
observance of the law on the subject. In England the custom which
allowed knights to dub other knights, very soon fell into disuse, so
that there are fewer examples of unknighting in this country than in
France, where the custom prevailed down to the middle of the
sixteenth century; and its abuses, of course, rendered the unmaking
of illegally constituted knights, if not common, at least an occasional
occurrence. Henry III., as I have said in another page, summoned
tenants in capite to receive knighthood from himself, and authorized
tenants of mesne lords to receive the honor from whom they
pleased. But there must have been considerable disrating of these
last distinguished persons, or such an abuse of creation, so to
speak, that the privilege was stopped, except by special permission
of the king. Some places, in France, however, declared that they
held a prescriptive right for burgesses to receive knighthood at the
hands of noblemen, without the royal permission. Hallam, quoting
Villaret, says that burgesses, in the great commercial towns, were
considered as of a superior class to the roturiers, and possessed a
kind of demi-nobility.
Ridiculous as modern knights, whether of town or country, have
been made upon the stage, it is indisputable that in some cases the
ridicule has not been what painters call “loaded,” and the reality was
in itself a caricature. I have read somewhere of one city gentleman,
who was knighted during his shrievalty, and who forthwith
emancipated himself a little from business, and aired his chivalrous
“sir” in gay company. He was once, however, sorely puzzled on
receiving a note of invitation from a lady whose soirées were the
especial delight of her guests, and whose note ended with the
initials, so absurdly placed at the termination of an invitation in
English. R. S. V. P., “réponse, s’il vous plait.” The newly-coined
knight, after allusions to the pressure of business, accepted the
hospitality offered him through the note, remarking at the same time,
that “all work and no play made Jack a dull boy,” and that he knew
nothing more to his taste, after a long day’s application, than what
her ladyship’s note appeared to present to him in the initials at its
foot; namely, a Regular Small Vist Party. If this anecdote be not
apocryphal, I suspect that the knight’s remark may have sprung less
from ignorance than humor, and that his reading of the initials was
meant as a censure upon an absurd fashion.
While speaking of city knights at home, and their humor, I will avail
myself of the opportunity to give an instance of wit in a poor
chevalier of the city of Paris, whose whole wealth consisted of a few
unproductive acres near the capital, and whose son had just married
a wealthy heiress of very low degree. “Il fait bien,” said the old
knight, “il fume mes terres!”
This was hardly courteous; but elevated courtesy was never wanting
among true knights, in the very rudest of times.
Strange contrasts of feeling were sometimes exhibited. Thus, when
the English were besieging Orleans, they grew suddenly tired of their
bloody work, on Christmas-day, and asked for a truce while they ate
their pudding. The request was not only readily granted, but the
French knights, hearing that the day was dull in the English camp,
obtained the permission of the bastard Dunois, to send over some
musicians to enliven the melancholy leaguers. The band played
lustily during the whole period of the truce, but the last notes had
scarcely ceased, and the “Godons” as Jeanne Darc rather
corruptively called our great sires, who were too much addicted to
swearing, had hardly ceased uttering their thanks for the musical
entertainment, when their cannonade was renewed by the besiegers
with such vigor, that the French knights swore—harmony had never
before been paid in such hard coin.
There was little ill-feeling consequent upon this. The pages in either
army were allowed to amuse themselves by slaying each other in a
two days’ duel, presided over by the respective generals-in-chief.
This was chivalrous proof that neither party bore malice, and they
beat out each other’s brains on the occasion, in testimony of
universal good-will, with as much delighted feeling as if they had all
been Irishmen. A further proof of absence of individual rancor may
be seen in the fact, that Suffolk sent a gift of pigs, dates, and raisins,
for the dessert of Dunois; and the latter acknowledged the present
by forwarding to the English general some fur for his robe—Suffolk
having complained bitterly of the cold of that memorable February,
1429.
This reminds me of a similar interchange of courtesy between
French and English antagonists, in later times. When brave Elliot
was defending Gibraltar from gallant Crillon, the former, who never
ate meat, suffered greatly (as did his scurvy-stricken men) from a
scarcity of vegetables. Crillon had more than he wanted, and he sent
of his superabundance, most liberally, to the foe whom he respected.
A whole cart-load of carrots and compliments made general and
garrison glad, and Elliot was as profuse in his gratitude as he was
bound to be. It may be remembered that similar exchanges of
courtesy and creature-comforts took place at Sebastopol. Sir
Edmund Lyons sent Admiral Nachimoff a fat buck, a gift which the
large-minded hero of the Sinope butchery repaid by a hard Dutch
cheese. It may be said too that the buck would have been more
appropriately sent to the half-starved English heroes who were
rotting in the trenches.
There were some other naval knights of old, touching whom I may
here say a word.
The history of the sea-kings or sea-knights, whose noble vocation it
was to descend from the north with little but ballast in the holds of
their vessels, and to return thither heavily laden with plunder and
glory, is tolerably well known to the majority of readers. The story of
the Flemish pirates, who, nearly eight centuries ago, carried terror to,
and brought spoil from the Mediterranean, is far less familiar. This
story is well illustrated in the “Biographie des hommes remarquables
de la Flandres Occidentale,” of whom the authors are M. Octave
Delepierre, the accomplished Belgian consul in this country, and Mr.
Carton.
The period is a warm June evening of the year 1097. Off the coast of
Cilicia, two large vessels, belonging to the Emperor Alexis
Comnenus, and manned by Constantinopolitan Greeks, were
surrounded and attacked by ten fast-sailing but small vessels,
belonging to the dreaded “Greek Pirates,” whose name alone
brought terror with the sound. On the prow of each light bark was a
rudely sculptured figure of a lion; from the summit of the tall mast
was displayed a green pennant, which was never hauled down, for
the good reason that the pirates never attacked but where success
seemed certain; and if defeat menaced them they could easily find
safety in flight.
There was scarcely a place on the coast which they had not, for ten
years past, visited; and many merchants purchased exemption from
attack by paying a species of very liberal black mail. It was beneath
the dignity of an emperor to buy safety from piratical rovers, and they
had little respect for his vessels, in consequence.
M. Delepierre informs us that these Flemish pirates had been,
originally, merchants, but that they thought it more profitable to steal
than to barter; and found “skimming the seas,” as the phrase went,
far more lucrative than living by the dull precepts of trade. Their three
principal chiefs were Zegher of Bruges, Gheraert of Courtrai, and
Wimer (whose name still lives in Wimereux) of Boulogne. The force
they had under them amounted to four hundred intrepid men, who
were at once sailors and soldiers, and who are described as being
so skilful that they could with one hand steer the ship, and with the
other wield the boarding-hatchet. It will be seen that our Laureate’s
exhortation to knavish tradesmen to lay down their weights and their
measures, and to mend their ways by taking to the vocation of arms,
had here a practical illustration. In the present case, M. Delepierre
suggests that the pirates were, probably, not less honest men than
the Greeks. The latter were ostensibly on their way to succor the
Crusaders, but Alexis was a double dealer, and occasionally
despatched forces against the infidel, which forces turned aside to
assault those Christian neighbors of his, who were too powerful to be
pleasant in such a vicinity, and to get rid of whom was to be devoutly
desired, and, at any cost, accomplished. The foreign policy of Alexis
was as villanously void of principle as that of any government under
a more advanced period of Christian civilization.
The Greek crews had been summoned to surrender. Gheraert of
Courtrai had called to them to that effect through his leathern
speaking-trumpet. He probably knew little of Greek, and the
Orientals could not have comprehended his Flemish. We may
conclude that his summons was in a macaronic sort of style; in which
two languages were used to convey one idea. The Hellenes replied
to it, however it may have sounded, by hurling at the Flemings a very
hurricane of stones.
The stout men from Flanders were not long in answering in their
turn. “They put into play,” says M. Delepierre, “their mechanical
slings. These were large baskets full of stones fastened to the end of
an elevated balance, the motion of which flung them to some
distance. They had other means of destruction, in enormous
engines, which hurled beams covered with iron, and monster arrows
wrapped in flaming rosin. With scythe-blades attached to long poles,
they severed the ropes and destroyed the sails, and then flinging out
their grapnels they made off with their prize.”
To this point the present battle had not yet come. It had lasted an
hour, the Greeks had suffered most by the means of attack above
noticed; and they had inflicted but trifling injury, comparatively, upon
the men of the green pennant. They refused, however, to surrender,
but prepared to fly. Wimer saw the preparatory movement, and, in a
loud voice, exclaimed:—“A dozen divers!”
Twelve men, quitting their posts, leaped over the side of the boat,
carrying enormous tarières (augers) with them. They disappeared
beneath the waves; appeared for a moment or two again above the
surface, in order to draw breath; once more plunged downward; and,
finally, at the end of ten minutes, climbed again into their small
vessel, exclaiming, “Master, it is done!”
The twelve divers had established twelve formidable leaks in the
larger of the two Greek vessels, and as it began to sink, the crew
agreed to surrender. The Green Pirates seized all that was on board
that and the other ship. In the latter, stripped of everything of value,
they allowed the two Greek crews to sail away; and then proceeded
toward the coast with their booty, consisting of rich stuffs, provisions
and arms. There was far more than they needed for their own wants;
and so, for the nonce, they turned traders again. They sold at a good
price what they had unscrupulously stolen, and the profits realized
by the Flemish rovers were enough to make all honest, but poor
traders, desire to turn corsairs.
Zegher ascended the Cydnus, in order to pay a professional visit to
Tarsis, and was not a little surprised, on approaching the city, to see
formidable preparations made to resist him. On drawing closer,
however, the pirate-leader found that Tarsis was in possession of the
army of Flemish crusaders under the great Count Baldwin; and each
party welcomed the other with joyous shouts of “Long live Flanders!”
“Long live the Lion!” The arrival of the fleet was of the greatest
advantage to the Flemings, who, though they had suffered less than
the French, Italian, and German legions, by whom they had been
preceded, and had been progressively triumphing since they had
landed, needed succors both of men and material, and lo! here were
the Green Pirates ready to furnish both, for a consideration. There
was abundance of feasting that night, and a very heavy sermon in
the morning.
Baldwin was himself the preacher. His style was a mixture of
exhorting with the threatening; and he was so little complimentary as
to tell the Green pirates that they were nothing better than brigands,
and were undoubtedly on their way to the devil. He added that he
would have treated them as people of such a character, going such a
way, only that they were his countrymen. And then he wept at the
very thought of their present demerits, and their possible destiny.
This practice of weeping was inherited by knights from the old Greek
heroes, and a chevalier in complete steel might shed tears till his suit
was rusty, without the slightest shame. The exhortation continued
without appearing to make any sensible impression upon the rovers.
Baldwin, however, pointed his address at the end, with an
observation that if they would join him in his career of arms, he
would give them lands that should make lords of the whole of them.
Upon this observation the Green Pirates, with a little modest allusion
to their unworthiness, declared that they were eager, one and all, to
turn crusaders.
Each man attached a small green cross, in cloth, to the top of his
sleeve; and joyfully followed Baldwin to the field. The count was no
more able to keep his word than a recruiting sergeant who promises
a recruit that he shall be made a field-marshal. Nor was he to blame,
for the greater part of his new allies perished; but enough were left to
make a score of very doughty knights.
Admirable sailors were the Northmen, especially the Anglo-
Normans, whether with respect to manœuvring or courage. “Close
quarters” formed the condition on which they liked to be with an
enemy. “Grapple and board” was their system as soon as they had
created a little confusion among the enemy with their cross-bows
and slings. The “mariners” in those days fought in armor, with heavy
swords, spears, and battle-axes. They were well furnished too with
bags of quick-lime, the contents of which they flung into the eyes of
their adversaries, when they could get to windward of them, an end
which they always had in view.
The first regular naval battle fought between the English and the
French was conducted by the former after the fashion above
mentioned. It was during the reign of Henry III., when Louis of
France, by the destruction of his army at “the fair of Lincoln,” was
shut up in London, and depended on the exertions of his wife,
Blanche of Castile, for his release. Blanche sent eighty large ships,
besides many smaller vessels, from Calais, under a piratical
commander, the celebrated Eustace Le Moine. Hubert de Burgh had
only forty vessels wherewith to proceed against this overwhelming
force; and on board of these the English knights proceeded, under
protest and with a world of grumbling, at being compelled to fight on
the waters when they had no sea-legs, and were accustomed to no
battles but those on land. No heed was taken of protest or
grumbling; the forty vessels were loosened from their moorings, and
away went the reluctant but strong-boned land sailors, all in shirts of
mail in place of Guernsey jackets, to contend for the first time with a
French fleet. The English ships contrived to get between Calais and
the enemy’s vessels, and fell upon the latter in their rear. The
English bowmen handled their favorite weapons with a deadly
dexterity; and as soon as their vessels were made fast to those of
the French, out flew the quick-lime, flung by the English, and carried
by the wind into the faces of the French. While these were stamping
with pain, screwing their eyes up to look through the lime-dust, or
turning their backs to avoid it, the English boarders made a rush, cut
down men, hacked away the rigging, and so utterly defeated the
French, unaccustomed to this sort of fighting, that of the great
French fleet only fifteen vessels escaped. The number of Gallic
knights and inferior officers captured was very large. As for Eustace
le Moine, he had slunk below to avoid the lime-powder and battle-
axes. He was seized by Richard Fitzroy, King John’s illegitimate son.
Fitzroy refused to give the recreant quarter, but hewed off his head
on the taffrail, and sent it from town to town through England as a
pleasant exhibition.
Errant knights in quest of adventure, and anxious to secure renown,
less frequently visited England than other countries. They appear to
have had a mortal dislike of the sea. This dislike was common to the
bravest and greatest among them. I may cite, as an instance, the
case of the Duke of Orleans and his cavaliers, captured at Agincourt,
and brought over to England, from Calais to Dover, by the gallant
and lucky Henry. The latter walked the deck during a heavy ground
swell, with as much enjoyment as though he had been to the matter
born. The French prince and his knights, on the other hand, were as
ignorant of the sea and as uneasy upon it as a modern English Lord
of the Admiralty. They suffered horribly, and one and all declared that
they would rather be daily exposed to the peril of battle, than cross
the straits of Dover once a month.
Nevertheless, stray knights did occasionally brave the dangers of the
deep, and step ashore on the coast of Kent with a challenge to all
comers of equal degree. We have an instance of this sort of
adventurer in Jacques de Lelaing, whose story is told in this volume.
We hear of another in the nameless knight of Aragon, who in the
reign of Henry V. set all London and many a provincial baronial hall
in commotion by his published invitation to all knights of the same
rank as himself, to come and give him a taste of their quality in a
bout at two-edged sword, axe, and dagger.
The challenge was promptly accepted by stout Sir Robert Cary. Sir
Robert was a poor knight, with nothing to lose, for his sire had lost all
he possessed before Sir Robert’s time, by being faithful to poor
Richard II., a virtue, for the exercise of which he was punished by
forfeiture of his estates, decreed against him by Henry IV. The
disinherited knight, therefore, had a chance of winning land as well
as honor, should he subdue the arrogant Aragonese. The two met in
the then fashionable district of Smithfield, and the Devonshire
swordsman, after a bloody and long-enduring fight, so thoroughly
vanquished the Spaniard, that the king, who delighted in such
encounters, and who was especially glad when victory was won by
the side he most favored, not only restored to Sir Robert the forfeited
paternal estates, but he also authorized him to wear the arms of the
much-bruised knight from beyond sea.
At a later period knightly estates went in the service of another king.
Sir Henry Cary risked life and property in the cause of Charles I., and
while he preserved the first, he was deprived of nearly all the latter.
The head of the family, no longer a knight, if I remember rightly, was
residing at Torr Bay, when the Old Chevalier was about to attempt to
regain the three crowns which, according to no less than a French
archiepiscopal authority, James II. had been simple enough to lose
for one mass. At this period, the English king that would be, sent the
Duke of Ormond to the head of the Cary family, and not only
conveyed to him an assurance that his services to the Stuarts had
not been forgotten; but, by way of guarantee that future, and perhaps
more than knightly honors should be heaped upon him, in case of
victory declaring for the Stuart cause, the chevalier sent him the
portraits of James II., and of that monarch’s wife, Mary of Modena.
Similar portraits are to be found among the cherished treasures of
many English families; and these are supposed to have been
originally distributed among various families, as pledges from the
giver, that for swords raised, money lost, or blood shed in the cause
of the Stuarts, knighthood and honors more substantial should follow
as soon as “the king” should “get his own again.”
To revert to Charles I., it may be added that he was not half so
energetic in trying to keep his own as his grandson was in trying to
recover what had been lost. An incident connected with the battle of
Rowton Heath will serve to exemplify this. Never did king have better
champion than Charles had on that day, in the able knight Sir
Marmaduke Langdale. The knight in question had gained a marked
advantage over his adversary, the equally able Poyntz. To cheer the
king, then beleaguered in Chester Castle, with the news, Sir
Marmaduke despatched Colonel Shakerley. He could not have
commissioned a better man. The colonel contrived to get into
Chester after crossing the Dee in a tub, which he worked with one
hand, while he towed his horse after him with the other. He delivered
his message, and offered to convey an answer or instructions back
to Sir Marmaduke, and by the same means, in a quarter of an hour.
The king hesitated; some sanction required for a certain course of
action proposed by Sir Marmaduke was not given, and Poyntz
recovered his lost ground, defeated the royal horse, and thus
effectually prevented Charles from obtaining access to Scotland and
Montrose.
I have given some illustrations of the means by which knighthood
was occasionally gained: an amusing illustration remains to be told.
Dangeau, in his memoirs, speaks of two French peeresses who lived
chiefly upon asses’ milk, but who, nevertheless, became afflicted
with some of the ills incident to humanity, and were ordered to take
physic. They were disgusted with the prescription, but got over the
difficulty charmingly by physicking the donkey. It was not an unusual
thing in France for very great people to treat their vices as they did
their ailments, by a vicarious treatment. Catherine de Medicis is one
out of many instances of this. She was desirous of succeeding in

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International Conference on Reliable

Systems Engineering (ICoRSE) - 2021

International Conference on Reliable Systems

Web Information Systems Engineering – WISE 2021: 22nd

HCI International 2021 Posters 23rd HCI International

Business Intelligence 6th International Conference CBI

Advances in the Human Side of Service Engineering:

Uncertainty in Mechanical Engineering Proceedings of

NFPA 92 Standard for Smoke Control Systems 2021 Edition

The Engineering of Reliable Embedded Systems Michael J.

Daniela Doina Cioboată Editor

More information about this series at http://www.springer.com/series/15179

ISSN 2367-3370 ISSN 2367-3389 (electronic)

Study of a Test Stand for Determining the Oil Density

Production Scheduling of Semiconductor Wafer Fabrication Facilities

Increasing the Accuracy of Calibration Device for Measuring

Mathematical Modeling and Simulation in Sheet Hydroforming

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Mihai Avram1 , Valerian-Emanuel Sârbu2(B) , and Mariana-Florentina Ştefănescu2

Abstract. The purpose of this paper is to document the development of a test

Keywords: Hydraulic oil · Density · Hydraulic drive system · The theoretical

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

• Rapid deployment of the equipment and its components

2 Methodology and Experimental Details

Observation: The proportionate butterfly valve DrP used is a proportional hydraulic

Proportional equipment used, proportional valve SP and the proportional butterfly

u0 = 0 V, uc1 = 0 V and uc2 = 0 V

3 Experimental Determination of Mineral Oil Density

Fig. 3. Experimental results

p = Pam − Pav = 20, 469 bar

Fig. 4. Variation of flow section depending on the position of the drawer

Sergey Dobrotvorskiy1(B) , Aleksenko Borys1 , Vitalii Yepifanov1 ,

Keywords: Nanopores · Air dryer · Regeneration · Microwave energy

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

a group of magnetrons to regenerate a large volume of adsorbent is the limited depth of

3 Materials and Methods

Table 1. Silica gel physical properties.

Parameter Dimension Value

Table 2. Linear dimensions of the adsorption column.

Index Size Dimension, mm

The impact on the adsorbent of high-frequency energy is carried out by applying an

where: u - is the velocity, p - is the pressure, and μ - is the dynamic viscosity.

where: θm - the value of porosity of the material.

ρCp u · ∇T + ∇ · q = Q + Qvd (5)

where: Cp - heat capacity value, T - temperature, Q - quantity of heat.

where: θρ - is the volume fraction of the material, kρ - is the thermal conductivity.

where μγ is the complex relative permeability; E – complex amplitude representing

ρCp u · ∇T = ∇ · (k∇T ) + Qe (13)

The force, which is effects on the water molecule is calculated as:

where F is the electric displacement, ρ – dipole moment, U – potential difference, d

4 Results and Discussion

R. El Abdi1(B) , R. Leite Pinto1 , G. Guérard2 , and C. Capena2

Keywords: Optical fibers · Thermo-mechanical stresses · Lifetime · Bending

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

2 Used Test Bench

Fig. 1. Ceramic mandrel with wound fibers

(N is the total number of tested samples).

If the rupture is characterized by a single defect category, Ln [(1/L) {Ln (1/(1−F))}]

4 Results and Discussion