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ACC JOURNAL je mezinárodní časopis, jehož vydavatelem je Technická univerzita v Liberci. Na jeho tvorbě se podílí šest vysokých škol sdružených v Akademickém koordinačním středisku v Euroregionu Nisa (ACC). Ročně vycházejí dvě čísla.

ACC JOURNAL je periodikum publikující původní recenzované vědecké práce, vědecké studie, příspěvky ke konferencím a výzkumným projektům. První vydání obsahuje příspěvky z oblasti přírodních věd a techniky, druhé je zaměřeno na oblast společenských věd a ekonomiky.

ACC JOURNAL má charakter recenzovaného časopisu. Jeho edice navazuje na sborník "Vědecká pojednání", který vycházel v letech 1995-2008. Od roku 2010 je ACC JOURNAL v databázi Rady pro vědu, výzkum, vývoj a inovace (Seznam recenzovaných neimpaktovaných časopisů vydávaných v České republice) hodnocených v RIVu.

ACC JOURNAL is an international journal, it is published at the Technical University of Liberec. Six high schools united in the Academic Coordination Centre in the Euroregion Nisa participate in its creation. There are two issues of the journal annually.

In the ACC JOURNAL original reviewed scientific studies, conference presentations and research project reports are published. The first issue focuses on natural sciences and technology; the second issue deals with social sciences and economics.

ACC JOURNAL is a reviewed one. It is building upon the tradition of the "Scientific Treaties" published between 1995 and 2008. The ACC JOURNAL has been in the database of the Research and Development Council since 2010 (List of reviewed non-impact journals published in the Czech Republic) recorded and evaluated in the Information Register of R&D results.

Recenzovali (reviewed by):

Prof. Ing. Jan Honců, CSc. Technical University of Liberec, Faculty of Mechanical Engineering, Liberec, Czech Republic Prof. Dr.-Ing. habil. Holger Theilig University of Applied Sciences Zittau/Görlitz, Faculty of Mechanical Engineering, Zittau, Germany

Acknowledgements:

This edition of ACC JOURNAL, Issue A, has been cofinanced from the European regional development fund

by the Euroregion Neisse-Nisa-Nysa.

__________________________________________________________________________________________ EUROREGION NYSA

Niniejsza publikacja jest realizowana w ramach projektu „.Wymiana studentów i wykładowców oraz wspólne publikacje KPSW JG i TUL” współfinansowanego ze środków Unii Europejskiej w ramach Europejskiego Funduszu Rozwoju Regionalnego oraz środków budżetu państwa za pośrednictwem Euroregionu Nysa. Tato publikace vznikla v rámci projektu „ Výměna studentů a přednášejících a společné publikace KPSW JG a TUL“ spolufinancovaného z prostředků Evropské unie v rámci Evropského fondu pro regionální rozvoj a také z prostředků státního rozpočtu prostřednictvím Euroregionu Nisa.

5

Contents

EXPERIMENTAL RESEARCH OF MIXING NOZZLE FOR EJECTORS ...................... 7 Petr Dolejš

GRAPH-BASED ANALYSIS OF PLANETARY GEARS ................................................... 15 Józef Drewniak, Jerzy Kopeć, Stanisław Zawiślak

SIMULATION OF BACKLASH-FREE GEAR RUN USING TOOTH WHEELS CONTAINING FLEXIBLE ELEMENTS .............................................................................. 25 Vojtěch Klouček

SIMULATION OF WELDING IN THE REPAIR OF GAS PIPELINES WITH STEEL SLEEVES ......................................................................................................... 32 Radoslav Koňár, Jaromír Moravec, Miloš Mičian

INFLUENCE OF SB ON GAS CONTENT AND FLOWABILITY OF ALLOY ALSI6CU4 .............................................................................. 43 Dušan Medlen, Iva Nová, Dana Bolibruchová, Dušan Urgela

INFLUENCE OF MECHANICAL STRESS ON EVAPORATION RESISTANCE OF KNITTED FABRICS ......................................................................................................... 52 M. Motawe, Antonín Havelka, Zdeněk Kůs

THE DYNAMIC ANALYSIS OF THE NEEDLE BAR MECHANISM OF SEWING MACHINES ....................................................................................................... 60 Karel Pejchar, Jaroslav Beran

A MECHANICAL MODEL OF THE VIBRATION CONVEYOR .................................... 71 Marek Pešík

TESTING AND SIMULATION OF VISCOELASTIC REINFORCEMENT APPLIED INTO CAR SEAT CONSTRUCTION ................................................................. 80 Michal Petrů, Ondřej Novák

COMPRESSION BEHAVIOUR AND ELASTIC RECOVERY OF HIGHLOFT MATERIALS (KELVIN-MAXWELL MODEL) .................................................................. 89 Jana Přívratská, Katarina Zelová

ANALYSIS OF DYNAMIC MODEL OF THE DRIVE OF SMALL DIAMETER KNITTING MACHINES ANGE 18.1 ..................................................................................... 94 Josef Skřivánek, Martin Bílek

6

LIST OF AUTHORS .............................................................................................................. 102

LIST OF REVIEWERS .......................................................................................................... 103

GUIDELINES FOR CONTRIBUTORS ............................................................................... 105

EDITORIAL BOARD ............................................................................................................. 111

7

EXPERIMENTAL RESEARCH OF MIXING NOZZLE FOR EJECTORS

Petr Dolejš

Technical University of Liberec

Faculty of Mechanical Engineering Studentská 2, 461 17, Liberec 1, Czech Republic

[email protected]

Abstract

In this article, two positions of a lobe-shaped nozzle intended for the ejector mixing process are compared. The objective of the experiments was the identification of the cross-shaped nozzle flow pattern. The measurements of nozzle velocity profiles were conducted at a pressure of 2 kPa. Separate nozzle velocity profiles were measured from the nozzle mouth up to the distance of 90 mm and 180 mm, in 15 mm or 30 mm intervals respectively. In this way, 10 velocity profiles were measured per each nozzle position and consequently used for the final diagram. An important principle for the recommendation of a nozzle for the mixing process was the characteristics of cross-shaped nozzle velocity profiles measured at different positions, using the modern contactless measurement method - Laser Doppler Anemometry (LDA). Based on the measured data, the cross-shaped nozzle velocity profiles were described in detail. Defects of the cross-shaped nozzle were identified by the experiments and thus its unsuitability for the ejector mixing process.

Introduction

Despite an extensive boom of software modeling techniques the experimental approach to the research handling the area of fluid mechanics is still an irreplaceable source of information. Even the best mathematical-physical model deals with simplified or idealized conditions. For that reason, it is necessary to adjust the model and verify it by comparing the results with a proven method.

In recent years, fluid mechanics has exploited more and more measuring methods that are based on optoelectronic principles, using light. These methods include, for example, LDA (Laser Doppler Anemometry), PDA (Phase Doppler Anemometry), PIV (Particle Image Velocimetry) etc. Laser anemometry seems to be an extremely exact tool for measuring real objects. Its benefit is that it is contactless. It measures a medium speed using microscopic particles that are diffused in the medium. The measurement is linear within the whole range. The results do not depend on the surrounding conditions, such as pressure, temperature, humidity etc.

Previously, the laboratories of the TUL have already dealt with experimental research of mixing nozzles for ejectors. The first measurement faced a big problem. A Pitot tube was used to affect significantly the ejector functionality. In addition, this affect was not constant, but depended on the tube insertion into the mixing chamber. The result recalculation was necessary. The next experimental method of the flow pattern examination was the method of hot wire (CTA method). However, the CTA method did not allow for the measuring of the flow pattern without any object influence – the CTA probe of the anemometer. The interruption of the flow by the probe led to a measurement error.

8

1 Laser Doppler Anemometry

The LDA method is the most commonly used modern contactless measurement technique for the research of liquid flow. It is best suited for studies of stationary flow. Due to a small measuring probe it allows an extraordinary spatial resolution. We have chosen this method for the aforementioned benefits.

1.1 The LDA method principle

LDA is a contact less measuring method that exploits the Doppler’s effect. LDA measures a difference in frequency of laser light diffused on a particle that is carried by the examined liquid.

To measure the frequency change (Doppler’s shift) the heterodyne detection is used, as shown in Fig. 1 Two laser beams intersect at an angle of , their intersection creates an optical probe. On a particle, passing through the optical probe, two light waves fall with a frequency of f, in the directions of unit vectors ei1 and ei2. [1]

Fig. 1 Heterodyne detection scheme

A detector detects the light, diffused by a particle. This detector registers the differential frequency, so called Doppler’s frequency fD. The Doppler’s frequency is proportional to the velocity component u. The velocity component u lies in the plane of the intersected laser beams and it is perpendicular to the central line of the angle , closed by the two beams. The velocity component of the flow is possible to evaluate from the Doppler’s frequency:

,)2/sin(2 Dfu

(1)

where is anangle of the two intersected laser beams, u is a component of a particle velocity v projected into a direction (ei2-ei1),λ is a wavelength of laser light.

9

1.1.1 Laser Doppler anemometer

A basic arrangement of a laser Doppler anemometer in the differential mode is shown in Fig. 2. The laser beam is led from a laser towards a divider, which divides the beam into two identical beams that are parallel with the central line of the system. Thetransmitting/receivinglens focalize these beams into a focus point. Within the focus point an optical probe consisting of the intersection of the two beams is created. A particle passing through this probe diffuses light. This light is led through optics to a detector. Two waves diffused by the particle are examined by the photo-detector using heterodyne detection. The photo-detector is positioned in a so-called backscatter. This arrangement has considerable benefits, for example, only one adjustment of the optical transmitting and detecting part is needed. The disadvantage of this method is the low intensity of the diffused light; therefore it is necessary to use a sufficiently powerful laser. The main task of the photo-detector is to transfer an optical Doppler’s signal to an electric signal and its consecutive amplification. The output signal of the photomultiplier is a current that contains information of the measured velocity. The aim of the evaluating processor of the LDA is to measure the frequency of the Doppler’s peak.

Fig. 2 Scheme of laser Doppler anemometer

1.1.2 Analysis of measured data

The output of the measurement at the position of the optical probe is a set of Doppler’s signals. These are furthermore converted to speed according to formula (1); the speed values are then evaluated by statistical analysis. In the LDA, these statistics normally provide for example average speed, standard deviation and turbulence intensity.

10

,100*,)(1

1,

1

1

22

1 uTuuu

Nu

Nu

N

ii

N

ii

(2)

where u is average speed, is variance and uT is turbulence intensity.

1.1.3 Limits and imperfection of the LDA method

Most possibly, exact current measurement, evenness of the measured medium saturation with tracer particles and their properties belong among the basic conditions for correct functionality of the LDA.

The limiting condition of the LDA applicability is the deviation of current direction from the measured velocity component. The band error, “fridge bias”, is possible to eliminate successfully if using a Brag’s cell. The velocity error, “velocity bias”, is possible to eliminate if introducing a weighting function inversely proportional to velocity [1].

2 Experiment

The experiment was carried out with a cross nozzle (Fig. 3).

Fig. 3 Cross nozzle [2]

2.1 Conditions of measurement

The measurement of the velocity profiles on the nozzle was performed at a pressure of 2 kPa. At this pressure of the flowing air, we can expect a maximum velocity of about 60m/s from the nozzle. In consideration of this speed such transmitting/receiving objectives were selected, so that the maximum Doppler’s frequency would not exceed the maximum frequency of approximately 150MHz, which was possible to measure with the used counter (Dantec company) . An objective with a focal distance of 250mm was selected whichfulfilled the defined condition.

2.2 Measurement

A laser Doppler’s anemometer in operation is shown in Fig. 4. The detail displays the nozzle and objective, focusing the laser beamson the focal point. The created focal point creates the optical probe.

11

Fig. 4 Optical probe with the nozzle

3 Results of the measurement

Individual velocity profiles of the nozzle were measured using laser Doppler’s anemometry from the nozzle aperture up to 90mm/15mm, and from 90 mm up to 180mm/30mm. This means that for one nozzle position, ten velocity profiles were gained, based on these profiles the final chart was drafted.

3.1 Cross nozzle

The cross nozzle was measured using the LDA method in the basic position (Fig. 5) and then rotated by 45° (Fig. 6).

Fig. 5 The cross nozzle with an indicated position of the measured velocity profile

Fig. 6 The cross nozzle with an indicated position of the measured velocity profile after rotating by 45°

1

2

Individumeasure

Fig. 7

Fig. 8

ual positionement resul

Velocity p

Velocity p

ns of the nots are docum

profiles of t

profiles of t

ozzle showmented in th

the cross no

the cross no

ed differenhe charts in

ozzle in thei

ozzle rotated

t characteriFig. 7 and

r basic posi

d 45°.

istics of theFig. 8.

ition.

e flow patteern. The

13

Conclusion

The experimental results of the cross nozzle in its basic position are shown in the chart in Fig. 7. Deformation of the velocity pattern of one side was noted. This deformation was probably caused by a defect in manufacturing, or by wear. The nozzle deformation caused that the symmetry of the flow was disturbed and the velocity dropped from the point of its maximum. With increasing distance from the nozzle’s aperture the velocity was slowly decreasing, the flow pattern decayed, and therefore there was less and less deformation to the velocity profile of the nozzle. The deformation had the biggest impact on the velocity pattern up to the distance of approximately 2.5 times the diameter of the nozzle.

In the case of the measurement of the cross nozzle rotated by 45°,no deformation influence on the examined airflow was detected. The results of the measurement are shown in Fig. 8. No other possible deformation of the flow pattern was noticed. The measured flow was, in this case, different especially in the shape of the core, which was narrower than in the previous case. The air flow velocities were almost identical in both measured cases.

Literature

[1] KOPECKÝ, V.: Metody Laserové anemometrie v mechanice tekutin, Tribun EU 2008.

[2] VÍT, T.; DANČOVÁ, V.; DVOŘÁK, V.: Experimental Fluid Mechanics, TU v Liberci 2006. ISBN 80-7372-141-4

___________________________________________________________________________ Ing. Petr Dolejš

14

EXPERIMENTÁLNÍ VÝZKUM SMĚŠOVACÍ TRYSKY PRO EJEKTORY

V tomto článku jsou porovnávány dvě polohy lalokovité trysky určené pro směšovací proces ejektoru. Předmětem pokusů bylo experimentální zjištění charakteristik proudových polí křížové trysky. Měření rychlostních profilů trysky probíhalo při tlaku 2 kPa. Jednotlivé rychlostní profily trysky byly měřeny od ústí trysky do 90mm po 15mm a od 90mm do 180mm po 30mm. Pro jednu polohu trysky bylo tedy změřeno 10 rychlostních profilů, které pak vytvořily výsledný graf. Důležitým hlediskem k doporučení trysky pro směšování byly charakteristiky rychlostních profilů křížové trysky měřené v různých polohách, které byly naměřené moderní bezkontaktní měřící metodou - laserová Dopplerovská anemometrie. Na základě naměřených dat jsou podrobně popsány rychlostní profily křížové trysky. Experimentováním byly zjištěny defekty na křížové trysce a tedy i její nevhodnost pro směšovací proces ejektoru.

EXPERIMENTALUNTERSUCHUNG ÜBER DIE MISCHDÜSE

FÜR EJEKTOREN

In diesem Artikel werden zwei Lagen der für den Mischprozess eines Ejektors bestimmten Zackendüse verglichen. Versuchsgegenstand war die experimentelle Bestimmung von Charakteristiken der Stromfelder der Kreuzdüse. Das Messen der Geschwindigkeitsprofile der Düse wurde unter einem Druck von 2 kPa durchgeführt. Die einzelnen Geschwindigkeitsprofile der Düse wurden von der Düsenöffnung bis zu 90 mm je nach 15 mm und von 90 mm bis zu 180 mm je nach 30 mm gemessen. Für eine Düsenlage wurden 10 Geschwindigkeitsprofile gemessen, die dann das Enddiagramm bilden. Wichtiger Gesichtspunkt für die Empfehlung einer Düse für Mischung waren die Charakteristiken der Geschwindigkeitsprofile der Kreuzdüse, die in verschiedenen Lagen unter Anwendung der modernen kontaktlosen Messmethode, Laser-Doppler-Anemometrie, gemessen wurden. Aufgrund der gemessenen Angaben werden die Geschwindigkeitsprofile der Kreuzdüse ausführlich beschrieben. Durch Versuche wurden Defekte an der Kreuzdüse festgestellt, demzufolge ist deren Anwendung für den Mischprozess des Ejektors nicht geeignet.

EKSPERYMENTALNE BADANIE DYSZY MIESZAJĄCEJ

DLA EJEKTORÓW

W niniejszym artykule porównywane są dwa położenia dyszy krzywkowej przeznaczonej do procesu mieszania w ejektorze. Przedmiotem przeprowadzonych prób było eksperymentalne ustalenie cech pól strumieni dyszy krzyżowej. Pomiary profili prędkości wykonywano przy ciśnieniu 2 kPa. Poszczególne profile prędkości dyszy mierzono od wylotu dyszy do 90mm co 15mm oraz od 90mm do 180mm co 30mm. Dla jednego położenia dyszy dokonano zatem pomiarów 10 profili prędkości, które następnie naniesiono na wykres wyników. Istotną kwestią w zakresie zalecenia dyszy do mieszania były cechy profili prędkości dyszy krzyżowej mierzone w różnych położeniach, których pomiary zostały wykonane przy zastosowaniu nowoczesnej bezkontaktowej metody pomiarowej - laserowej Anemometrii Dopplerowskiej. Na podstawie danych pomiarowych szczegółowo opisano profile prędkości dyszy krzyżowej. W wyniku przeprowadzonych eksperymentów stwierdzono usterki na dyszy krzyżowej, czyli nie jest ona odpowiednia dla procesu mieszania ejektora.

15

GRAPH-BASED ANALYSIS OF PLANETARY GEARS

Józef Drewniak Jerzy Kopeć

Stanisław Zawiślak

Technical University of Bielsko-Biała

Faculty of Mechanical Engineering and Computer Science Willowa 2, 43-309, Bielsko-Biała, Poland

[email protected] [email protected]

[email protected]

Abstract

In this paper, the graph-based models of planetary gears are discussed. The considered methods are as follows: linear (Hsu’s) graph, contour (Marghitu’s) graphs and bondgraphs. The original rules for the use of graph based methods were modified by the authors making them more adequate and more useful. The selected planetary gear was analyzed to show a course of calculations for the proposed methods in comparison with the traditional Willis method. The advantages of the graph based method consist in submission of an algebraic structure of a gear – which allows for an application of some AI approaches. Bondgraphs models of a subgear were presented. It additionally allows for algorithmic generation not only kinematical equations but also for relationships according to forces and accelerations or power.

Introduction

Planetary gears are modeled by means of many different approaches. However, just recently, their graph-based models [1-10] are intensively developed. The following graphs were used for this task: bondgraphs [1, 9], linear graphs [2, 3, 8] and contour graphs [2, 3, 5] as well as some others [9, 10].

In this paper, the aforementioned graphs were used for kinematical analysis of aselected planetary gear. The applied methods were utilized and compared. The aim of this paper is to show the advantages of the graph-based method i.e. algorithmic approach.

The additional benefits of modeling of gears via graphs consist in submission of algebraic encoding of the structure of a planetary gear [10]. It – in turn – allows for an application of Artificial Intelligence (AI) approaches and methods [4,6,7,8] (e.g.: graph grammar and evolutionary algorithms). Due to this, a designer has a powerful tool for supporting several design tasks at the conceptual stage of the design. In general, such activities in graph modeling have been performed as for example: synthesis of planetary gears [3] and enumeration of their kinematic structures [8] which allows for creation of atlases of all possible design solutions.

We calculated the ratio of the considered selected planetary gear by means of the traditional Willis method as well as graph based methods. In case of bondgraphs, only the introductory stage of modeling is shown here. In fact, this method is especially powerful because it enables simulation [1], but it exceeds the assumed scope of this paper.

16

1 A selected planetary gear

The functional scheme of the considered selected planetary gear is presented in Fig.1.

F

nj

z 5z j

z'4 z"4

D

EC

A

z 1

n1

z 2B

z 3

0 0

j

Fig. 1 A functional scheme of an selected planetary gear

Low value of ratio could be achieved in another way, however, a gear is chosen just to show a course of ratio calculations. The assumed numbers of teeth are also an example. The values are as follows: 201 z , 602 z , 1403 z , (-140 for Willis approach), 30'4 z , 50''4 z ,

205 z . Planets 2 and 4 are slightly different because planet 4 consists of two geared wheels

mounted stiffly on one axis. The geared wheel 5 is braked, therefore:

.05 (1)

The input element is the wheel 1 and the output element is the arm (carrier) j, respectively.

2 Rules of assignment: "graph ↔ planetary gear"

General rules of assignment of a graph to a gear are as follows: (i) abstraction i.e. we consider only the elements which are involved in kinematic movements of a gear (geared wheels, sun wheels, wheels with internal teeth rings, planetary gears and arms) and a support system embedded in a housing; (ii) we neglect other gear parts (e.g. bearings, seals, covers etc. ) and other aspects such as e.g. friction, lubrication or vibrations; (iii) we represent the gear parts as graph vertices; (iv) we represent mutual relations of these parts as gear edges or arcs.

A linear graph of the planetary gear (Fig.1) is shown in Fig. 2. The dashed line(the edges) representspairs of two geared wheels in mesh e.g. edge (1,2) connects vertices 1 and 2, where vertex 1represents input wheel 1 and vertex 2 represents planetary geared wheel 2. Continuous line-edge (2,j) represents a pair: planet 2 and carrier j. The dashed-line edge (4‘/4“, 5) is drawn as a double line to visualize the fact that the wheel 5 is braked. The polygon (1, 3, j, 5, 0) is in fact a clique induced on the mentioned vertices but only for visual reasons it is usually drawn as a shaded (even) polygon according to Hsu’s idea. Exceptionally, in our case, some edges are explicitly drawn to enable a detailed explanation (i.e. edge (1,j) and edge (0,j) ).

A contour graph of the same planetary gear is presented in Fig. 3. The original drawing rules were here preserved i.e. vertices as small dots for linear graphs and vertices as circles with vertices numbers inside them for contour graphs (Marghitu‘s), respectively.

17

In the case of a contour digraph (Fig. 3) – we draw an arc (i,j) if the element i passes rotational movement onto the element j or rotates around another element. E.g.: arc (0,1) symbolizes that element 1 rotates supported by a bearing system 0, arc (1,2) symbolizes that rotational movement is passed from wheel 1 onto planet 2, etc. Every contour has its circulation. Due to counter circulations two arcs can be drawn i.e. (0,3) and (3,0), simultaneously.

1

2

j

4'/4''

5

3

0

in

Fig. 2 Linear (Hsu‘s) graph of the selected planetary gear

j

1

4'/4''

20 I

3

II

5

IV

III

Fig. 3 Contour (Marghitu‘s) graph of the selected planetary gear

We distinguish sets of so called f-cycles [8,10] or contours in adequate graphs. Then we assign a code to each of them. Based on these codes, we can write the kinematic equations in the algorithmic manner. The selectedf-cycle is marked by means of bold lines in Fig. 2. The selectedf-cycle and contour were drawn by means of bold lines: (1,2)j and (0,1,2,j,0) – so there is an equivalence between these two approaches if we additionally consider the vertex 0.

3 Graph-based kinematical analysis of planetary gears

In what follows, we would like to show how the gear ratio can be calculated. The general rule is defined: based upon the graph model of a gear - we generate a system of equations which describe the kinematics of a gear. Based upon these systems we can calculate a ratio. The rules of assignment of some types of equations are gathered in Tab. 1.

18

Tab. 1 Kinematics equation of a planetary gear for both its graph-based models

Graph representation

linear graph contour graph

Schematic representation of an elementary subgear

i k

j

0

j

i

k

0

Code assigned to graph representation

kji, or (0,i,j,k,0)

(see Fig. 2)

00 kji

(see Fig. 3)

Kinematics equations generated upon the codes

kjjiki N

0

00

kjBjiA

kkjjiio

rr

where: i and j matching (geared) elements, k – carrier;

ω with single index – absolute rotational velocities;

ω with double indices – relative rotational velocities;

sign – or + depends on external or internal matching;

r – radiuses (see Fig. 3); radiuses equal to 0 are omitted.

In case of a linear graph of a gear we consider all f-cycles built upon all dashed line-edges. In case of a contour graph we consider all its contours. From the graph-theoretical point of view a contour graph consists of all independent (in the light of linear spaces theory) contours.

A code of an f-cycle (i,j)k consists of a code of dashed line-edge (i,j) where one element means a planet wheel and the second one a sun wheel or a wheel with an internal teeth ring. Description k represents a carrier of the mentioned planetary wheel. The elements are written according to the sequence of their notions – assuming that the numbers are placed before letters. The order of indices in the formulas given in Tab. 1 is fully fixed so it reduces a possibility of mistakes.

A code of a contour can be considered in different ways, however we prefer to consider the contours, which start and end in vertex 0. It is connected with the whole theory of contour graphs [5]. Mainly, it is due to the fact that relative quantities are considered. These quantities have to be converted into the absolute ones (9). The solution of the system of equations is obtained via eliminating all relative quantities (e.g. rotational velocities) one by one.

19

4 Ratio calculation

The ratio of the considered gear is calculated via three different approaches.

4.1 Willis method

In case of Willis method we can consider separately consecutive subgears and their local ratios. For the subgear consisting of elements: 1,2, 3 and j we have:

.1

2

2

3

3

13,1 z

z

z

zi

j

j

(2)

For the second subgear, we can write:

jj z

z

z

zi '4

''4

5

3

315,

5

(3)

and finally the overall ratio can be calculated:

.1'45''4

'45

1

31,1 zzzz

zz

z

zi

jjj

(4)

So, inserting the assumed teeth numbers the considered ratio is as follows:

.230204050

3020

20

1401,1

ji (4a)

For comparison, we repeat these calculations based upon the discussed graphs (Fig. 2 and 3).

4.2 Linear graph approach to planetary ratio calculation

Based upon the graph (Fig. 2) of the considered gear, we can distinguish the following f-cycles: (1,2)j; (2,3)j; (4‘/4“, j)3 and (4‘/4“, j)3. Assigning an equation to every f-cycle and taking into account the assumption, we obtain the following system of equations:

.

05

3'43'4

35''543''4

3322

2211

jj

jj

jj

N

N

N

N

(5)

Solving the system – we can write:

jjjjj

jj NNNN

NNN

2132

'4''54

'432211 (6)

and finally we have:

20

.2120

601

60

140

30

40

50

2030

40

60

140

20

601,1

jjn

(7)

Despite the fact that the formula is slightly different from the previous one, the same ratio was obtained.

4.3 Contour graph approach to planetary ratio calculation

The course of calculations is similar. We have to write down all the contours: (0,1,2,j,0);(0,1,2,3,0);(0,3,4,j,0) and (0,3,4,5,0). Every contour generates two equations here, but in general [5], also the equations concerning accelerations and forces can be written. Radiuses are measured from the main gear axis till adequate points A, B etc. Based upon these contours (Fig. 3) the system of equations can be written:

.

0

0

0

0

0

0

0

0

0

550

5443

05544330

443

044330

3221

03322110

221

022110

FE

jDE

jj

CA

jBA

jj

rr

rr

rr

rr

(8)

To solve this system, we utilize the following properties:

jiij

.0 kk (9)

Due to the fact that all considered rotational velocities as vectors act along the same axis and angles between every r and ω are equal to 90º (sin 90º = 1) therefore we can consider scalar quantities instead of vector ones. So eliminating all relative rotational velocities and turning some of them into the absolute ones – we have:

.

3

311

jDE

D

DE

D

FE

F

CA

C

CA

Cj

BA

B

rr

r

rr

r

rr

r

rr

r

rr

r

rr

r

(10)

Additionally, we assume that all geared wheels are cylindrical and they have the same module. So, the solution of this system is the same as the previous one:

.21 j

(11)

To sum up, the same final result was obtained in all three courses of calculations.

21

4.4 Bondgraph model of planetary gear

Bondgraphs have also been frequently used for modeling of different mechanic and mechatronic systems, but especially gears were considered very rarely. Here we consider other very simple planetary gears shown in Fig. 4a and Fig. 5. The aim is also to show a course of modeling.

The dynamical model of the considered planetary gear can be derived using a bond-graph method. The bondgraphs or power flow graphs are suitable for dynamic modeling of mechanical systems. For the single stage gear the bondgraph has the form shown in Fig. 4b. To draw the bongraphs, we start from so called “skeleton” (0-nodes and 1-nodes and power flow bonds) connected with ideal transformer TF. Transformer coefficient n is equal to the gear transmission ratio. The inertial elements I describe inertial forces from the pinion and the gear wheel. For the planetary gear shown in Fig. 5, the modeling procedure is more complicated. The skeleton has to reflect the kinematics dependences of the pinion, carrier and planetary wheels. The bondgraph shown in Fig.6 is relevant to an operation mode when the outer wheel 3I is braked and the output power is carrier jI .The transformer coefficient

describes transition ratios. There is the commercial software that can handle the bondgraph models (i.e. Controllab 20-sim).

a)

A

z 1

n1

z 2 B

0

b)

13

2

I:J1

TF:n11

electricmotor

5I:J2

6

input shaft

output shaft

gear

loadSf: w0

exci

tati

on

4

1 Se:Mobc (t)

I:J2

Fig.4 Single stage spur gear and its bondgraph

A

z 1

n 1

z 2B

j

0

z 3

nj

n 3

Fig. 5 Second planetary gear

22

1

1

0 01TFTF1

I: m 2

1v = 0

::

1/2

TF: R

1

Se: -Mobc

I: I j

R+r

I: I 1

1TF

I: I 2

:

1/2r

Sf: w0

M w

Fig. 6 Expanded bondgraph for the planetary gear (Fig. 5)

In all the figures braking elements are shown via a pictogram of brake - crossed areas. The standard software (e.g. [11]) allows for the input of bond graphs structures as well as the simulation of behavior of the modeled artifacts – because the appropriate systems of equations are generated automatically inside the system. Conclusion

In this paper, three graph-based models were considered. The planetary gear ratio was calculated by means of Willis method as well as two graph-based methods. The identical results were obtained taking into account numerical values however the different formulas were obtained depending on the system of the notions considered in a particular model. It is a useful feature – it allows not only for checking the correctness of all approaches but also gives a deeper insight into the considered structure of a gear. The analysis of radiuses - in the case of the contour graph approach - forces a designer to check unambiguity of radiuses (especially rE). Some further advantages of the graph-based approaches to modeling of planetary gears were shown in the cited references [4, 6, 8]. It is worth to underline that some of them e.g. creation of the complete atlases of the functional schemes of particular types of gears [8] could not be done systematically using other methods.

23

Literature

[1] CERVANTES, J.J.; et. all. Simulation of planetary gear trains, modelling and numerical validation. Proc. ImechE 223 (2009) Part K, 53-71

[2] DREWNIAK, J.; ZAWIŚLAK, S. Linear-graph and contour-graph-based models of planetary gears, Journal of Theoretical and Applied Mechanics 48 (2) (2010) 415-433

[3] DREWNIAK, J.; ZAWIŚLAK, S. Synthesis of planetary gears by means of artificial intelligence approach – graph based modeling, Solid State Phenomena, 164 (2010) 243-248

[4] LI, X.; SCHMIDT, L. Grammar-based designer assistance tool for epicyclic gear trains, J. of Mechanical Design, 126 (2004), 895-902

[5] MARGHITU, D.B. Kinematic chains and machine components design, Academic Press, London as well as Elsevier, San Diego 2005

[6] RAO, A.C. A genetic algorithm for topological characteristics of kinematic chains, J. of Mechanical Design 122(2000) 228-231

[7] SCHMIDT, L.; SHETTY, H.; CHASE, S.C. A graph grammar approach for structure synthesis of mechanisms,. J. of Mechanical Design 122 (2000) 371-376

[8] TSAI, L.W. Mechanism design: enumeration of kinematic structures according to function, CRC, Boca Raton, USA 2001

[9] WOJNAROWSKI, J.; KOPEĆ, J.; ZAWIŚLAK, S. Graph and Gears, Journal of Theoretical and Applied Mechanics, 44 (2006), 139-162

[10] ZAWIŚLAK, S. The graph-based methodology as an artificial intelligence aid for mechanical engineering design, Akademia Techniczno-Humanistyczna, Bielsko-Biała 2010.

[11] www.20sim.com/, Controllab 20-sim (available from the webpage) ___________________________________________________________________________ Prof. ATH Józef Drewniak, Ph.D., D.Sc., Dr Jerzy Kopeć, Ph.D.,

Dr Stanisław Zawislak, Ph.D.

24

ANALÝZA PLANETOVÝCH PŘEVODŮ POMOCÍ GRAFICKÝCH METOD

V předloženém příspěvku jsou diskutovány grafické modely planetových převodů založené na metodách lineárních (Hsu) grafů, křivkových (Marghitu) grafů a vazebních grafů. Původní pravidla využití grafických metod byla autory modifikována a připravena k větší využitelnosti. Byl proveden rozbor vybraného planetového převodu a představen výpočtový postup, který byl porovnán s výsledky získanými tradiční Willisovou metodou. Výhody grafických metod spočívají ve vytvoření soustavy algebraických rovnic převodu, který umožňuje aplikovat některé přístupy umělé inteligence (AI). Byl uveden model vazebního grafu dílčího převodu. Tento model umožňuje nejen vytvořit kinematické vazby, ale také řešit silové a výkonové poměry.

GRAPHEN-BASIERTE ANALYSE VON PLANETENGETRIEBEN

In der vorliegenden Arbeit werden die graphen-basierten Modelle von Planetengetrieben diskutiert. Die betrachteten Verfahren sind folgende: lineare Graphen (Hsu’s), Konturengraphen (Marghitu’s) und Bondgraphen. Die original zugeordneten Grafik-Regeln wurden von den Autoren angepasst und anwendungsbereiter gemacht. Ein beispielhaftes Planetengetriebe wird analysiert, um den Berechnungsgang zu zeigen für die vorgeschlagenen Methoden sowie durch die traditionelle Willis-Methode (zum Vergleich). Vorteile der graphenbasierten Methoden sind die Erstellung einer algebraischen Struktur eines Getriebes – welche eine Anwendung einiger AI-Ansätze ermöglichen. Bondgraph-Modelle eines Subsystems werden vorgestellt. Es erlaubt zusätzlich zu den algorithmischen Ansätzen nicht nur kinematische Gleichungen, sondern auch solche für die Beziehungen von Kräften und Beschleunigungen oder Leistung.

ANALIZA PRZEKŁADNI PLANETARNYCH

ZA POMOCĄ METOD GRAFOWYCH

W niniejszej pracy omawiane są modele grafowe przekładni planetarnych. Rozważa się następujące metody: grafów linowych (Hsu), grafów konturowych (Marghitu) oraz grafów wiązań tzw. bondgrafów. Oryginalne zasady przyporządkowywania grafów zostały w pewnym zakresie zmodyfikowane przez autorów (niniejszej pracy) – co powoduje, że są one bardziej przydatne. Przykładowa przekładnia planetarna jest analizowana przede wszystkim dla przedstawienia przebiegu modelowania oraz obliczeń. Ponadto wyniki porównano z tradycyjną metodą Willisa. Zalety metod grafowych (modelowania przekładni) polegają na tym, że uzyskuje się algebraiczne zakodowanie (poprez wybrane struktury) przekładni planetarnej – co z kolei umożliwia zastosowanie wybranych metod sztucznej inteligencji (AI). Zamieszczono także bondgrafowy model wybranego podsystemu w rozważanej przekładni planetarnej. Ten model umożliwia także algorytmiczne generowanie równań kinematyki, a dodatkowo także zależności dla sił, przyspieszeń czy mocy.

25

SIMULATION OF BACKLASH-FREE GEAR RUN USING TOOTH WHEELS CONTAINING FLEXIBLE ELEMENTS

Vojtěch Klouček



[email protected] VÚTS Liberec, a.s.

Design Of Machinery U Jezu 525/4, 461 19, Liberec 1, Czech Republic

[email protected]

Abstract

The paper describes one of the principles of the backlash-free gear using tooth wheels. A design of a backlash-free gearbox with countershafts is solved in detail. Backlashes in a gear of tooth wheels and bearings are determined by a preloaded torsion-bar spring. A dependence of reaction forces applied to the tooth system and bearings on the torque bar preload is examined. Using a computer program created in the Maple environment, a loaded gear run is simulated in the speed reversal. The results are used to checkthe strength, material fatigue, and service life of dynamically loaded gear components .

Keywords: Backlash-free gear, gearing, torsion-bar spring, preload, accurate position control system

Introduction

In engineering practice, it is often necessary to position accurately physical objects such as work pieces, tools, mounted parts, conveyed (handled, transported) materials, finished products etc. A movable axis of a machine tool, a rotary positioning table, a robotic manipulator and many others can serve as a positioning device. In such cases it is necessary to accelerate and decelerate objects having a considerable weight, which implies that the drives of positioning systems work with relatively great forces and torques, and at relatively small speeds. According to the motion type, it is possible to classify drives into a) rotary ones, and b) linear ones. Electric motors of different designs belong to the most widespread rotary drives. However, these motors reach optimal efficiency and load characteristics at higher speeds and lower torques than the positioning mechanisms require. Therefore it is necessary to interpose a suitably designed reducing gear between the motor and the driven mechanism. Similar to any moving mechanism, the gearbox is produced with clearances and dimension tolerances. Between its input and output shafts, there are several series arranged clearances like this; therefore their sizes are added up. An adjustment of these backlashes during a reversal of the sense of the shaft rotation is a problem all the time. The paper describes one of the methods how to adjust these backlashes and to simulate the run of the loaded backlash-free gearbox.

26

1 Design

1.1 Principle of the backlash-free gearbox

Fig. 1a represents schematically the principle of the backlash-free gear with countershafts. The torsion-bar spring is mounted preloaded at a pre-determined value of the torque so that pinions act on meshing gears in opposite directions. When the rotary motion is transmitted, the load is transferred either by one path or by the other one.

1.2 Mounting conditions of gearing

The gearing (see Fig. 1a) is a closed range of tooth wheels. Therefore, when designing itis necessary to respect the limits given by the distances between the axes and the peripheral velocities of the tooth wheels. In the general case (Fig. 2a) the condition (1) has to be fulfilled

21

11

12

22

31

32

d

d

d

d

d

d (1)

Providing the same module of the tooth system in all the gears, it is possible to replace the pitch diameters by the number of teeth (2) in the equation (1)

21

11

12

22

31

32

z

z

z

z

z

z (2)

The advantage of this type of gearing is ahigh variability in dimensions and therefore a large area for optimization of specific applications. The following case was chosen for the prototype design and the subsequent calculations: 132311211 ddddd and

242221 dddd (Fig. 2b).

Fig. 1 a) anti-backlash gear assembly, b) prototype design of the backlash-free gearbox

27

Fig. 2 Mounting conditions a) general case, b) prototype design

Tab. 1 lists technical parameters of the gearbox, which are used for subsequent calculations.

Tab. 1 Technical parameters of gearbox

rated power P 2.9 [kW]

input torque 1M 18.6 [Nm]

input speed 1n 1500 [rpm]

gear module m 1.5 [mm]

tooth number 1z 31 [–]

tooth number 2z 108 [–]

reduction ratio i 12.1 [–]

2 Force conditions

2.1 Static equilibrium

The gearing according to Fig. 1a is a six-partcompound mechanism (including a frame). In Fig. 3 particular parts are released and drawn in with all theacting forces. It is necessary to determine 38 unknown forces and moments; the moments of Mtk (preload of torsion-bar spring) and M2 (output shaft load) are the parameters of the equation system. Asequilibrium of the system of bodies in a space is concerned, 30 equations of equilibrium are available; remaining 8 equations result from the tooth system geometry (four gears of tooth wheels, 2 equations for each of them).

28

Fig. 3 External forces and forces on bearings, gear meshes and within torsion-bar spring

2.2 Tests of dynamics

A model according to Fig. 4 was created in order to test dynamics. The gearbox is connected by a ball screw with a weight that is supported by a linear ball guide. A known desired kinematics of the weight motion is the model input. Reaction forces in the gearbox are calculated depending on the time. Especially tangential forces in gears of pinions are checked

29

– to keep the correct function of the gearbox , they have to be positive under all circumstances.

Fig. 4 Dynamic model

For purpose of a dynamic solution, it is necessary to know not only geometric characteristics but also mass ones. The weight mass is 100kg. Moments of inertia for tooth wheels, shafts and a ball screw were determined using a 3D model in the SolidWorks environment. For calculating, the universal calculation algorithm was made up in the Maple environment.

Fig. 5 Weight position versus time

Fig. 6 Gearbox input shaft speed versus time

30

Fig. 7 Reaction forces in mesh of pinions versus time (Fig. 3)

Conclusion

The above mentioned method can be used for optimizing the gearbox dimensions. All the parameters of the created algorithm of calculation are established as variables, i.e. this algorithm is universal and applicable to all gearboxes having the same design. Each force applied to the calculation can be expressed separately as a function of time. Therefore, results are substantial for dimensioning of stressed parts as well as for checking of material fatigue. Also, the kinematics of an output mass is freely modifiable.

Acknowledgements:

This work was supported by MPO ČR, research project TIP, no. FR–TI1/594, Research of sophisticated methods of design and development of special-purpose machines, components and peripherals of industry machines.

Literature

[1] HALE, L.C., SLOCUM, A.H.: Design of Anti-Backlash Transmissions For Precision Position Control Systems.Precision Engineering, Volume 16, Issue 4, October 1994, Pages244-258

[2] BAUMGARTEN, K., SCHLOEGLMANN, K.: Mechanical Gear Drive. U.S. Patent 4,953,417, Sept. 4, 1990

[3] HANNEL, C.L.: Anti-Backlash Gear Assembly. U.S. Patent 4,805,475, Feb. 21, 1989

___________________________________________________________________________ Ing.VojtěchKlouček

31

SIMULACE PROVOZU BEZVŮLOVÉHO PŘEVODU OZUBENÝMI KOLY S ELASTICKÝMI PRVKY

Článek obsahuje popis jednoho z principů bezvůlového převodu ozubenými koly. Detailně je řešena konstrukce bezvůlové převodovky s předlohovými hřídeli. Vůle v záběrech ozubených kol a v ložiscích jsou vymezeny pomocí předepjaté torzní tyče. Vyšetřena je závislost reakčních sil, působících na ozubení a ložiska, na předpětí torzní tyče. Pomocí výpočetního programu, vytvořeného v prostředí Maple, je simulován provoz zatíženého převodu při reverzaci otáček. Výsledky jsou použity pro kontrolu pevnosti, únavy materiálu a životnosti dynamicky zatížených komponent převodu.

SIMULATION DES BETRIEBS EINES ÜBERSETZUNGSGETRIEBES MIT HILFE VON ZAHNRÄDERN MIT ELASTISCHEN ELEMENTEN

Der Artikel enthält eine Beschreibung eines der Grundsätze einer spielraumfreien Übertragung durch Zahnräder. Dabei wird detailliert die Konstruktion eines spielraumfreien Getriebes mit einer Zwischenvorlegewelle gelöst. Der Spielraum beim Ineinandergreifen der Zahnräder und in den Lagern wird mit Hilfe eines vorgespannten Torsionsstabs definiert. Untersucht wird die Abhängigkeit der Reaktionskräfte, welche auf die Zahnräder wirken, und des Lagers von der Vorspannung des Torsionsstabs. Mit Hilfe eines Computer-Programms, das in der Maple-Umgebung geschaffen worden ist, wird der Betrieb der belasteten Übertragung bei einer Reversierung der Drehzahl simuliert. Die Ergebnisse werden verwendet, um die Festigkeit, Materialermüdung und Lebensdauer der dynamisch belasteten Bauteile der Übertragung zu kontrollieren.

SYMULACJA PRACY BEZLUZOWEJ PRZEKŁADNI Z KOŁAMI

ZĘBATYMI Z ELEMENTAMI ELASTYCZNYMI

Artykuł opisuje jedną z zasad działania bezluzowej przekładni z kołami zębatymi. Szczegółowo omówiono konstrukcję przekładni z wałami pośrednimi. Luz przy ruchu kół zębatych oraz w łożyskach określony jest przy pomocy naprężonego skrętnego drążka. Na naprężeniu drążka skrętnego zbadano zależność sił reakcji działających na przekładnie i łożyska. Przy pomocy programu komputerowego, stworzonego w środowisku Maple, przeprowadzono symulację pracy obciążonej przekładni przy nawrotności obrotów. Wyniki wykorzystano do sprawdzenia wytrzymałości, "zmęczenia" materiału i żywotności dynamicznie obciążanych elementów przekładni.

32

SIMULATION OF WELDING IN THE REPAIR OF GAS PIPELINES WITH STEEL SLEEVES

Radoslav Koňár

*Jaromír Moravec **Miloš Mičian

University of Žilina

Faculty of Mechanical Engineering Univerzitná 1, 010 26, Žilina, Slovak Republic

[email protected] * Technical University of Liberec


[email protected] ** University of Žilina

Faculty of Mechanical Engineering Univerzitná 1, 010 26, Žilina, Slovak Republic

[email protected]

Abstract

The theoretical part of the paper deals with basic information about repair of gas pipeline with steel repair sleeves and simulation programme SYSWELD. The experimental part includes analysis of boundary conditions in two-pass fillet welding joint. By analyzing the boundary conditions welding speed, temperature cycles, macrosctructural analysis and its digitization can be determined. Using these boundary conditions welding process in programme SYSWELD was simulated. The results of the simulation are illustrated by means of temperature fields and temperature cycles.

Introduction

The article deals with the issues of repairing defects in steel gas pipes, in particular of permanent repairs employing steel sleeves.

1 Permanent repair of defects in gas pipelines employing steel sleeves

The Steel Repair Sleeves can be used for permanent repairing of high pressure gas,pipeline defects without interrupting its operation. With using these repair methods, we can repair defects such as internal and external corrosion, gouges, dents, grooves, arc burns, cracks, defective girth welds, laminations and leaks [2].

The steel sleeve is composed of segmented steel casing, fitted on two steel distance rings, which defines the space between the sleeve and the repaired pipe. This space is filled with glass beads and epoxy (composite). When epoxide is cured, it provides a perfect transmission of stresses from the pipeline to the sleeve, while there is an equal stress distribution in the pipeline and the sleeve. The type of the material and the thickness of the sleeve and distance rings must be same as those of the repaired pipeline. Required mechanical properties of composites are obtained after 24 hours of curing. Good space filling composites are checked through the inspection holes [2].

33

1–steel segmented sleeve, 2–distance rings, 3-composite, 4–inspection holes, D –pipeline defect, ++–weld.

Fig. 1 Principle repairs gas pipeline using steel repair sleeve [2]

Depending on the seriousness and type of defect on the pipeline sleeves can be divided to: ● cold sleeve – steel casing fitted on two steel distance rings is welded only longitudinal

butt weld, ● hot sleeve - steel casing fitted on two steel distance rings is welded longitudinal butt

weld and also is welded with fillet weld to distance rings [2].

2 SYSWELD

SYSWELD is a Finite Element software that simulates all usual welding processes such as MMA, MIG, TIG, spot welding, laser welding, heat treatment like bulk hardening, surface hardening, tempering and hardening and tempering, as well as thermo-chemical treatment like case hardening, carbonitriding, nitriding [1].

The software calculates dimensional variations and distortions of parts, hardness, strength and strain at break of the material in use, plus residual stresses, during and at the end of the welding or heat treatment process [1].

Simulation of a welding process requires two successive analyses: ● first a thermo-metallurgical analysis, ● followed by a mechanical analysis.

2.1 Definition of heat source in SYSWELD

Temperature T(x,y,z,t) is the function of coordinates in volume and time. Precious determination of temperature field during welding (that means mainly shape and size of heat affected zone) is the first and very important step for real determination of right material structure. Therefore finding the right mathematical description for heat source is very important for numerical simulations. Simulation system SYSWELD used for numerical calculations of heat following heat sources:2D Gaussian model – for surface thermal treatment of material, 3D Gaussian model – for simulation of welding with high power density in impact area and 3D Glodak model – for shielded metal arc welding, submerged arc welding, GTAW, GMAW. Because of its versatileness this type of heat source will be closely described [3].

2.2 Goldak model of heat source

This type of heat source can be used for most fusion welding conventional methods. Combination of two interlocking ellipsoids describes the real state so far best. By contrast to previous heat source the double-ellipsoid heat source is described by two equations individually for each ellipsoid. Compared to ellipsoid heat source in following equations there

3

34

are paramaterial

Double-and (3).

Fig. 2

,

,

Where l

where: , ,

, , ,

, , ,

ameters f1 anl (into indiv

2

-ellipsoid h

Goldak d

6. √3.

. .

6. √3.

. .

location of h

.

.

nd f2. Thesevidual ellips

heat source

double ellips

.

. . √.

.

. . √.

heat source

- - - - -

- - - - -

e are constansoids) and th

is shown in

soidal heat

. .

. .

is given by

- heat flow d- overall hea- coordinate- coordinate- constants imaterial,

- overall we- instantaneo- welding ve- location of- z-coordina

nts which inhe valid equ

n Fig.2 and

source mod

y equation:

density intoat, es of fusion es of point,influencing

elding time,ous weldingelocity, f heat sourcate at the clo

nfluence theuation for th

d is describ

del [3]]

o the materia

zone,

energy flow

g time,

ce in dependose of weldi

e energy flohem is:

bes by follo

al,

w intensity

dence on weing.

ow intensity

owing equat

distribution

elding time,

y into the

(1)

tions (2)

(2)

(3)

(4)

n into

35

For using double-ellipsoid model it is necessary to know size of the fusion zone (parameters

). These parameters are determinated on the basis of carried out experiments. Parameters are taken from the macro-scratch patterns. Non-modified double-ellipsoid model of heat source has already been used since1997. During the following years experiments were carried out which claimed that this model (thus model in non-modified form) isn´t possible to be used as a general source for all methods of fusion welding. Hence in these days double-ellipsoid heat source in a non-modified form is used. The modification lies in the change of constants in exponent. It is possible to use the modified source for most fusion welding methods except for welding methods with high concentration of energy like e.g. welding by laser, plasma or electron beam.

3 Experimental part

This experiment includes the analysis of boundary conditions for the simulation of welding in the repair of gas pipelines with steel sleeve and welding simulation using this boundary condition for two-pass weld.

3.1 Experimental sample

The model used for the experiment was compounded of two 60° pipe sections of materials L360NB (pipe and distance ring). The pipe has a diameter of 323,9 mm, pipe thickness 10mm and length 260 mm. Distance ring has a diameter of 333,9 mm, ring thickness 10mm and length 90 mm. Welding joint was welded using the MMA process. Experimental sample was welded with two fillet passes of weld. These passes of weld are only a part of the finished weld.

Fig. 3 Experimental sample, scheme (up), real sample (down)

36

3.2 Experimental measurements during and after welding

During welding there were measured welding parameters, welding time and thermal cycles in three points. After welding the weld was analysed. The complete analysis of weld for simulation in simulation programme SYSWELD contains:

● parameters of welding ( Uw, Iw ), ● cross-sectional geometry of the welds ( weld metal, heat affected zone ), ● welding speed ( sw ), ● temperature cycles.

Tab. 1 Parameters of welding

Uw- welding voltage, Iw- welding current, sw- welding speed, Qr- real heat input (η=0,8)

Fig. 4 Macrostructural analysis

Digitized weld macrostructures (Fig. 4) we get from cross-sectional parameters of welds (Fig. 5), which are necessary for the definition of Goldak heat source model.

Sz1 = 17,2 mm2 - weld surface, Sz2 = 16 mm2

Fig. 5 Digitized cross-sectional parameters of the weld

Weld Uw [V] Iw [A] sw [mm.s-1] Qr [J.cm-1]

Weld 1 23,6 92 2,2 7895

Weld 2 23,6 92 2,25 7719

Parameters of welding

37

Temperature cycles were measured by three thermocouples. Their location is shown on Fig. 6.

Fig. 6 Location of thermocouples

Fig. 7 Temperature cycles in three thermocouples

Temperature cycles are shown on Fig. 7 and their characteristic attributes in Tab. 2.

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600 700

Tem

per

atu

re [

°C]

Time [s]

Temperature cycles

Thermocouple 1

Thermocouple 2

Thermocouple 3

38

Tab. 2 Characteristic attributes of temperature cycle

4 Simulation in program SYSWELD

Numerical simulation process consists of several following steps: 1. Creating geometrical model and its distribution to FEM mesh, 2. Definition input data and boundary condition, 3. Simulation and presentation of results.

The model has the same geometrical dimensions as the experimental sample. Preparation and distribution of geometrical model to FEM mesh was created in VisualMesh. VisualMesh is a programme designed for meshing 3D geometrical models. Meshed FEM model can be seen on the Fig. 8. Distribution model has 61591 finite elements and 50918 nodes. The smallest element used in the FEM model is in the area of the weld with the dimension of 1,0mm×1,0mm×1,5mm.

Fig. 8 FEM model

Input data and boundary conditions used for simulation are: material database of the model was steel S355J2G3, but material of experimental sample was steel L360NB. We could use this database, because both of steels have the same mechanical and physical properties. Parameters of Goldak model and welding speed are in Tab. 3. In the simulation, temperature fields and temperature cycles were simulated for both passes of weld. Graphic results of the simulation are on the Fig. 9. and Fig. 10.

Thermocouple Tmax [°C] r300 [°C.s-1] t100 [s]

1 465 9,78 1132 480 10,6 1173 322 6,5 112

Thermocouple Tmax [°C] r300 [°C.s-1] t100 [s]

1 373 8,7 1362 360 8,5 1443 212 - 126

Characteristic attributes of temperature cycles

2. pass of weld

1. pass of weld

39

Tab. 3 Parameters of Goldak model and welding speed

Fig. 9 Simulated temperature fields for the first pass of weld

Fig. 10 Simulated temperature fields for the second pass of weld

Temperature cycles (Fig. 11, Fig. 12) were illustrated in three finite nodes. Temperature cycles were plotted in the same points, which were measured experimentally.

a [mm] b [mm] c1 [mm] c2 [mm] Q [W]

1. 2,5 5 2 5 2000 2,22. 3,5 2 2 5 1400 2,2

Parameters of Goldak modelWeld pass

Welding speed

[mm.s-1]

40

Fig. 11 Simulated temperature cycles for the first weld pass

Fig. 12 Simulated temperature cycle for the second weld pass

Tab. 4 Maximal temperature of simulated temperature cycles

1st weld pass 2nd weld pass

1 556 390

2 670 4103 510 365

Tmax [°C]Thermocouple

41

Conclusion

The theoretical part of the paper includes information about repair of gas pipeline with steel repair sleeves and welding simulation in programme SYSWELD. The experimental part includes analysis of boundary conditions and simulation of welding in the repair of gas pipelines with steel sleeves. There are results of simulation for two-pass weld. Results of simulation and experiment are not the same. The same results can not be reached because they are influenced by many factors (boundary condition, input data, definition of heat source).. Welding simulation has become a strong tool in technological practice. It helps to solve complex problems in welding efficiently and in a relatively short time.

Acknowledgments: This work has been supported by Scientific Grant Agency of Ministry of Education of the Slovak republic, grant VEGA No. 1/0186/09 and VEGA No. 1/0150/08.

Literature

[1] MORAVEC, J. Simulace tavného svařování - simulační program SYSWELD. In Zvárač. ISSN 1336-5045, 2009, vol. VI., issue 2., p. 9-12.

[2] PAŘÍZEK, P.; BRYNYCH, A., STUKBAUER, M. Trvalé opravy ocelových potrubí bez přerušení provozu aplikací objímek. In Plyn. vol. LXXXVI., online: http://www.ceps-as.cz/download/Opravy-ocelovych-potrubi-bez-preruseni-provozu-aplikaci-objimek_PLYN_2006-11.pdf, 2006.

[3] MORAVEC, J. Numerical simulations utilization for welding hardly weldable materials based on iron aluminides. Technical university of Liberec, first edition, 2010. ISBN 978-80-7372-682-9, 2010.

___________________________________________________________________________ Ing. Radoslav Koňár, Ing. Jaromír Moravec, PhD., doc. Ing. Miloš Mičian, PhD.

42

SIMULACE SVAŘOVÁNÍ PŘI OPRAVĚ PLYNOVODNÍHO POTRUBÍ POMOCÍ OBJÍMEK

Teoretická část článku se zabývá základními informacemi o opravách plynovodních potrubí pomocí ocelových objímek a simulačním systémem SYSWELD. Experimentální část zahrnuje analýzu okrajových podmínek pro proces simulace dvouvrstvého obvodového svaru. Součástí analýzy okrajových podmínek je vyhodnocení svařovacích parametrů, rychlosti svařování, teplotních cyklů, makrostrukturální rozbor a její digitalizace. Využitím těchto okrajových podmínek byl nasimulován proces svařování v systému SYSWELD. Výsledky simulace jsou vykresleny pomoci teplotních polí a teplotních cyklů.

SCHWEISSSIMULATION BEI DER REPARATUR

DER GASLEITUNGEN MIT STAHLHÜLSE

Der theoretische Teil des Manuskripts beschäftigt sich mit grundlegenden Informationen über die Reparaturen der Gasleitungen mit Stahlhülsen und das Simulationsprogramm SYSWELD. Der experimentelleTeil umfasst die Analyse der Randbedingungen der Simulation des Doppelschichtschweißens. Teil der Analyse der Randbedingungen ist es, die Schweißparameter, Schweißgeschwindigkeit, Temperatur-Zyklen, makrostrukturelle Analyse und ihre Digitalisierung zu bewerten. Mit diesen Randbedingungen wurde der Schweißprozess im Programm SYSWELD simuliert. Die Ergebnisse der Simulation werden mit Hilfe von Temperaturfelder und Temperaturzyklen dargestellt.

SYMULACJA SPAWANIA W NAPRAWACH RUROCIĄGÓW

GAZOWYCH PRZY POMOCY STALOWYCH TULEI

Część teoretyczna artykułu dotyczy podstawowych informacji na temat naprawy gazociągu z użyciem stalowych tulei i przy pomocy systemu symulacji SYSWELD. Część doświadczalna obejmuje analizę granicznych warunków spawania dwuprzebiegowego. Analiza obejmuje także ocenę parametrów spawania, prędkość spawania, cykle temperatury, analizę makrostrukturalną i jej digitalizację. W wyniku zastosowania warunków granicznych dokonano symulacji procesu spawania w systemie SYSWELD .Wyniki symulacji zostały przedstawione za pomocą pól temperatury i cyklów temperatury.

43

INFLUENCE OF SB ON GAS CONTENT AND FLOWABILITY OF ALLOY ALSI6CU4

Dušan Medlen

*Iva Nová **Dana Bolibruchová

***Dušan Urgela

University of Žilina Department of Technological Engineering

Univerzitná 1, 010 26 Žilina, Slovakia [email protected]

*Technical University of Liberec Faculty of Mechanical Engineering

Studentská 2, 461 17, Liberec 1, Czech Republic [email protected]

**University of Žilina Department of Technological Engineering


***University of Žilina Department of Technological Engineering


Abstract

Cast aluminum-silicon alloys are used in a number of automotive and industrial weight sensitive applications because of their low weight and very good castability. Modifiers are usually added to molten aluminum-silicon alloys to refine the eutectic phase particle shape and improve the mechanical properties of the final cast products and Al-Si alloys cast properties. In terms of aluminum-silicon, this usually involves the addition of strontium (Sr), sodium (Na) or antimony (Sb). The cast properties fluidity and mould filling capacity play a key role in the production of thin-section and geometrically complex cast parts. The presence of trapped gas or shrinkage pores in certain locations within castings has been shown to influence fatigue life. In this paper the influence of Sb on the gas content and flowability of AlSi6Cu4 has been researched.

Introduction

The excellent castability and mechanical properties of the AlSi6Cu4 alloy make it a popular foundry alloy for automotive applications. [1] Nowadays foundry plants are forced to reduce the wall thickness of cast pieces, to keep the narrow tolerance extent (combustion chamber, canal position) and to minimize the surface roughness (suction canal). The higher requirements on cast pieces make the construction more extensive and more complicated. [2]

The cast properties and mechanical properties of the AlSi6Cu4 alloys can be improved not only through modifying grain refinement but also through applying heat treatment and other technologies. In practice, the most common elements with the modifying effect are strontium, sodium and antimony. Adding these elements leads to a change in the shape of eutectic silicon, resulting in an increase of the mechanical and cast characteristics of the alloys. [1, 3]

44

Many experiments have been carried out to study and explain the effect of eutectic modifiers on hydrogen, microporosity and flowability. In general, it is observed that modified castings contain more porosity than unmodified ones. However, there is no consensus on the mechanism. Some possible reasons have been proposed and studied. In general, modifiers can

increase the inclusion content in the melt, decrease hydrogen solubility in the solid metal, change the solid-liquid interface morphology, reduce the surface tension of the liquid metal and increase the volumetric shrinkage. [1]

The AlSi6Cu4 castings must meet the high requirements not only on the mechanical properties but must meet high requirements on pressure tightness as well. Strontium is now widely used in practice for the modification of the AlSi6Cu4 alloy. When modifying the AlSi6Cu4 alloys by strontium, it was found out that the alloy subjected to this type of modification has higher values of the gas content, leading to higher porosity and thus reducing the pressure tightness. The aim of the experimental work was to investigate the influence of antimony on the gas content of the aluminum alloy AlSi6Cu4. [4, 5]

1 Experimental procedure

1.1 Melt treatment and casting procedures

The Aluminum alloy AlSi6Cu4 was used as the experimental material. The chemical composition of the alloy is listed in Tab. 1. The melting process and the modification were carried out in a graphite-chamotte melting crucible in an resistance oven. The grain refinement process using the refining salt AlCuAB6 was carried out while overheating the metal bath to 730 °C ± 5 °C. The modification process using antimony was carried out under the same technological conditions.

The amount of antimony chosen for each cast is listed in Tab. 2. This amount was determined and based on the most widely used quantities shown in the literature for Al-Si-Cu based alloys.

Tab. 1 Chemical composition of the AlSi6Cu4 alloy

Elements Si Fe Cu Mn Mg Ni Zn Ti Cr (wt.%) 6,52 0,43 3,88 0,45 0,29 0,01 0,46 0,15 0,01

Tab. 2 Amount of antimony for each cast of AlSi6Cu4 alloy used in the present work

Number of cast 1 2 3 4 5 6 7 8 9 10 11 Amount of Sb (ppm) 0 100 300 500 800 1000 1500 2000 2500 3000 10000

1.2 Gas content of the AlSi6Cu4 alloy

To improve the mechanical properties of these materials, the common practice is to refine the microstructure of the casting, such as modification. It has been shown that the defect area and distance from the free surface are important factors that determine the impact of defects on the fatigue life of castings. A large level of porosity, which is located in the center of the casting, may not effect the mechanical properties or the fatigue performance. A smaller, isolated pore near the surface may have a significant impact. The designers need to know how the cast part geometry and process will impact the porosity formation. As such, it is important to develop a comprehensive model to predict the size and location of microporosity in a casting as a function of the process variables. Microporosity usually results from a failure of the

45

interdendritic feeding or of the exsolution of the dissolved gas from the melt, or a combination of the two. [1]

To detect the gas content the Vacuum Density Tester 3VT-LC, the vacuum forming and the weighing-machine MK 2200LC were used for the weight identification of the experimental samples (Fig. 1). The weighing-machine evaluated the density of the samples and also the percentage, based on the mathematical and physical relationships and formulas, and determined the density index - DI. In each cast there were made two samples where the first one was solidifying in the air and the second one was placed in a vacuum for 7 minutes. The cross-section cuts of the individual samples can be seen in Tab. 3.

Fig. 1 Vacuum Density Tester 3VT-LC and weighing-machine MK 2200LC

Tab. 3 Cross-section cuts of AlSi6Cu4 modified by Sb

air vacuum air vacuum Cast no. 1 (0 ppm Sb) Cast no. 2 (100 ppm Sb)

air vacuum air vacuum Cast no. 3 (300 ppm) Cast no. 4 (500 ppm Sb)

4

46

The samconside

Fig. 2 sgraduateBased odetermithe expe

air Cast no

air Cast no

air Cast no

mples of Ared as a brie

shows the ced amountson the comned amounerimental sa

o. 5 (800 pp

. 7 (1 500 p

. 9 (2 500 p

AlSi6Cu4 mef overview

calculated vs of antimonmparison Tnt of the gasamples.

vacuumpm Sb)

vacuumppm Sb)

vacuumppm Sb)

air Cast no

modified byw of the poro

values of thny on the b

Tab. 3 and s content w

o. 11 (10 00

y antimony osity format

he density ibasis of the

Fig. 2, itwas confirm

air Cast n

air Cast n

air Cast n

vacuum00 ppm Sb)

solidified tion and loc

ndex of themathemati

t can be ned by obser

no. 6 (1 000

no. 8 (2 000

no. 10 (3 00

m

in the air cation.

e AlSi6Cu4ical and phynoted that trving the cr

vacuum0 ppm Sb)

vacuum0 ppm Sb)

vacuum00 ppm Sb)

in Tab. 3,

4 alloy modysical relatithe mathemross-section

m

m

m

, can be

dified by ionships. matically n cuts of

47

The unmodified AlSi6Cu4 alloy showed DI = 11.11%, while by adding a Sb modifier there were obtained significant changes, approx. a 63 percent reduction, in the gas content corresponding to 500 ppm Sb.

Fig. 2 Density index of AlSi6Cu4 modified by Sb

1.3 Flowability of the AlSi6Cu4 alloy

The literature survey has shown that the addition of strontium (Sr) decreases the flowability of the aluminium alloys. The authors have revealed in their works that the modification in a sand form reduces the flowability of an AlSi alloy from 5 to 7%, while in a steel mould the reduction is a little bit smaller varying between 2% or 3% [6, 7]. Mollard [8] has found out that the flow property of the aluminium alloys can be reduced up to 8% due to Sr addition. Kotte and Serak [9, 10] have shown that the lowering of the flowability through Sr addition is not so high as through the modification with sodium. According to them, the reason for the strong decrease of the flowability of the AlSi alloys through the sodium (Na) addition might be due to its effect on the surface tension of the AlSi alloys. The influence of antimony (Sb) on AlSi6Cu4 has not been investigated.

In this subchapter the effect of the antimony addition on the flowability of the AlSi6Cu4 alloy has been investigated. The amount of antimony was varied from 0 ppm up to 10 000 ppm (Tab. 2). The process parameters such as the casting temperature 730°C and the pouring temperature 730°C were held constant during these experiments. The accuracy of the casting is limited by the type of sand and the molding process. In terms of the flowability experiments, sand molds were used. The used molding sand consisted of silica sand (SiO2) 85%, bentonite (clay) 11%, and water 4%.

Traditionally, the flowability is measured by using the spiral test. The flowability is determined through the flow length of an alloy in a spiral contour. Fig. 3 shows the values of the flow length (cm) for each spiral. The final casts (spirals) from each casting used for the evaluation of the flow length are shown in Tab. 4.

11,11

12,59

5,51

4,40

6,27

4,78

9,26

7,75 7,78

13,10

5,49

3,00

4,00

5,00

6,00

7,00

8,00

9,00

10,00

11,00

12,00

13,00

14,00

0 1 2 3 4 5 6 7 8 9 10 11

Den

sity

In

dex

DI

( %

)

Cast number

48

Fig. 3 Flow length of AlSi6Cu4 modified by Sb

Tab. 4 Spiral test samples used for evaluation of the flow length of AlSi6Cu4

Cast no. 1 (0 ppm Sb)





Cast no. 6 (1 000 ppm Sb)






53

60

67

62

69

80

72 72

75

77

63

50

55

60

65

70

75

80

85

0 1 2 3 4 5 6 7 8 9 10 11

Flo

w le

ngt

h (

cm)

Cast number

49

Conclusion

In this work the influence of antimony on the AlSi6Cu4 alloy on the gas content and flowability has been investigated.

When modifying the AlSi6Cu4 alloys by antimony, it was found, that the alloy subjected to this type of modification has lower values of the gas content, leading to the lower porosity that has an effect on the pressure tightness comparing to modifying the AlSi6Cu4 alloys by strontium. Based on the experimental results of the gas content (Tab. 3 and 4), it can be claimed that the most appropriate amount of antimony with the lowest DI= 4,04 % is 500 ppm Sb. The gas content of the tested AlSi6Cu4 alloy sample, modified by 500 ppm Sb, decreased down to approx. 37 % of the original unmodified alloy (DI= 11,11%).

The spiral test experiments have shown that the amount of antimony in the aluminium melt has an effect on the flow length. The increase in the amount of antimony extends significantly the flow length of the aluminium melt. Based on the experimental results, the spiral test experiments (Tab. 5 and 6) can claim that the most appropriate amount of antimony for the flow length of AlSi6Cu4 is 1 000 ppm Sb. By addition of 1 000 ppm Sb the flow length increased to 51 % (80 cm) of the original unmodified alloy (53 cm).

Combining the best achieved results of these two experiments we can get 2 combinations: A. Choosing the best achieved result in the gas content experiments - 500 ppm Sb (decreased to 37%) - the flow length increased to approx. 14 % of the unmodified AlSi6Cu4. B. Choosing the best achieved result in the spiral test experiments – 1 000 ppm Sb (51 % increase) - DI decreased to approx. 43 % of the unmodified AlSi6Cu4.

Acknowledgement: The authors wish to thank the European Regional Development Fund for the received financial support to create the present paper within the execution of the project called "The Equipment for the Production of the Prototype Parts by Casting on a Computer-controlled Base" with the ITMS code 26220220047.

50

Literature

[1] CONLEY, J.G.; HUANG, J.; ASADA, J.; AKIBA, K..: Modeling the effects of cooling rate, hydrogen content, grain refiner and modifier on microporosity formation in Al A356 alloy. Materials Science and Engineering A 285, 2000. 49-55

[2] BOUSKA, O.: The effect of different casting parameters on the relationship between flowability, mould filling capacity and cooling conditions of al-si alloys. Metalurgija - Journal of metallurgy, Serbia, 2008. 17-30

[3] MEDLEN, D.; BOLIBRUCHOVÁ, D.: Teoretical studies of AlSi6Cu4 alloys. Technológ Vol. 2, 2010. 151-156

[4] GRZINCIC, M.: Manufacturing trends for engine blocks of automobiles. Slévárenství Vol. 2-3, 2003. 74-80

[5] ROMANKIEWICZ, R.; ROMANKIEWICZ, F.: Influence of modification of silumin AlSi6Cu4 on fracture morphology. Journal of machine manufacturing, vol. XLIX, 2009.

[6] BOLIBRUCHOVÁ, D.; TILLOVÁ, E.: Foundry Alloys Al-Si, EDIS Žilina, 2005. 180 [7] SABATINO, M. D.; SHANKA, S.; APELIAN, D.; ARNBERG, L.: Influence of

temperature and alloying elements on fluidity of Al-Si alloys. Doctoral Thesis Fluidity of aluminium foundry alloys, Trondheim, 2005

[8] MOLLARD, F.R.; FLEMMINGS, M.C.; NYAMA E.F: Understanding aluminium fluidity: the key to advanced cast products. AFS Trans., 1987. vol. 95, p. 647-652

[9] KOTTE, R.: Strontium modification gives critical melt control, Modern Casting, 1985. 33-35

[10] SERAK, V.: Modifikace slitiny AlSi10Mg sodikem a stronciem, Sbornik Konference Aluminium, 2001

___________________________________________________________________________

Ing. Dušan Medlen, Prof. Ing. Iva Nová, CSc., Doc. Ing. Dana Bolibruchová, PhD.,

Ing. Dušan Urgela

51

VLIV SB NA NAPLYNENÍ A ZABÍHAVOST SLITINY ALSI6CU4

Slévárenské Al-Si slitiny se používají v řadě automobilových a průmyslových aplikací náročných na nízké tíhové účinky z důvodu jejich relativně malé měrné hmotnosti a velmi dobré slévatelnosti. Modifikátory se obvykle přidávají do roztavených Al-Si pro zjemnění tvaru částic eutektické fáze a zlepšení mechanických vlastností finálních odlitků Al-Si slitin a jejich slévárenské vlastnosti. Pro slitiny Al-Si toto obvykle zahrnuje přidání stroncia (Sr), sodíku (Na), nebo antimonu (Sb). Od slévárenských vlastností jako tekutost a schopnost vyplnění formy hraje klíčovou roli v produkci tenkostěnných, geometricky složitých odlitků. Bylo prokázáno, že přítomnost zachyceného plynu a tedy pórů v některých místech odlitků, má vliv na únavovou životnost. V tomto příspěvku byl zkoumán vliv Sb na naplynení a zabíhavost AlSi6Cu4.

DER EINFLUSS VON SB AUF DEN GASGEHALT UND DIE FLIESSFÄHIGKEIT DER LEGIERUNG ALSI6CU4

Aluminium-Silizium-Legierungen sind werden in der großenr Anzahl in der Automobil- und Industrieelektronik aufgrund ihresr geringen Gewichts und ihrer sehr guten Gießbarkeit verwendet. Modifikatoren sind werden normalerweise im geschmolzenen Aluminium-Silizium-Legierungen zugefügt, um die Partikelform von der eutektischen Phase zu verfeinern und die mechanischen Eigenschaften ders fertigen Gussteile und der Al-Si-Legierungen und deren gegossenen Eigenschaften zu verbessern. Für Aluminium-Silizium beinhandelthaltet es sich normalerweise um die Zugabe von Strontium (Sr), Natrium (Na) oder Antimon (Sb). Von den Gusseigenschaften spielen Fließfähigkeit und Formfüllungsvermögen bei der Produktion von Dünnschicht- und geometrisch komplexen Gussteilen eine Schlüsselrolle. Die Anwesenheit von aufgefangenem Gas oder die Schrumpfung der Poren an bestimmten Orten im Guss führt zu einer Beeinflussung desr Lebensdauer. In dieser Arbeit wurde der Einfluss von Sb auf den Gasgehalt und Fließfähigkeit von AlSi6Cu4 untersucht.

WPŁYW SB NA ZAWARTOŚĆ GAZU I LEJNOŚĆ STOPU ALSI6CU4

Odlewy stopu aluminiowo-krzemowego mają często zastosowanie w rozwiązaniach przemysłowych i motoryzacyjnych wrażliwych na ciężar, ponieważ są lekkie oraz mają bardzo dobrą lejność. Modyfikatory dodaje się zazwyczaj do roztopionych stopów Al-Si w celu złagodzenia kształtu cząstek fazy eutektycznej i poprawy właściwości mechanicznych produktów końcowych ze stopów aluminiowo-krzemowych (Al-Si). Ten stop zwykle wymaga dodania strontu (Sr), sodu (Na) lub antymonu (Sb). Właściwości lejności i zdolności napełniania formy odgrywają kluczową rolę w produkcji form o cienkich ściankach i geometrycznie skomplikowanych. Stwierdzono, że obecność gazu, czyli pęcherzyków w niektórych miejscach odlewu wpływa na żywotność i tzw. "zmęczenie materiału". W niniejszym artykule badano wpływ antymonu (Sb) na zawartość gazu oraz płynność AlSi6Cu4.

52

INFLUENCE OF MECHANICAL STRESS ON EVAPORATION RESISTANCE OF KNITTED FABRICS

M. Motawe

*Antonín Havelka **Zdeněk Kůs


Faculty of Textile Studentska 2 ,461 17 Liberec, Czech Republic

[email protected] *Technical University of Liberec


[email protected] **Technical University of Liberec


[email protected]

Abstract

In this research, the evaporation resistance Ret [m2Pa/W] of knitted fabrics made from different core elastic ratios have been investigated; these fabrics have been extended to different levels and the evaporation resistance have been measured under these variations of extensions. It was found, that the evaporation resistance for the knitted fabric from elastic core yarn under the study decreased with the increase of the extension in the course direction.

Introduction

Moisture transport through textiles is one of the factors that influence the thermo Physiological comfort of the human being. The moisture can be transferred through a textile material in the form of vapors and liquids. The analysis of the scientific literature shows a high and constant interest in the problem of reliable determination of vapor permeability and the evaporation resistance properties of the textile materials [1 – 5].

The task of clothing is, beside fashionable embodiment and expression, the protection against harmful environmental stresses including the climatic conditions. On this account, well being, health and productivity of humans largely depend on clothing. Humans usually wear clothing all day long - even in bed we are surrounded by textiles; therefore it is often characterized as a “second skin”. Except in tropical latitudes, a person needs a constant protection to avoid simply freezing [6], so we can tell that the thermal properties are among the most important features of textiles [7-8].

The human body converts the energy provided by food into work and heat, depending mainly on the level of activity.

The main part of the moisture transfer occurs through the skin, since the skin is usually largely covered with clothing, and the moisture release of the human body is strongly influenced by the heat and moisture transfer through clothing [9, 10].

53

1 Test methodology and materials used for measuring evaporation resistance [m2Pa/W]

The Permetest instrument enables the determination of the relative WVP [%] and evaporation resistance Ret [m2Pa/W] of dry and wet fabrics within 3 -5 minutes- (Fig. 1).

Fig. 1 Permetest used for measuring the evaporation resistance

The measuring head of this small Skin Model is covered by a resistant semi-permeable foil which lets the liquid water transport from the measuring system into the sample. The cooling heat flow caused by water evaporation from the thin porous layer is quickly recorded by a special computer evaluated sensing system. In terms of heat transfer, this instrument presents the model of real human skin. Given by a new concept of measurement, which enables distinguishing small changes of water amount absorbed in the fabric during the unsteady state of diffusion and to record e.g. the heat of sorption, a very good measurement reproducibility was achieved, with CV often under 3%. The instrument provides all kinds of measurements similar to the ISO Standard 11092 and the results are evaluated by the identical procedure as required in this standard. The correlation coefficient of measurements related to the ISO Standard SKINMODEL exceeds 0.9. The results are treated statistically, displayed and recorded for next use [11]. When the results of measurement should be expressed in terms of the water vapor resistance Ret [m2Pa/W] according to the ISO 11092 Standard, then the following relationship is applied:

Ret = (pwsat - pwo) (1/qo - 1/qs) = C(100 - φ)(1/qo – 1/qs) (1)

Here, qs and qo mean heat loses of the moist measuring head in Free State and covered by a sample. The values of water vapor partial pressures pwsat and pwo in Pascals in this equation represent the water vapor saturate partial pressure valid for the temperature of the air in the measuring laboratory to 22-25C0, and the partial water vapor pressure in the laboratory air. The constant C will be determined by the calibration procedure. For this purpose, a special hydrophobic polypropylene reference fabric is used with the instrument. Besides the water vapor resistance, the relative water vapor permeability of the textile sample pwv can also be determined by the instrument. This practical parameter is given by the relation:

pwv [%] = 100 qs/qo (2)

54

1.1 Test samples The transport of heat and moisture through fabrics is one of the major concerns in the design of functional clothing such as sports wear. In the clothing research field, researchers usually assess the transport of heat and moisture through fabrics by using a sweating hot plate [12-15], but here the permetest was used to evaluate the evaporation resistance for the elastic fabrics which have been manufactured to achieve some requirements that other fabrics cannot achieve. The use of elastic yarn has resulted in fabrics that fit better on the body like a second skin and have good shape retention without any deformation throughout the life of the garment.

In this work three elastic knitted Rib 1x1 constructed fabrics with different Lycra ratios were used to measure the evaporation resistance [m2Pa/W] under different extensions as mentioned later. The elastic core yarn was used to produce this knitted fabric, Lycra was used as the core and the outer layer (sheath) was cotton. In terms of the core: sheath ratios for the three different types were: 8% Lycra: 92% cotton, 6% Lycra: 94% cotton and 4% Lycra: 96% cotton, and the count of the yarn for producing this fabric was 19.6 Tex for all the three different fabrics. A special frame was manufactured to obtain the different extensions for the used fabric (Fig. 2).

The different ratios of extension were applied in the course direction, 10%, 20%, 30%, 40% and 50% from the original length; at each extension of the fabric, the evaporation resistance was measured, three different tests were held for each extension and the mean value was calculated.

Fig. 2 Symbolic drawing of the extension frame made for applying mechanical tension

2 Effect of mechanical stress on the evaporation resistance [m2Pa/W]

Elastic core yarns have become established in many new application areas. They are used in sports wear, leisure garments and children’s wear, in high quality outer wear, in functional clothes and in technical products. Core yarn can be either elastic or rigid filament which is covered with natural or synthetic fibers. It is an ingenious idea as elastic or rigid material can be produced without sacrificing the texture or quality of traditional fibers. This is probably why its use in the textile sector is becoming more and more popular.

In this work the evaporation resistance of a Rib 1x1 knitted elastic fabric was measured with applying different degrees of extension from 10% to 50% and the water evaporation

55

resistance [Ret] was measured at each extension. Tab. 1 shows the variation in the evaporation resistance at each level of extension for the different samples.

Tab. 1 Ret [m2Pa/W] values at different extensions

Ext. % Ret [m2Pa/W]

Lycra 4% Ret [m2Pa/W]


Lycra 8% 0% 4.18 4.53 4.83 10% 3.81 4.18 4.46 20% 3.67 3.82 4.19 30% 3.25 3.46 3.56 40% 3.19 3.38 3.47 50% 3.12 3.27 3.38

The results show that applying different extensions to the Rib 1x1 elastic knitted fabric has an obvious effect on the evaporation resistence. As we can see from Fig. 3, the evaporation resistance for the measured fabrics decreases by the increase of the extension for all the different samples with the different Lycra ratios: 4%,6%,8%. Tab. 2 shows the Ret change percentage. We can say that the evaporative resistance [m2Pa/W] in the Lycra 4% decreased by 25.35% when applying 50% extension from the relaxed position, while decreased by 27.8% in Lycra 6% and by 30% in Lycra 8% at the same extension percentage.

Tab. 2 Ret [m2Pa/W] decrease percentage by different mechanical tension applied

Change% of Ret[m2Pa/W] Extension

% Ret [m2Pa/W]



Lycra 8%

0% 0 0 0

10% 8.85 7.72 7.66

20% 12.2 15.67 13.25

30% 22.24 23.62 26.29

40% 23.68 25.38 28.15

50% 25.35 27.81 30.02

56

Fig. 3 Interaction effect of different extensions and Lycra percentage on Ret [m2Pa/W]

Applying mathematical treatment the next equation was obtained:

z = 3.8 + 0.24x - 0.58y + 0.01x2 + 0.03y2 - 0.09xy (3)

where z = Ret , x = Lycra, y = Extension ratio. Fig. 3 also shows the interaction between the different Lycra ratios and the different extension applied to the elastic knitted fabric and their effect on the evaporation resistance of these fabrics. It also shows that the evaporation resistance increases with the increase of the Lycra ratio at each of the extension levels as observed from the equation (3). It is obvious from R2 = 99.5 % that when applying various extensions in the course direction in all of these cases we notice a significant effect on the evaporation resistance Ret [m2Pa/W] of the fabrics made from core yarns with different elastic ratios as previously mentioned. Concerning the water vapor permeability of these fabrics and using Fick’s equation, [16]

(4)

the rate of water vapor transfer for a fabric is directly proportional to the partial water vapor ∆p. It is a linear relationship to the vapor pressure inversely proportional to the evaporation resistance and Tm which is the latent heat of vaporization of water at the temperature Tm of the measuring unit. We can count the approximate diffusion of water vapor transfer, i.e. when Ret [m2Pa/W] for the 8% Lycra sample in the beginning of the extension (0%) was 4.83 [m2Pa/W] and by applying the maximum extension (50%), the evaporation resistance was 3.38 [m2Pa/W]. It was found out that the water vapor permeability increased about 42% which is a significant increase for the water vapor permeability.

57

Conclusion

In this work it was noticed that the evaporation resistance of Rib 1x1 knitted fabrics made from elastic core yarns was obviously affected by applying different levels of extensions, by increasing the extension for the tested fabrics. It was noticed that the evaporation resistance decreased rapidly at the beginning and at a certain level – here it was about 30% - the evaporation resistance decreased slightly and it was nearly the same, maybe due to the change of the fabric construction and due to the fact that the porous area in the fabric is nearly the same according to the different level of the applied tension. It could be concluded that the tight elastic knitted fabric could lead to more comfortable properties if it was used during practicing a light activity, but when practicing a heavy activity, the comfort of these fabrics will decrease due to the heavy sweat production, and it will also be difficult to get rid of this sweat in that liquid form and in this case the garment will stick to the body causing a lack of comfort. It was also concluded that the evaporation resistance increases with the increase of the elastomer ratio in the fabric. These results could be applied in designing functional, more comfortable garments concerning the different dimensions of the body’s different parts where we can apply different elastomer ratios and tightness to achieve the optimal comfortable wear.

58

Literature

[1] WATKINS, D. A.; SLATER. ,K.: The moisture-vapour perme-ability of textile fabrics . Journal of the Textile Institute. 72 (1) 11 – 18 (1981)

[2] GIBSON, P.W.: Effect of Temperature on Water Vapor Transport through Polymer Membrane Laminates. Journal of Polymer Testing. 19 (6) 673-691 (2000)

[3] QU, J.; RUCKMAN. J.: A new calculation method of water vapour permeability at unsteady states.Journal of the Textile Institute. 97 (5) 449 – 453 (2006)

[4] BROJESWARI DAS, A.; DAS, A.; KOTHARI, V.K.; FANGUEIRO R.; DE ARAÚJO, M.: Moisture transmission through textiles Part I: Processes involved in moisture transmission and the factors at play .AUTEX Research Journal. 7(2) 100- 110(2007)

[5] BROJESWARI DAS, A.; DAS, A.; KOTHARI, V.K.; FANGUEIRO R.; DE ARAÚJO, M.: Moisture transm-ission through textiles Part II: Evaluation Methods and Mathematical Modelling. AUTEX Research Journal. 7 (3) 194-216 (2007)

[6] HES, L.: The Effect of Planar Conduction of Moisture on Measured Water Vapor Permeability of thin woven fabrics. Fall Fiber Society Conference, Lake Tahoe (2002)

[7] KAWABATA S.: A Guide Line for Manufacturing Ideal Fabrics. International Journal of Clothing Science and Technology. 12( 3) 134-140(2000)

[8] LE C.V., LY N.G.: Heat and Moisture Transfer in Textile Assemblies. Text. Res.J. 65(4),203 (1995)

[9] BLIESNER W. C.:A Study of the Porous Structure of Fibrous Sheets Using Permeability Techniques. [Dissertation Thesis]. Appleton, the Institute of Paper Chemistry (1963)

[10] HAVELKA, A.,HALASOVÁ A.:The heat and moisture transport through clothing material. Proceedings of 4th Central European Conference, TU of Liberec. 141-142, Liberec (2005)

[11] HES L.; DOLEZAL I.: A New Portable Computer-Controlled Skin Model for Fast Determination of Water Vapor and Thermal Resistance of Fabrics. Asian Textile Conference(ATC7),New Delhi(2003)

[12] B. Farnworth, P.A. Dolhan.: Heat and water transport through cotton and polypropylene under wear. J. Text. Inst. 55 627 – 630 (1985)

[13] MCCULLOUGH, E.A.; KWON, M.; SHIM. H.: A comparison of standard methods for measuring water vapour permeability of fabrics. Meas. Sci. Technol. (14) 1402–1408 (2003)

[14] FAN, J.T.; CHENG, X.Y.: Heat and moisture transfer with sorption and phase change through clothing assemblies. Part I: Experimental investigation, Text.Res.J.75 99–105 (2005)

[15] PRAHSARN, C.; BARKER; R.L.. GUPTA, B.S: Moisture vapor transport behavior of polyester knit fabrics. Text. Res. J. 75 346–351 (2005)

[16] AE - GYEONG OH.: The measurement of water vapour transfer rate through clothing system with air gap between layers. Heat Mass Transfer (44) 375–379 (2008)

___________________________________________________________________________

M. Motawe, doc. Ing. Antonín Havelka, CSc., Prof. Dr. Ing. Zdeněk Kůs

59

VLIV MECHANICKÉHO ZATĚŽOVÁNÍ NA PRODYŠNOST ÚPLETŮ

V tomto výzkumu byla šetřena prodyšnost Ret [m2Pa/W] úpletů vyrobených z různě elastických vláken. Tyto látky byly napínány a jejich prodyšnost byla měřena v závislosti na různých napětích. Bylo zjištěno, že se prodyšnost testovaných úpletů z různě elastických vláken snižuje s rostoucím napětím.

DER EINFLUSS VON MECHANISCHEM DRUCK

AUF DIE DURCHLÄSSIGKEIT GESTRICKTER TEXTILWAREN

In dieser Forschungsarbeit wurde die Durchlässigkeit Ret [m2Pa/W] gestrickter Textilprodukte, die aus unterschiedlich elastischen Fasern gemacht sind, untersucht. Dieses Textilprodukt wurde über verschiedene Ebenen gespannt und die Durchlässigkeit bei allen verschiedenen Spannungen gemessen. Dabei stellte sich heraus, dass die Durchlässigkeit der getesteten gestrickten Textilien aus unterschiedlich elastischen Fasern mit dem Anstieg der Spannung in Laufrichtung nachließ.

WPŁYW OBCIĄŻENIA MECHANICZNEGO

NA PRZEWIEWNOŚĆ DZIANIN

W prowadzonych badaniach badano przewiewność Ret [m2Pa/W] dzianin wyprodukowanych z włókien o różnej elastyczności. Tkaniny te były naprężane a ich przewiewność badano przy różnych naprężeniach. Stwierdzono, że przewiewność badanych dzianin z włókiem o różnej elastyczności zmiejsza się wraz z rosnącym naprężeniem.

60

THE DYNAMIC ANALYSIS OF THE NEEDLE BAR MECHANISM OF SEWING MACHINES

Karel Pejchar

* Jaroslav Beran





[email protected]

Abstract

The article is concerned with the dynamic analysis of the mechanism of the needle transfer, which has been carried out by means of Lagrange equations of the second kind, with the purpose to determine kinematic magnitudes of the individual elements. There have been established geometrical and physical properties of the individual elements, and the initial conditions have been determined. Furthermore, there have been compiled motion equations, and they have been complemented with the boundary conditions providing for the proper function of the mechanism. A program for the solution of the proper motion equations has been generated in the environment of Matlab Simulink, including the boundary and initial conditions. The results of the dynamic analysis have been processed graphically.

Introduction

The present trend in the development of sewing machines is to shorten the sewing times in the sewing process and to increase the productivity. The endeavour to increase the productivity of these machines requires a thorough understanding of all processes related to the operation of sewing machines. The object of this study is to perform an identification of the needle transfer mechanism, which will lead to the determination of kinematic magnitudes of the individual elements of this mechanism. The identification of the mechanism of the needle transfer will be carried out by the analytic method of Lagrange equations of the second kind, which allow formulating the laws of motion by means of scalar quantities. The proper solution of the motion equations obtained by Lagrange method will be carried out by means of the software Matlab Simulink.

1 Description of the needle transfer mechanism

The needle transfer mechanism performs a rectilinear reverse movement that has been realised by a cam mechanism in the existing machine [2]. The newly proposed functional model of the machine consists of a crank mechanism with servo-drive converting rotary swinging motion into the rectilinear reverse movement. The needle transfer mechanism (Fig. 1) forms a part of the system that allows imitating the hand stitch. Its task consists in providing for the transfer of the floating needle between two needle bars operating above the work table of the machine and below it. The floating needle is clamped by collets (Fig. 1, item 12) in the needle bar, owing to the pressing force of the springs, items 11 and 15. The

61

unlocking of the collets is actuated during the movement of the needle bar by the impact of its controlling element (items 1, 6, 11, 3, 10, 17, 16) upon the machine frame before the dead centre of the needle transfer, where the impact is damped by a rubber pad (item 10). The stop block can be seen in Fig. 2.

The jacket of the needle bar (Fig. 1, item 2) goes on moving to the bottom dead centre and completes the process of the needle transfer.

Fig. 1 Sectional view of the needle transfer mechanism

Fig. 2 Newly proposed crank mechanism

There has been carried out experimental measuring of the force response of the springs (see Fig. 1, items 11 and 15) in order to establish the stiffness of these springs [1], and there has been taken a record by a high-speed camera, leading to determine the values of their intrinsic damping [1]. The results of these measurements are shown in Tab. 1. Another flexible element is the rubber pad (Fig. 2) mentioned previously. As for this pad, there has been carried out experimental measuring in order to establish the force required for the compression of the rubber pad. The resulting diagram of this force response is shown in the Fig. 3. In the record there can be seen the expected non-linear behaviour of the rubber pad during its compression. The course of the acting force has been approximated by a polynomial of the third degree (1) where x stands for the deformation of the rubber pad [1]. The equation of the dissipative force of the rubber pad is given by the relation (2). The coefficient of the linear damping figuring in the equation (2) is determined from the real behaviour of the system of the needle mechanism [1]. The mechanism of the needle bar and its proper function are provided by the system of the stop blocks. The coefficient of the restitution of these stops has been adjusted to such a value that the behaviour of the

62

mathematical model would be as close as possible to the behaviour of the real mechanism which has been examined by means of the high-speed camera.

Tab. 1 Values of stiffness and intrinsic damping of the springs

Stiffness kj [N/m] Intrinsic damping bj [N.s/m] Spring item 11 (index 1) 900 13.16 Spring item 15 (index 2) 690 3.32

Rubber pad item 10 (index 3) - 28.5

0

100

200

300

400

500

600

700

800

900

1000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

forc

e [N

]

compression [mm]

Fig. 3 Force necessary for compression of the rubber pad

F3(x) = 1573,9x3 - 2e-10 x2 + 445,17x (1)

(2)

2 Description of the mathematical model

The mechanism of the needle transfer has been simplified to three elements 1, 2 and 3 only, of the masses m1, m2 and m3 (see Fig. 5). The element 1 represents the jacket of the needle bar mechanism, the element 2 represents the controlling element of the mechanism and the element 3 represents the collets with the cage gripping the needle. The individual elements of the mechanism are represented by the perfectly rigid bodies and they are interconnected by springs and dampers. The element 1 is excited kinetically. The course of the excitement is shown in the following Fig. 4 and it matches the machine speed at 250 cpm. Moreover, the element 2 is influenced by the forces F3 and F4. The force F3 arises from the effect of the rubber pad (see Fig. 1. and Fig. 2) and the force F4 is the dissipative force. These two forces bear upon the body only in the moment when the position of the element 2 reaches the position of the stop (see Fig. 2).

63

The analysis of the needle transfer mechanism has been carried out for two variants. The first variant has been the model of the original concept, and the other one the model of the optimised concept with a modified inner cylinder. Tab. 2 presents the initial conditions for the simplified mathematical model. Tab. 3 resumes geometrical values of the model including other parameters necessary for the description of the system.

‐300000

‐250000

‐200000

‐150000

‐100000

‐50000

0

50000

100000

150000

200000

250000

300000

0 0,0025 0,005 0,0075 0,01 0,0125 0,015 0,0175 0,02 0,0225 0,025

acceleration [mm/s^2]

time [s]

Fig. 4 The course of acceleration of the element 1 during the movement from the upper position to the lower one

Tab. 2 Initial conditions for the needle bar mechanisms of original and optimised designs

Mech. of needle bar – orig. design Element 1

Element 2 Element 3

Initial position [m] 0 0.0719 0.0929

Initial value of velocity [m/s] 0 0 0

Initial value of acceleration [m/s2] 0 0 0

Mech. of needle bar – opt. design Element 1 Element 2 Element 3

Initial position [m] 0 0.0669 0.0929

Initial value of velocity [m/s] 0 0 0

Initial value of acceleration [m/s2] 0 0 0

64

Fig. 5 Scheme of simplified mode of needle bar mechanism

Tab. 3 Geometrical and mass magnitudes of system elements

Mass m1 of element 1[kg] 0.1196

Mass m2 of element 2 [kg] 0.0426

Mass m3 of element 3 [kg] 0.0051

Unmount.length of spring l01 [m] 0.089

Unmount.length of spring l02 [m] 0.0292

Value A [m] 0.0268

Value D [m] 0.0547

Value E [m] 0.0081

Length of spring after mounting lp1 [m] in original design

0.0718


0.0129

Length of spring after mounting lp1 [m] in optimised design

0.0668


0.0179

65

3 Compilation of motion equations

In order to obtain the motion equations, there has been employed the analytic method of Lagrange equations of the second kind for the homonomous couplings. The equation (3) has the usual form of Lagrange equations of the second kind (LEIID) for the system with potential, dissipative and operating forces, where qj stands for the generalised coordinate, Ek for the kinetic energy of the system, Ep for the potential energy of the system, Rd for the dissipative energy and Qj for the operating force [4]. In our case, the generalised coordinates are x2 and x3. The values of the intrinsic damping bj and the stiffness of the springs kj have been taken from Tab. 1. This mathematical model does not include the force of gravity.

. (3)

First of all, for the chosen analytic method LEIID the kinetic energy of the whole system (4) has been determined.

+ . (4)

Next, the potential energy of the whole system (5) has been established.

,

0,0949 0,0949,

0,0949 . (5)

The dissipative energy of the whole system is given by the sum of the individual components of the dissipative function (6).

1

2

1

2

1

2. (6)

The equation (3) shows the component of the operating force. In the system of the needle transfer mechanism there is no function of any operating force component; therefore, the element Qj=0. In the next step, the derivatives of the individual energy components according to the respective coordinates have been found. The derivative of kinetic energy according to the individual coordinates is

(7)

and

. (8)

The derivative of the potential energy according to the individual coordinates (x2, x3) is

1573,9 0,0949

2 10 0,0949 445,17 0,0949 (9)

and

. (10)

66

The derivative of the dissipative energy indicated by the sign is

(11)

and

. (12)

Subsequently, it is possible to perform the substitutions in the equation (3) and to compile the motion equations for the elements 2 and 3 of the system. The relation (13) constitutes the motion equation for the element 2 and the relation (14) is the motion equation for the element 3 of the system. It is

1573,90,0949 2 10 0,0949 445,17 0,0949

(13)

and

(14)

For the generation of the mathematical model there have been determined the boundary conditions simulating the system of stop blocks and cams which provide for the proper functioning of the needle transfer mechanism in the real model.

(15)

(16)

0,0989 (17)

0,0989 , 0 (18)

(19)

0 , (20)

The boundary condition (15) simulates the impact of the element 2 upon the transversal of the pin guided by the element 1. The condition (16) simulates the stop block consisting of two balls resting on the conical surface of the element 1. The conditions (17) and (18) simulate the impact of the rubber pad (or the element 2) on the machine frame. This impact comes up as soon as the element 2 reaches the position 0.0989 [m]. In this moment, the forces F3 and F4 start to act. The conditions (19) and (20) indicate that in the moment of the contact of the points F and G (see Fig. 3) the element 3 impacts with the element 2. The coefficient of the restitution between the elements 2 and 3 has been set up to the value 0.6. In the moment when the element 3 does not bounce from the element 2 anymore, the condition (20) is fulfilled. In this moment, the kinematic magnitudes (acceleration and velocity) of the element 3 are identical with the values of the acceleration and velocity of the element 2. The elements 2 and 3 perform a rectilinear reverse movement still, caused by the effect of the force by the rubber pad.

The equations (13, 14) have been resolved by means of the software Matlab with Simulink module.

67

4 Results of the kinematic analysis

The results of the kinematic magnitudes (position, velocity, acceleration) are shown in the following figures. Figs 6-8 show the courses of the kinematic magnitudes of the elements 1, 2, 3 for the original concept and for the optimised concept. Fig. 9 shows the courses of the positions of the points F and G for the original concept and for the optimised concept.

0 0.005 0.01 0.015 0.02-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

4000The course of acceleration

time[s]

acce

lera

tion[

m/s

2 ]

a1-opt

a2-opta3-opta1-puva2-puv

a3-puv

Fig. 6 Acceleration of elements 1, 2, 3 for the mechanisms of original design (puv) and of the optimised one (opt)

0 0.005 0.01 0.015 0.02 0.025-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3The course of velocity

time[s]

velo

city

[m/s

]

v1-optv2-optv3-optv1-puvv2-puvv3-puv

Fig. 7 Velocity of elements 1, 2, 3 for the mechanisms of original design (puv) and of the

optimised one (opt)

68

0 0.005 0.01 0.015 0.02 0.0250

0.02

0.04

0.06

0.08

0.1

0.12

0.14The course of position

time[s]

posi

tion[

m]

p1-optp2-optp3-optp1-puvp2-puvp3-puv

Fig. 8 Position of elements 1, 2, 3 for the mechanisms of original design (puv) and of the optimised one (opt)

0 0.005 0.01 0.015 0.02 0.0250.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

0.155Position of points F and G

time[s]

posi

tion[

m]

pF-optpG-optpF-puvpG-puv

Fig. 9 Positions of the points F and G for the mechanisms of original design (puv) and of the optimised one (opt)

Fig. 6 to Fig. 8 show that - in the original concept of the needle transfer mechanism - the controlling element is disengaged from the jacket in the machine speed at 250 cpm. Owing to this disengagement of the controlling element, the velocity of the impact of the element 2 on the stop block increases as well – see Fig. 4. In the original concept, at the time t=0.01575s the rubber pad is compressed and the element 2 bounces from the stop block. In the optimised concept, the rubber pad gets compressed at the time t=0.01796s. In the original design, the maximum acceleration of the element 2 comes up at the time t=0.0161s meanwhile in the

69

optimised design the maximum acceleration comes up at the time t=0.01815s. At the time t=0.01923s, the elements 3 and 2 get in mutual contact (see Fig. 9). The element 1 goes on completing its movement up to the value 0.0326m, which is necessary for the sufficient opening of the collets.

Conclusion

There has been generated a simplified model representing the mechanism of the needle bar, and the geometrical and mass parameters of the system elements have been determined. Subsequently, the motion equations have been compiled by means of Lagrange equations of the second kind. These motion equations have been complemented with the initial and boundary conditions. The motion equations have been solved in the environment of Matlab Simulink and the results have been processed graphically.

It has been ascertained that during the movement from the upper position of the needle transfer mechanism to the lower there are produced the impacts generating the high values of the acceleration of the element 2. Moreover, there occur the mutual impacts of the elements 2 and 3. These impacts are the source of the high levels of the noise and vibration intensity transferred upon the machine frame, which is confirmed by the experimental measuring performed on the real machine, too [5]. This mathematical model of the needle bar mechanism will constitute a part of the total identification of the system in the future, too, together with the crank mechanism and the servo-drive.

Acknowledgements:

The paper has been elaborated in the frame of the solution of the grant project: 1M0553.

Literature

[1] PEJCHAR, K., BERAN, J.: Optimization of the needle bar mechanism /article/. In. X. International Scientific Conference Transfer 2009, 17th – 18th November 2009. Trenčín, p. 44. Slovak Republic. ISBN 978—80—8075—414—3

[2] PEJCHAR, K.: Analysis and optimization of dynamic behavior of sewing machines. /Diploma work/. Liberec, TUL 2008,

[3] BERAN, J., PEJCHAR, K., KOMÁREK, J.,: Analysis and optimization of needle bar transfer mechanism. ACC JOURNAL 2010, year XVI, Issue A, Natural Sciences and Technology, ISSN 1803-9782

[4] JULIŠ, K., BREPTA, R.,: Mechanika II Dynamika, Volume 1, SNTL Praha 1987, L13-E1-V-41f/2270

[5] PEJCHAR, K., BERAN, J., Experimental analysis of the mechanism of sewing machine. Acta Universitatis Cibiniensis, Vol. LVIII, 2009, s. 55 - 60, Sibiu, Romania, ISSN 1583 - 7149.

___________________________________________________________________________ Ing. Karel Pejchar, prof. Ing. Jaroslav Beran, CSc.

70

DYNAMICKÁ ANALÝZA MECHANISMU JEHELNÍ TYČE U ŠICÍCH STROJŮ

Článek pojednává o dynamické analýze mechanismu předávání jehly, která byla provedena pomocí Lagrangeových rovnic druhého druhu s cílem určit kinematické veličiny jednotlivých členů. Byly určeny geometrické a fyzikální vlastnosti jednotlivých členů a určeny počáteční podmínky. Dále byly sestaveny pohybové rovnice, které byly doplněny o okrajové podmínky zajišťujícími správnou funkci mechanismu. V prostředí Matlab Simulink byl vytvořen program pro řešení vlastních pohybových rovnic včetně okrajových a počátečních podmínek. Výsledky dynamické analýzy byly graficky zpracovány.

DYNAMISCHE ANALYSE DES MECHANISMUS

DER NADELSTANGE BEI NÄHMASCHINEN

Der Artikel behandelt die dynamische Analyse des Mechanismus des Übergebens der Nadel, die mittels der Lagrange-Gleichungen zweiter Art mit dem Ziel erfolgte, die kinematischen Größen der einzelnen Glieder zu bestimmen. Es wurden die geometrischen und physikalischen Eigenschaften der einzelnen Glieder sowie die Anfangsbedingungen bestimmt. Ferner wurden Bewegungsgleichungen aufgestellt, die um die Randbedingungen ergänzt wurden, die die korrekte Funktion des Mechanismus gewährleisten. Im Medium Matlab Simulink wurde ein Programm für die Lösung der eigenen Bewegungsgleichungen, einschließlich der Rand- und Anfangsbedingungen, erstellt. Die Ergebnisse der dynamischen Analyse wurden grafisch dargestellt.

ANALIZA DYNAMICZNA MECHANIZMU PROWADNICY IGŁY

W MASZYNACH SZWALNICZYCH

Artykuł traktuje o analizie dynamicznej mechanizmu przemieszczania igły, którą przeprowadzono z pomocą równań Lagrange‘a drugiego rzędu, w celu określenia wielkości kinematycznych poszczególnych elementów. Zostały określone właściwości geometryczne i fizyczne poszczególnych elementów oraz określono warunki początkowe. Następnie zestawiono równania ruchu, które dopełniono warunkami brzegowymi zapewniającymi prawidłowe funkcjonowanie mechanizmu. W środowisku Matlab Simulink opracowano program do rozwiązywania właściwych równań ruchu wraz z warunkami brzegowymi i początkowymi. Wyniki analizy dynamicznej opracowano w formie graficznej.

71

A MECHANICAL MODEL OF THE VIBRATION CONVEYOR

Marek Pešík



[email protected]

Abstract

Vibrating conveyors as components of assembly lines are used in various technical branches, especially in the automotive industry. They do not only provide mechanical handling of differently shaped and sized parts, but they also allow the transport of loose materials. Hereby the main principle for the transportation of parts is based on the oscillating movements of the carrying element which, at the same time, imparts the vertical and horizontal velocity to the transported item. The vibration conveyors are driven by means of mechanical exciters or electromagnetic components. The mechanical exciters, based on the rotation of an unbalanced object, are either directly attached to the carrying element of the conveyer or are connected to the element that is joined to the conveyor by a flexible linkage. The electromagnetic components induce periodic power or moments between the carrying element and the frame. Generally, it is aimed to tune the system in a way to have the natural frequency according to the main transportation movement matching or nearly matching with the exciter frequency. The transport performance in relation to the energetic requirements of the drive is highest in the resonance zone.

Introduction

Vibrating conveyors have the carrying element often directly connected to the frame by either leaf springs or through an inertia element aiming on reactive dynamic power minimization. The leaf springs form a flexible linkage between the carrying element and either the frame or the inertia mass, and they perform a lead mechanism function simultaneously. From the mechanical point of view, it is basically a two mass model with one of the bodies (either the frame or the inertia mass) connected flexibly to the base or to the frame for reasons of vibroisolation. The second object is connected by a movable and flexible link-up. To provide an optimal vibration conveyor performance, it is necessary to know the influence of different dynamic system parameters on the natural frequency according to the main transportation movement. This is only possible by assembling and analysing its mechanical model. The following article deals with the set up of such a mechanical vibration conveyor model with either a translational motion or a screw motion.

1 Construction of Vibration Conveyors

In general, vibrating conveyors have their carrying elements adjusted to the shape and size of the objects to be handled. Additionally, the carrying surface is modified towards abrasion resistance and, commonly, to achieve a larger friction coefficient. Further, the surface has a significant influence on the emitted conveyor noise. The carrying element is directly connected either to the frame or to the inertia element by use of the springs. Generally, the flexible connection consists of the leaf springs whose stiffness is relatively easy to adapt;

72

hence, they perform simultaneously the conducting mechanism function. Hereby, the cross stiffness of the spring is significantly lower than the longitudinal stiffness.

The leaf springs are to be positioned as a parallelogram system that determines the relation between the horizontal and vertical amplitudes of the oscillating movement of the carrying element. This way it consequently estimates the velocity of the component or material transfer. Vibration conveyers are constructed to provide the translational or screw motions.

1.1 Conveyors with the translational motion

Translationally moved conveyors (Fig. 1) have their tubing or flume-shaped carrying elements connected with the frame by elastic elements. Thus, the transport is handled by both vertically and horizontally directed oscillation movements that perform at the same time. Both movements are bonded with each other by means of a lead mechanism caused by a parallelogram or analogue with the leaf springs. The dynamically forced power is generated via one or two mechanical excites that are connected to the carrying element.

Fig. 1 Vibration conveyor with translational motion

1.2 Conveyor with the screw motion

Conveyors with the screw motion (Fig. 2) have a cylinder-shaped carrying element on whose cylinder there are placed ground component parts that move via spiral lanes along the inner cylinder wall surface. Their transport is realized simultaneously with both the oscillatory translation movement and the oscillatory rotation movement of the carrying element which is usually connected to the frame by help of the leaf springs. These leaf springs are either placed symmetrically towards the cylinder base and the frame or with respect to the inertia mass. The handled components move then via the spiral lane. The force power will be initiated by one or more central electromagnets placed on the longitudinal axis of the carrying element. It is further possible to place the magnets in a symmetric relation to the perimeter of the carrying element.

73

Fig. 2 Vibration conveyor with screw motion

2 Mechanical vibrating conveyor model

Summing up, each vibration conveyor has a carrying element that is connected to frame or inertia mass by a movable and elastic linkage. The movable connection is realized with a lead mechanism that defines the mutual relation between the cinematic quantities of horizontal and vertical movement. The elastic connection then consists of e.g. pitched springs or leaf springs that can also carry out a lead mechanism function. To reduce the transmission of dynamic forces, the conveyer frame is elastically connected with the underlay.

Basically, from the mechanical point of view, we analyse a two mass model with one of the bodies performing a general motion, whereas the second body is connected through a lead mechanism having specified its cinematic connection.

With respect to the nature of the conveyor, we can, in the dynamic model, assume one or two symmetrical planes. In the first case, we consider the general plane motion of the frame and the relative movement of the carrying element that is connected via the lead mechanism. In the second case, the movement is traceable in one upright axis and the rotation of both the frame and the carrying element around that axis.

2.1 Conveyors with the translational motion

The conveyor frame is determined by the mass 1m and its moment of inertia about the axis passing vertically through its centre of gravity towards the symmetrical axis. To connect with the underlay we apply stiffness to the elastic connection in both the longitudinal direction yk1

and the cross direction xk1 as well as to the damping coefficients yb1 and xb1 . The

positioning of the spring fixtures at the frame and their distances to the horizontal axis in line with the stiffness coefficients xk1 and yk1 determine the torsion stiffness coefficient

zk 1

(Fig. 3).

74

Fig. 3 Mechanical conveyor model with translational motion

The carrying element will be determined by the mass 1m and the moment of inertia zJ2 about the horizontal axis passing through the centre of gravity. The movable connection with respect to the frame is realized by help of a parallelogram with levers of the length l and the basic angle of the levers to the vertical direction. The elastic connection with the frame

apply the springs of stiffness xk1 and yk1 . Further the fixture distances from the centre of the

carrying element gravity also determine the torsion stiffness z

k 1 (Fig. 3).

The Lagrange equation provides an equations-of-motion system

.0

dq

dE

qd

dE

dq

dE

qd

dE

dt

d pdkk

(1)

Firstly, it is possible to express the kinetic energy of the system

,2

1

2

1

2

1

2

1

2

1

2

1 222

222

222

211

211

211 zzzzk JymxmJymxmE (2)

followed by the potential energy of the system is

.2

1

2

1

2

12

1

2

1

2

1

2122

2122

2122

211

211

211

zzssyssx

zyxp

z

z

kyykxxk

kykxkE

(3)

As the potential energy of the formally applied springs with stiffness coefficients xk2 , yk2

and z

k 2 and connection points ( sx1 , sy1 ) and ( sx2 , sy2 ) complies with the leaf spring

energy of coefficient 2k , this relation (3) is rewritable as follows:

bgl

r

T2

1T

2m

2zJ

m1 J1z

y2

y1

x2

x1

f2z

1zf

k2

1k

y

b1

1k fz

75

.2

1

2

1

2

1

2

1 22

211

211

211 lkkykxkE zyxp z

(4)

It is possible to express similarly the damping energy dE dissipated by the dampers in an

equivalent way. However, as its application in the following analysis of natural frequencies would have only formal effect, it is overridden in the following relations.

For the considered coordinate data 1x , 1y , z1 , 2x , 2y and z2 describing the kinematic condition of the vibration conveyor system, the following requirements are to be effective:

,coscos 112 rlxx z (5)

,sinsin 112 rlyy z (6)

and

.21 zz (7)

After their substitution into the simplified Lagrange equation:

0

dq

dE

qd

dE

dt

d pk

(8)

including time t and the generalized coordinate q into which it is possible to put 1x , 1y , z1 and gradually, we receive four motion equations of the system.

As far as for the adjustment there results the following:

,0coscos 11122121 xkrmlmxmm xz (9)

,0sinsin 11122121 ykrmlmymm yz (10)

,0sinsincoscos

sincos

112

11212

221

z

zzz

zklrm

yxrmrmJJ

(11)

.0sinsincoscos

sincos

212

1122

lkrm

yxmlm

z

(12)

The mentioned differential equations system is possible to apply in respect to natural frequencies and to ensure the influence of the system’s parameters on their values. A correct tuning of the system with respect to the resonance zone enables high vibration performances at relatively low energy exposures.

2.2 Conveyors with the screw motion

The conveyor frame is again determined with the mass 1m and the moment of inertia yJ1

about the vertical axis passing through its centre of gravity. To connect it with the underlay, we apply the stiffness of the elastic supports in the longitudinal direction yk1 as well as in the

torsion direction y

k 1 . The damping coefficients yb1 and y

b 1 (Fig. 4) are possible to be

inducted in an equivalent way.

76

Fig. 4 Mechanical conveyor model with screw motion

The carrying element will have determined the mass 1m and the moment of inertia yJ2 about

the vertical axis passing through its centre of gravity. The movable connection in respect to the frame is realized by help of the leaf springs of the length l and the basic angle of the levers. The elastic and damping connection with the frame is formed by the springs of stiffness yk2 and

yk 2 as well as by the dampers with the damping coefficients yb2 and

yb 2

.

Again, an equations-of-motion system can be gained using the Lagrange equation. Firstly, it is possible to express the kinetic energy of the system providing the considered movements into a direction and around the vertical axis passing through the centre of gravity of both the carrying element and the frame.

,2

1

2

1

2

1

2

1 222

222

211

211 yyyyk JymJymE (13)

Subsequently, it is possible to express the system’s potential energy.

.2

1

2

1

2

1

2

1 2122

2122

211

211 yyyyyyp kyykkykE

y (14)

It is possible to express the damping energy dE dissipated by the dampers in an equivalent

way. However, for the same reasons as mentioned before, it will not be considered in the following natural frequencies calculation.

Due to the fact that the potential energy of the formally applied springs with the rigidity coefficients yk2 and yk 2 is identical with the leaf springs energy with stiffness

coefficient 2k , the relation (14) is rewritable as follows:

y

f2y

1yk1kyf

yk2f

2ykl

r

b

y2

1y

1yf

m2 J2y

1m

1yJ

2k

77

.2

1

2

1

2

1 22

211

211 lkkykE yyp y

(15)

For the considered coordinates 1y , y1 , 2y and y2 describing the kinematic condition of

the vibration conveyor system with a combined motion, the following requirements are to be effective:

sin12 lyy (16)

and

.cos12 r

lyy (17)

After their substitution into the equation (8) it is possible to gain three motion equations of the system for the coordinates 1y , y1 and . The result of the adjustment will be as follows:

,0sin 112121 yklmymm y (18)

,0cos 112121 yzyzy yk

r

lJJJ (19)

.0

coscossinsin

2

2

2

2122

212

lkr

lJr

Jlmym yyy

(20)

The referred differential equations system is, similarly to the example mentioned before, possible to be applied in respect to natural frequencies as well as to ensure the influence of the system’s parameters on their values. Again, the correct tuning of system with respect to the resonant zone will enable high vibration performances at relatively low energy exposures.

Conclusion

The analysed mechanical vibration conveyor models with both the translational motion and the screw motion together with their related motion equations provide the system tuning that considers the natural frequency of the main vibration movement. It is the only possible approach in order to ensure transportation efficiency performing at the smallest possible mechanical resistance just in the resonant zone. In terms of vibrating conveyors with the translational motion it is possible to obtain the correct tuning through the adjustment of the stiffness of the carrying element or the frame elastic connection. In case of conveyors with the screw movement the mentioned result is possible to be achieved by adjusting the mass parameters of the carrying element.

Acknowledgements:

The paper has been elaborated in the frame of the solution of the grant project: 1M0553

78

Literature

[1] KOŽEŠNÍK, J.: Kmitání mechanických soustav. Praha, 2008.

[2] HARRIS, C.M.: Shock and Vibration Handbook. Fifth edition. McGraw-Hill. NewYork, 2005.

[3] BRADSKÝ, Z.; VRZALA, R.: Mechanika III. Dynamika. Liberec, 1986.

[4] DRESIG, H.; HOLZWEIßIG, F.: Maschinendynamik. 8. Auflage.Springer Verlag. Berlin, 2008.

[5] NĚMEČEK, P.; PEŠÍK, M.: PUV 2011-24384 Kruhový vibrační dopravník. ___________________________________________________________________________ Ing. Marek Pešík

79

MECHANICKÝ MODEL VIBRAČNÍHO DOPRAVNÍKU

V různých odvětvích technické praxe, zejména pak v automobilovém průmyslu, se používají jako součásti montážních linek vibrační dopravníky. Umožňují transportovat nejen díly různých tvarů a velikostí, ale i sypké materiály. Princip dopravy dílů je založen na kmitavém pohybu nosného členu ve směru, který uděluje dopravovanému předmětu současně vertikální i horizontální rychlost. Pohon vibračních dopravníků se provádí pomocí mechanických nebo elektromagnetických budičů. Mechanické budiče založené na rotaci nevyvážené hmoty jsou připojeny buď přímo k nosnému členu dopravníku nebo ke členu, který je s ním spojen pružnou vazbou. Elektromagnetické budiče vytvářejí periodické sily nebo momenty mezi nosičem a rámem. V zásadě je snaha naladit systém tak, aby vlastní frekvence příslušná hlavnímu transportnímu pohybu byla blízká nebo shodná s frekvencí budící. V rezonanční oblasti je dopravní výkon nejvyšší ve vztahu k energetickým nárokům pohonu.

MECHANISCHES MODEL EINES VIBRATIONSTRANSPORTERS

In verschiedenen Gebieten der technischen Praxis, vor allem in der Automobilindustrie, werden Vibrationstransporter als Teile von Montagelinien verwendet. Sie ermöglichen nicht nur Bauteilen von verschiedenen Formen und Größen, aber auch Schüttmateriale zu transportieren. Das Prinzip des Transports der Bauteile wird auf der Schwingungsbewegung der Träger gegründet, der dem transportierten Bauteil gleichzeitig horizontale und vertikale Geschwindigkeit gibt. Der Antrieb von Vibrationstransportern wird durch mechanische oder elektromagnetische Erreger durchgeführt. Die mechanischen Erreger gegründete auf der Rotation der nicht ausgewuchtete Masse sind mit dem Träger unmittelbar verbunden oder werden zum Bauteil, der mit dem Träger durch elastisch verbunden ist, befestigt. Die elektromagnetischen Erreger bilden periodische Kräfte oder Momente zwischen dem Träger und dem Rahmen. Grundsätzlich gibt es Mühe das System so abzustimmen, dass die Eigenfrequenz entsprechende der Haupttransportbewegung sehr nah oder ganz gleiche mit der Erregungsfrequenz würde. Im Resonanzbereich ist die höchste Transportleistung in der Beziehung zum Energieverbrauch des Antriebs.

MECHANICZNY MODEL PRZENOŚNIKA WIBRACYJNEGO

W różnych dziedzinach praktyki technicznej, a zwłaszcza w przemyśle motoryzacyjnym, przenośniki wibracyjne używane są jako elementy linii montażowych. Pozwalają one nie tylko na transport części o różnym kształcie i wielkości, lecz także materiałów sypkich. Zasada transportu części polega na ruchu wahadłowym elementu nośnego w kierunku, który nadaje transportowanemu elementowi jednocześnie nie tylko prędkość poziomą, ale też pionową. Przenośniki wibracyjne napędzane są za pomocą mechanicznych wzbudnic lub czujników elektromagnetycznych. Mechaniczne wzbudnice wykorzystują rotację niewyważonej masy i są podłączone bezpośrednio do elementu nośnego przenośnika lub do elementu, który jest z nim połączony elastycznie. Elektromagnetyczne elementy generują siły okresowe albo momenty między nośnikiem a ramą. W zasadzie podejmowane są starania, aby system ustawić tak, aby częstotliwość głównego ruchu transportowego była zbliżona lub zgodna z częstotliwością wzbudnicy. W przestrzeni rezonansowej jest efekt transportowy największy w stosunku do zapotrzebowania energetycznego napędu.

80

TESTING AND SIMULATION OF VISCOELASTIC REINFORCEMENT APPLIED INTO CAR SEAT CONSTRUCTION

Michal Petrů

*Ondřej Novák


Faculty of Mechanical Engineering Studentská 2, 461 17, Liberec 1, Česká republika

[email protected] *Technical University of Liberec Faculty of Textile Engineering

Fakulta textilní, Katedra netkaných textilií Studentská 2, 461 17, Liberec 1, Česká republika

[email protected]

Abstract

Currently, the car manufacturers are dealing with optimization of seats, especially by reduction of weight and height, considering energy and ecological aspects of the used materials, at the same time maintaining or improving the existing parameters of the seat and back seat. Much emphasis is given to parameters of seating comfort and safety of car seats during a car crash. One possibility of seat weight reduction is by changing the construction of the seat cushion by incorporating viscoelastic composite reinforcement. Experimental quasi-static and dynamic tests were performed for samples of viscoelastic composite reinforcement materials for evaluation of mechanical properties. For deformation analysis of viscoelastic reinforcement, dummies (virtual human body) were loaded in a car seat and FEM simulation models were applied.

Introduction

At present, the research and development activities of car seats is focused on innovation that can bring weight reduction and energy efficient and environmentally friendly materials. The weight reduction of the car seat comes from car manufacturers´ concept of car weight reduction for decreasing fuel consumption and improving environmental friendliness. The principle is to reduce the weight of each component of the whole car, which in total leads to a significant reduction of the car weight. Therefore, a great effort is currently focused on supplementing or replacing the dominant material of car seats i.e. comfort layer - polyurethane foam - with low-density and energy efficient materials, which should be easily recyclable [5], [16]. That can bring not only energy savings and environmental improvements, but also certain improvement of desired properties. For significant weight reduction of car seats, it is required to make constructional changes of the whole seat, especially of the frame. Basically, the seat consists of a supporting frame, seat and backrest, which firmly holds a comfortable layer coated with upholstery fabric. It is known that the weight and body build of a passenger directly affects the interaction with the seat [7], [8], [12] [13]. Therefore, the passenger´s weight becomes a major parameter, which is crucial for modification of the seat, because the seat is designed especially for safety and comfort of the passengers. Weight reduction for the seat frame will ultimately reduce the weight of the whole seat, but it also reduces the deformation stiffness which is required for the crash safety [6]. Thus the optimization may be done by modification of the seat frame [8], where the security

parametremovedconstrucas the mwas to frame stexperimcarried dummycreation

Fig. 1

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Tested orthotrobehavioto hypecertain tensor aand cananisotrothe elasvolume

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81

82

and is described in the tensor dependence. Then the strain energy A is given by (1) and is described in the tensor dependence.

,volAizoAA (J))C()C( 1

where )C(izoA decribes izochoric part of the deformation energy function, )C(volA is

volumetric the deformation energy function, responsible for a volume change. C (2) is

modified Cauchy strain tensor C (3), x

XF

is material deformation gradient, I is identity

matrix and the expression IJ1/3 is connected with parts changing volume during the deformation.

FFC T 2

FFC T 3

IFJFFIJF 1/31/3 4

Therefore, the resulting stress is describable with 2.Piola-Kirchhoff stress tensor S 5 , which is also divided into two parts (izochoric and volumetric).

volizo SSC

(C)S

A

2 5

C

)C(Sizo

izoA

2 6

C

(J)Svol

volA

2 7

where izoS is 2. Piola-Kirchhoff stress tensor for izochoric part of deformation energy

function, volS is 2. Piola-Kirchhoff stress tensor for izochoric part of volumetric deformation

energy function.

2 Experimental measurements and simulation

2.1 Experimental example

Tested samples of composite reinforcement material have differently arranged structures. Fig. 1 shows isotropic elastic coating and Fig. 2 shows isotropic hyperelastic coating. It leads to different mechanical properties. Important material and geometrical parameters of tested samples are given in Tab. 1.

83

Fig. 2 Tested samples of composite reinforcement material applied into car seat construction

Tab. 1 Material and geometrical parameters of tested samples

Sample Thickness

[mm] Size [mm]

Surface weight[kg/m2]

Density [kg/m3]

Sample 1 0,67 100x50 858,92 1768

Sample 1 1,61 100x50 1695 1052,8

2.2 Experimental measurements

For determination of sample mechanical properties, quasi-static and dynamic experimental measurements were carried out. Firstly, the tensile test of samples was carried out according to ISO ČSN EN ISO 13934-1 (100 mm.min-1) standard on dynamometer Labortech 2.050 (Fig. 3). Samples in the machine and cross direction were loaded at force of 60 N. This corresponds with the weight of 120 kg. Whereas, a man weighing 100 kg loads the comfortable layer of car seats with the load of 60kg [5], [13]. Measurements were carried out in 5 cycles.

84

Experimental samples were also tested for the dynamic mechanical behavior by the help of "crash" test. The experiment was performed on the test equipment placed in laboratories of Department of Technology. The principle of the experimental test is shown schematically in Fig. 4 (lefthand side). This is a free fall of loading board from height mmh 800 on jaws, with which the experimental sample is clamped. The impact speed is 12,14 hkmv . The speed and path of free falling test was captured with high speed camera system Aramis.

2.3 Methodology of FEM simulation tests

Virtual simulation model was created in the program PAM CRASH for composite reinforcement applied in the construction of the seat cushion holder. This program is suitable for simulation of the material non-linearities, contact non-linearity and large geometric strains [5] [6]. It also allows to simulate the viscoelastic composite materials. The finite element mesh of designed seat cushion was created in special program Altair HyperMesh 9.0 [14]. For the simulation of tested viscoelastic composite reinforcement samples, “Materials 150 - Layered Membrane Element” was chosen. This material model allows defining the parameters for orthotropic layer and isotropic coating [15], which are derived from experimental measurements. This material model uses the total Lagrange formulation of strain and works on the principle of strain energy according to equation (1). Material parameters of the virtual dummy are based on [10]. The features of material model for the designed car seat cushion and a virtual dummy are given in Tab. 2. Boundary conditions were set as follows: bottom part of the seat was fixed in all directions (rotation 0iR and shifts 0iU , where

ZYXi ,, ). The virtual dummy with a weight of 100 kg was kept under gravity into the seats on the viscoelastic composite reinforcement with pretension of 60 N. The way of dummy position setting is schematically shown in Fig. 6.

Tab. 2 Material characteristics of the virtual dummy and seat model

Part Material model

Density [mm]

Young`s modulus

[GPa]

Poisson number

[-]

Virtual Dummy

Elastic Plastic 1000 0.250 0.3

Seat Elastic 7850 210 0.3

85

3 Results

Results of experimental measurements for the tested samples exhibit an anisotropic behavior. From quasi-static tests the fifth cycle was evaluated. Both samples exhibit hysteresis but sample 2 shows about 20% higher hysteresis. That causes higher damping effect. The measured data from the dynamic experiments were filtered and obtained results exhibit a significant elongation of samples. The sample 2 with hyperelastic coating exhibits higher elongation (about 32% approx.), which may lead to higher dynamic load beading capacity. Also force at break was 28% higher. Complete results are shown in Fig. 7, including a comparison of simulation and experiment.

Results of dummy position settings on pretensioned composite reinforcement are shown in Fig. 8. The distribution of deformation on tested composite reinforcements are shown

86

in Fig. 9. In the case of sample 1 the deformation is distributed on the whole area of reinforcement with elongation of 7.3mm. Sample 2 exhibits signifiant deformation especially in the area of pelvis bone contact with the einforcement. The elongation of sample 2 is 12.1mm, which is similar to the hyperelastic materials behaviour [3].

Fig. 8 Initial position (Dummy without contact), Result position(Dummy sits)

Fig. 9 Distribution of strain in samples (seated virtual dummy)

Conclusion

This article deals with testing and analysis of viscoelastic reinforcement, which can be applied in the construction of car seat as a cushion support. Its usage can lead to the weight reduction (Fig. 1). The experimental measurements were carried out and it was found that sample 2 exhibits more suitable properties, especially better damping (Fig. 7) and higher force at break. The distribution of strain on the composite reinforcement applied as a seat cushion holder (Fig. 9) is affected by their material properties. Sample 1 with isotropic elastic coating showed the distribution of deformation across the surface of reinforcement. Sample 2 with hyperelastic coating exhibited a significant deformation in the contact with pelvic bones of the virtual dummy. In general, it can be noted that sample 2 would be applicable to the car seat as reinforcement. Also it is necessary to determine its appropriate pretension, in order to enable its continuous setting. This would achieve the appropriate setting of the reinforcement stiffness for different passenger weights. This work was supported from project of Student Grant Competition.

Sample 1 Sample 2

87

Literature [1] SUBASHI, G.H.M.J.; NAWAYSEH, N.; MATSUMOTO, Y.; GRIFFIN, M.J.:

Nonlinear subjective and dynamic responses of seated subjects exposed to horizontal whole-body vibration, Journal of Sound and Vibration, Vol. 321, Issues 1 - 2, Pages 416-434, 2009

[2] HOLZAPFEL, G.A.: Nonlinear Solid Mechanics – A kontinuum approach forEngineering, John Willey& Sons Limited, 2000, ISBN 0471823198

[3] TRAN HUU NAM: Mechanical properties of the composite material with elastomeric matrix reinforced by textile cords, Ph.D Thesis, Technical University of Liberec, 2004.

[4] HOLZAPFEL, G.A., GASSER, T.: A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications.Comput. Meth. Appl.Mech. Eng., 2001. Vol. 190, p.p 4379–4403.

[5] PETRŮ, M.; NOVÁK, O.: Analysis and testing of mechanical properties of polyurethane foam and materials for nonpolyurethane car seat cushions, 4 th International Mechanical Engineering Forum, CZU Praha, 2011, ISBN 978-80- 213- 2156- 4

[6] PETRŮ, M.; PETŘÍK, J.: Development and optimization of the headrests car seat [online], Buletin of Applied Mechanics, CVUT Praha, 6 (22), 2010:34-40. WWW: <bulletin-am.cz/index.php/vam/article/download/159/159 >

[7] RAGAN, R.; KERNOZEK, T.W.; BIDAR, M.; MATHESON J.W.: Seat interface pressures on various thicknesses of foam wheelchair cushions: a finite modeling approach. Archives of Physical Medicine and Rehabilitation, 83, 2002: 872–875.

[8] FLIEGEL, V.; MARTONKA, R.: Automobile seats - simulation characteristics seats. Acta Mechanica Slovaca, 2008, ISSN 1335-2393.

[9] MARTONKA,R.: Measuring properties of car seats and its inovation, Ph.D. Thesis, Technical University of Liberc, 2010, ISBN 80-7083-922-9

[10] ZHAO J.;NARWANI G.: Development of a Human Body finite element model for restraint system R&D applicationst takata – Automotive Systems Laboratory, Inc.Paper Number 05-0399

[11] PETRŮ,M.;PETŘÍK,J.: Systems to optimize comfort and developments of car seat [online], Acta Technica Coriniensis - Bulletin of Engineering, ANNALS of Faculty Engineering Hunedoara, Romania, International Journal of Engineering, Fascicule 4, 2009: 55 -59. WWW: <acta.fih.upt.ro/pdf/2009-4/ACTA-2009-4-10.pdf>

[12] FLIEGEL, V.; MARTONKA, R.: Biomechanics system – human and seat. In Zb. Medzin. konferencie Modelovanie mechanických a mechatronických sústav MMaMS2007., TU Košice, UVZ Hermany, AT&P Journal Plus, 2007

[13] PETŘÍK, J.: Iteration of the automobile seat and weight, Ph.D. Thesis, Technical University of Liberec, 2008

[14] ALTAIR HYPERMESH 9.0, http://www.altairhyperworks.com [15] PAM-CRASH/SAFE™: Reference and Solver notes manual, Version 2005, 2008 [16] PETRŮ, M.; NOVÁK, O: Mechanical properties measurement and comparison of

polyurethane foam substitute, ACC JOURNAL 2010, Issue A, Natural Sciences and Technology, 16, 2010: 50 -59. ISSN 1803-9782

___________________________________________________________________________ Ing. Michal Petrů, Ing.Ondřej Novák, Ph.D.

88

TESTOVÁNÍ A SIMULACE VISKOELASTICKÉ KOMPOZITNÍ VÝZTUHY PRO KONSTRUKČNÍ APLIKACI DO AUTOSEDAČKY

V současné době se vývoj a výrobci automobilových sedaček zabývají optimalizací autosedačky a to především v oblasti snižování hmotnosti, výšky autosedačky a také energetické a ekologické úspornosti použitých materiálů při zachování či zlepšení stávajících parametrů současného sedáku a opěráku autosedačky, zejména parametrů kvality komfortu sezení a také bezpečnosti sedačky při nárazu automobilu. Jednou z možností snížení hmotnosti je konstrukční úprava sedáku autosedačky se začleněním kompozitní viskoelastické výztuhy. Byly provedeny experimentální kvazistatické a dynamické zkoušky testovacích vzorků viskoelastické kompozitní výztuhy pro definování mechanických vlastností. Pro analyzování deformace viskoelastické výztuhy aplikované do automobilové sedačky byly sestaveny simulační modely v prostředí MKP s hmotnostním zatížením virtuální figurínou.

TESTEN UND SIMULATION VISKOELASTISCHER

KOMPOSITIONSVERSTEIFUNG FÜR DIE KONSTRUKTIONSANWENDUNG BEI AUTOSITZEN

Zurzeit beschäftigen sich Entwicklung und Hersteller von Autositzen mit der Optimalisierung von Autositzen, und zwar vor allem auf dem Gebiet der Materialverringerung, der Höhe der Autositze und auch der energetischen und ökonomischen Sparsamkeit der verwendeten Materialien beim Erhalt oder der Verbesserung der bestehenden Parameter des gegenwärtigen Sitzes und der Lehne bei einem Stoß des Automobils. Eine der Möglichkeiten der Materialverringerung besteht in einer Konstruktionsverbesserung des Autositzes unter Eingliederung einer kompositorischen viskoelastischen Versteifung. Es wurden experimentelle quasistatische und dynamische Prüfungen von Testmustern viskoelastischer kompositorischer Versteifungen für die Definition der mechanischen Eigenschaften durchgeführt. Zur Analyse der Deformation der viskoelastischen Versteifung, wie sie in Autositzen verwendet werden, wurden Simulationsmodelle im Umfeld MKP mit einer Materialbelastung einer virtuellen Puppe zusammengestellt.

TESTOWANIE I SYMULACJA WISKOELASTYCZNEGO

KOMPOZYTOWEGO WYPEŁNIENIA DO ZASTOSOWAŃ KONSTRUKCYJNYCH W FOTELACH SAMOCHODOWYCH

W obecnych czasach prace podejmowane w ramach rozwoju i produkcji foteli samochodowych skierowane są na optymalizację fotelu samochodowego, zwłaszcza pod kątem zmniejszania jego masy, wysokości fotelu samochodowego oraz energetycznej i ekologicznej oszczędności stosowanych materiałów przy zachowaniu lub poprawie istniejących parametrów siedziska i oparcia fotelu samochodowego, w szczególności parametrów jakości komfortu siedzenia oraz bezpieczeństwa fotelu w przypadku uderzenia samochodu. Jedną z możliwości obniżenia masy jest konstrukcyjna zmiana siedziska przy zastosowaniu kompozytowego wiskoelastycznego wypełnienia. Przeprowadzano eksperymentalne badania quasistatyczne i dynamiczne próbek testowych wiskoelastycznego kompozytowego wypełnienia w celu określenia właściwości mechanicznych. W celu przeprowadzena analizy deformacji wypełnienia wiskoelastycznego stosowanego w siedziskach samochodowych opracowano modele symulacyjne w środowisku MKP przy obciążeniu manekinem wirtualnym.

89

COMPRESSION BEHAVIOUR AND ELASTIC RECOVERY OF HIGHLOFT MATERIALS (KELVIN-MAXWELL MODEL)

Jana Přívratská

*Katarina Zelová


Faculty of Science, Humanities and Education Studentská 2, 461 17, Liberec 1, Czech Republic

[email protected] *Technical University of Liberec Faculty of Textile Engineering,

Studentská 2, 461 17, Liberec1, Czech Republic [email protected]

Abstract

The behavior in compression and the elastic recovery of highsloft materials can be described by a Kelvin-Maxwell rheological model. The proposed model is a serial combination of the Kelvin model (parallel connection of Newtonian viscous fluids and elastic materials) and the Maxwell model (serial combination of Newtonian viscous fluids and elastic materials). This combination is able to cover the plastic deformation and relaxation behavior.

In this paper an algorithm for the determination of the input parameters of the proposed rheological model based on experimental data on condition that the load phase is carried out at constant stress for the time 0t will be presented.

Introduction

It was shown in [1, 2, 3] that the compression resistance and the elastic recovery (Fig. 1) of highloft nonwovens (low density fibrous network structures characterised by a high ratio of thickness to weight per unit area)

Fig. 1 Behavior of a highloft material in loading-recovery test

can be described by a rheological model composed of Kelvin and Maxwell models arranged in series (K-M model), (Fig. 2).

90

Fig. 2 Kelvin-Maxwell model

1 Model Description

The resulting strain ε of this model is the sum of the strain 1ε of the Kelvin model and

( 2 3ε ε+ ) of the Maxwell one, where 2ε describes the strain of its elastic part and 3ε the

strain of its plastic part. Both parts, Maxwell and Kelvin, are under the same stress σ [4]

3 12 2 3 1 1 1

ε εσ ε η ε η

d dE E

dt dt , (1)

where 1E , 2E are Young modules of springs (elastic elements) and 1η , 2η are viscosities of

viscosity elements. The stress-strain relation is determined by the differential equation [2]

2 21 1 2 1

2 2 22 21 2 1 1 3 1

σ 1 1 σ ε εσ

η η η η η η

E E E Ed d d dE E E

dt dtdt dt . (2)

1.1 Loading Modus

The material is compressed at time 0t by a constant stress 0σ and kept for some time 0t .

As 2

2

σ σ0

d d

dtdt for 0t t , equation (2) will be simpler

21 1

0 21 3 1

1 ε εσ

η η η

E Ed d

dtdt . (3)

Its solution under the initial conditions

0

2

σε 0t

E

(4)

(a jump of strain of the elastic part in Kelvin model) and

0 0

3 1

σ σε0

η η

dt

dt

(5)

(velocity of plastic strain of the first and the third part of M-K model) is for 0 Lt t

1

1η0 0 0

2 1 3

σ σ σε 1

η

Et

t e tE E

(6)

91

where Lt is the time when maximal compression is reached (strain ε 1 ).

For Lt t the compression strain is constant, ε 1t .

1.2 Elastic Recovery Regime

At the time 0t t , the stress 0σ is removed and that is followed by a jump of strain 0 20ε ε .

This represents the elastic recovery of the material. The plastic or tenacious strain is equal to

30ε . As the stress σ 0t for 0t t , the left side of equation (2) is zero and we get

21

21

ε ε0

η

Ed d

dtdt

. (7)

The solution of the differential equation (7) for elastic recovery regime is under the initial conditions

10 20 30

1

εε ε

η

Edt t

dt and 1

0 20 301

εε ε

η

Edt t

dt

, (8)

1

01η

30 20 30ε ε ε ε

Et t

t e

, 0 Lt t

(9)

1

1η30 20 30ε ε ε ε

LE

t tt e

, 0 Lt t . (10)

2 Determination of Model Parameters

The analysis of measured stress-strain and recovery curves (Fig. 1) makes it possible to find the input parameters 1 2 1 3, ,η ,ηE E for the M-K model. In experiments we can measure

0σ , 0ε , 20ε and 30ε . The parameter 2E is determined from the equation (1)

0 02

2 0 20

σ σ

ε ε εE

. (11)

The parameter 3η is determined from the equations (1) and (6), as 30ε represents residual

plastic strain

03 0

30

ση

εt . (12)

The rate 1

1η

Ex can be determined from the elastic recovery curve (10)

1 30

2 1 2 30

ε ε1lnε ε

tx

t t t

. (13)

92

Comparing the equations (6) and (9) it is possible to find

001

20 30

σ1

ε εxtE e

for 0 Lt t (14)

or

01

20 30

σ1

ε εLxtE e

for 0 Lt t . (15)

Than

11η

E

x . (16)

Conclusion

The determination of input parameters for the Kelvin-Maxwell model from experiments enables to find a set of constants characterizing highloft materials. With these results it is possible to perform computer simulations of other theoretical experiments in order to propose their optimum design.

Literature

[1] BHARANITHARAN, R.; PŘÍVRATSKÁ, J.; JIRSÁK, O.:Modelling of Compressional Properties of Highloft Textiles. In Proceedings of STRUTEX, Liberec 2003, pp. 427–431. ISBN 80- 783-769-1.

[2] PŘÍVRATSKÁ, J.; JIRSÁK, O.; BHARANITHARAN, R.: Maxwell-Kelvin model for highloft materials. In Proceedings of Programs and Algorithms of Numerical Mathematics 12, Prague 2004, pp.196-199. ISBN 80-85823-53-5.

[3] DONG, X.; ZHANG, J.; ZHANG, Y.; YAO, M.: A study on the relaxation behavior of fabric's crease recovery angle, International Journal of Clothing Science and Technology, Vol. 15, No.1, 2003, pp. 47-55.

[4] SOBOTKA, Z.: Reologie hmot a konstrukcí, Academia, Praha 1981. ___________________________________________________________________________ Prof. RNDr. Jana Přívratská, CSc. Ph.D., Ing. Katarina Zelová

93

CHOVÁNÍ VYSOCE OBJEMNÝCH MATERIÁLŮ PŘI KOMPRESI A ELASTICKÉM ZOTAVENÍ

(KELVINŮV-MAXWELLŮV MODEL)

Chování při kompresi a pružné zotavení vysoce objemných materiálů lze popsat pomocí Kelvinova-Maxwellova reologického modelu. Jde o sériové spojení Kelvinova modelu (paralelní spojení newtonovské viskózní kapaliny a hookovské elastické látky) a Maxwellova modelu (sériová kombinace newtonovské viskózní kapaliny a hookovské elastické látky). Tato kombinace je schopna obsáhnout plastickou deformaci i relaxační chování.

Uvádíme algoritmus, jak určit vstupní parametry pro tento reologický model pomocí experimentálních dat v případě, že zátěžová fáze probíhá při konstantním napětí po dobu 0t .

VERHALTEN VON HIGHLOFT MATERIALEN UNTER

DRUCKBEANSPRUCHUNG UND DAS RÜCKSTELLVERMÖGEN (KELVIN-MAXWELL-MODELL)

Das Verhalten von hochflorigen (highloft) Materialien unter Druckbelastung und deren elastische Erholung kann durch ein Kelvin-Maxwell Modell beschrieben werden. Es ist dies die Reihenschaltung eines Kelvin-Modells (Parallelschaltung von Newtonschen viskosen Flüssigkeiten und elastischen Materialien) und eines Maxwell-Modells (serielle Kombination von Newtonschen viskosen Flüssigkeiten und elastischen Materialien). Diese Kombination ist in der Lage, die plastische Verformung und das Relaxationsverhalten abzubilden.

Es wird ein Algorithmus vorgestellt, mit dem die relevanten Parameter für das beschriebene rheologische Modell aus experimentellen Daten bestimmt werden können, wenn die Belastungsphase der Zeit 0t unter konstanter Spannung erfolgt.

ZACHOWANIE WYSOKO OBJĘTOŚCIOWYCH

MATERIAŁÓW PRZY KOMPRESJI I ELASTYCZNYM ODKSZTAŁCENIU

(MODEL KELVINA-MAXWELLA)

Zachowanie przy kompresji i elastycznym odkształceniu wysoko objętościowych materiałów można opisać przy wykorzystaniu reologicznego modelu Kelvina-Maxwella. Jest to szeregowe połączenie modelu Kelvina (równoległe połączenie lepkiej cieczy Newtona i materiału elastycznego Hooka) oraz modelu Maxwella (szeregowe połączenie lepkiej cieczy Newtona i materiału elastycznego Hooka). To połączenie jest w stanie objąć zniekształcenie plastyczne oraz odkształcenie (zachowanie "relaksu").

Prezentujemy algorytm w celu określenia parametrów wejściowych dla tego modelu reologicznego przy pomocy danych doświadczalnych, gdy faza obciążenia odbywa się przy stałym napięciu przez czas 0t .

94

ANALYSIS OF DYNAMIC MODEL OF THE DRIVE OF SMALL DIAMETER KNITTING MACHINES ANGE 18.1

Josef Skřivánek *Martin Bílek


Czech Republic [email protected]

*Technical University of Liberec Czech Republic

[email protected]

Abstract

The paper deals with dynamic analysis of the driving system of small diameter knitting machines. Its main object is the description and analysis of the existing structural configuration of the drive. The present arrangement of the drive provides for a coupled motion of the needle cylinder and the dial, realized by a single driving unit. From the technological point of view, it is necessary to provide for a minimum deviation of swinging of principal parts of the machine during an operating cycle. The paper describes the compilation of a mathematical model. The motion equations have been devised by means of Lagrange equations of the second kind. They have been solved by means of the software Matlab and its superstructure Simulink. As the result, there have been obtained the courses of kinematic variables of basic parts of the driving system.

Introduction

The first step towards a modernization and optimization of the driving system is an evaluation of the existing state. The evaluation consists in an identification of courses of kinematic variables and determination of a maximum admissible deviation in the mutual swinging of the cylinder (Fig. 1, item V) and the dial (Fig. 1, item 8), which constitutes a technological condition. The cylinder and the dial are the two principal sub-systems of the knitting machine realizing the knitting process.

The Fig. 1 shows a diagrammatical view of the drive, which represents the existing design of the driving system of small diameter knitting machines Ange, made by the manufacturer of small diameter knitting machines Uniplet Třebíč a.s.

The existing designing concept provides for a mechanical coupling between the motion of the needle cylinder (Fig. 1, item 9) and that of the dial of the knitting machine (8).

These two elements have equal r. p.m., and for a proper operation of the machine, their mutual adjustment must be very precise – given by a prescribed technological condition. This chain consists of gear wheels (Fig. 1, items 0-7) and shafts (Fig. 1, items 23, 45, 78).

95

Fig. 1 Kinematic diagram of the drive of cylinder and dial of Ange 18.1

1 Mathematical model of the drive of Ange 18.1

In order to describe the behaviour of the studied system, it is necessary to devise a suitable mathematical model, able to describe its behaviour during an operating cycle with a defined precision. The individual parts of the system are influenced by a number of forces, the magnitudes of which are determined by the technological process and are variable in time. These forces include e.g. the forces necessary for lifting the needles and sinkers, the passive resistances in individual kinematic couples, passive resistances in the groove of the needle cylinder etc. However, from the view of the overall loading of the partial assemblies of the system, the magnitudes of certain forces are negligible, and in devising the mathematical model, they can be disregarded without an impact on the precision of the solution.

The proper mathematical model of the driving system of knitting machines (see Fig. 1) has been devised under the following conditions. The masses of individual elements of the mechanism (elements 0-8) including the pertinent parts of the shafts and of the seating are substituted by mass points. With the mass points, their inertia moments have been determined.

The shafts interconnecting the gear wheels transmitting the driving moment are considered to be elastic elements, and are substituted by torsional stiffness k (R0, 23, 45, 78). The mass of the needle cylinder 9 is considered including the needles, sinkers and its other components. It is divided into two mass points. These mass points are linked by a torsional spring. The elastic elements are attenuated by viscous damping with the damping co-efficient b.

1.1 Conditions

In the calculation there are considered the plays in gear wheels. These plays are substituted by angular deflections of gear wheels of the mechanism. The plays have been determined from drawings. For the compilation of motion equations of the system defined as above, there have been used the Lagrange equations of the second kind in the following form:

96

The proper mathematical model of the driving system of knitting machines (see Fig. 1) has been devised under the following conditions:

a) the masses of individual elements of the mechanism (elements 0-8) including the pertinent parts of the shafts and of the seating are substituted by mass points. With the mass points, their inertia moments have been determined.

b) the shafts interconnecting the gear wheels transmitting the driving moment are considered to be elastic elements, and are substituted by torsional stiffness (R0, 23, 45, 78).

c) the mass of the needle cylinder 9 is considered including the needles, sinkers and its other components. It is divided into two mass points. These mass points are linked by a torsional spring.

d) the elastic elements are attenuated by viscous damping with the damping co-efficient b.

e) in the calculation there are considered the plays in kinematic couples. These plays are substituted by angular deflections of gear wheels of the mechanism.

For the compilation of motion equations of the system defined as above, there have been used the Lagrange equations of the second kind in the following form:

i

.d

ji

P

i

K

i

K

q

RQ

q

E

q

E

q

E

dt

d (1)

For the system in Fig. 2, we can elicit the following energy equations:

...

.....

VV

..

0K

II2

1I

IIIIIIIE

288

277

266

255

244

233

222

2211

20

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

(2)

27878

24545

22323

21

2

2

12

1

2

1

2

1

2

1

)(k

)(k)(k)(k)(kE VVR0R0P

(3)

27878

24545

22323

21

2

2

1

2

1

2

1

2

1

2

1

)(b

)(b)(b)(b)(bR

..

.....

V

.

VR

..

0R0d

(4)

The quantities appearing in the equations:

EK- kinetic energy, EP- potential energy, Rd- dissipative function, qi –generalised co-ordinate,

ib - co-efficient of viscous damping [Nm.s.rad-1], ik - co-efficient of stiffness

[Nm.rad-1], - transmission, I -moment of inertia [kg.m2], - swinging [rad], - angular velocity [rad.s-1], - angular acceleration [rad.s-2]

97

The subscripts in the designations of quantities express the relation to the elements of the drive. Once we perform the respective derivatives and insertions into the basic form of the Lagrange equation of the second kind, we obtain the actual motion equations. The number of equations corresponds to the respective generalised co-ordinates in the same sequence as the preceding derivative.

02323011

0022323011002022

201100

)(k)η(k

)(k)η(b)η(b)(b)ηIηI(I

VV

R0R

...

V

.

VR

..

R

..

(5)

0)11 VV

.

V

.

VV

..

V (k)(bI (6)

034454523233445452323234433 )η(k)(k)η(b)(b)ηI(I

...... (7)

0577878

454557457845452577

256655

)η(k

)(k)η(b)(b)ηIηI(I......

(8)

08 787877888 )(k)(bI....

(9)

The principal parameters for the solution of a dynamic model are the moments of inertia, stiffness and damping of individual elements of the drive of cylinder and dial of small diameter knitting machines. The principal parts of the driving system have been set up as a 3D model by means of the CAD software Pro/Engineer. By means of these models, there have been determined the inertia moments of the system elements, as well as the Method of final elements have been used to determine torsional stiffness of shafts and of needle cylinder. Another parameter included in the equations is the coefficient of viscous damping. The relation for calculation of the said coefficients is based on logarithmic decrement, moment of inertia and stiffness of the respective component. The plays have been included in the solution by means of the following conditions.

0 iiPiiiP (10)

iiiPiiPiiiP ΦΦ (11)

iiiPiiPiiiP ΦΦ (12)

For i = 0, 1, 2, 3, 4, 5, 6, 7, 8.

Transmissions appearing in the equations

0101 , 0202 , 3434 , 5656 , 5757

The matrix shape of the movement equations

0 qqq...

KBI (13)

98

q)q(.

KBIq..

1 (14)

For the derived motion equations there has been devised a mathematical model in the software Matlab. For the solution of these motion equations there has been employed the environment Matlab, including its superstructure Simulink. The individual equations have been written in matrix form, and subsequently solved by sequential integration by means of solver in the software Simulink. There has been employed a solver using the standard Dormand-Prince method, termed ode45.

By solution of the devised motion equations for the assigned initial conditions there has been obtained the response of the system to the prescribed kinematic excitation, namely to the course of acceleration during knitting the sock heel or toe. This knitting regime has been chosen because it makes highest demands on the driving system. The course of acceleration is idealised, and it is always assigned to the rotor of the electric motor.

Tab. 1 Mass and Materials properties

Component name Part Moment of inertia [Kg*m2]

Stiffness [N*m* rad-1]

Damping [N*m*s*rad-1]

gear wheel 0 0 9.8299361e-5 - - gear wheel 1 1 2.1271433e-2 - - gear wheel 2 2 1.3357134e-3 - - gear wheel 3 3 3.0747164e-5 - - gear wheel 4 4 2.8658272e-4 - - gear wheel 5 5 1.8609515e-4 - - gear wheel 6 6 2.5144821e-4 - - gear wheel 7 7 1.49e-4 - - Dial 8 2.4e-4 - - Needle cylinder V 2.3864947e-2 200750 25.5625 Shaft R0 R0 8.1e-4 12954 1.4087 Shaft 23 23 72.6e-6 3423 0.1100 Shaft 45 45 8.425e-5 4500 0.1359 Shaft 78 78 2.96e-6 2560 0.0192

2 Results of the dynamic analysis

The results of the analysis indicate an important effect of plays in the system. They bring about high impact forces at a change of direction of the movement of individual gear wheels in gear sets. In the Fig. 4 there can be seen considerable peaks in acceleration, due namely to the adjustment of plays and the subsequent mutual impact of individual dents.

These values are as much as 3 times larger in comparison with a system without plays. In a similar way – although not so considerably –the adjustment of plays manifests itself in the courses of the velocity (Fig. 5), too. A deformation of the course of velocity in comparison with the theoretical course is notable here as well. The Fig. 3 displays the difference of velocities of the needle cylinder and of the dial. Plays in the system and the resiliency of individual elements of the system bring about deviations in the position of the output element of the kinematic structure (dial – element 8). The course of the difference in the swinging of the dial with respect to the needle cylinder is shown in the Fig. 2.

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Fig. 2 Difference of positions of the cylinder and the dial

Fig. 3 Difference of velocities of the cylinder and the dial

Fig. 4 Courses of accelerations of individual elements of the drive

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Fig. 5 Courses of velocities of individual elements of the drive

Conclusion

The paper describes the compilation of a mathematical model of the drive of small diameter knitting machines. As the result, there have been obtained the courses of kinematic quantities, and there has been determined the maximum deviation of the positions of the cylinder and of the dial in the worst loading condition. There has been studied the system of knitting machines ANGE 18.1, where the analysis has brought the value of the maximum deviation of positions 4.8 °.

A previous study [1] has demonstrated the advantages of a reduction of the number of elements in the driving system. This structural modification reduces the energy required for the drive of the principal parts of the machine by as much as 30%. It can be achieved by employment of controlled drives. Based on these facts, there will be devised a new mathematical model, taking in consideration a new configuration of the driving system with the application of unit drives.

The compiled mathematical model will serve as optimization tool for subsequent dynamic tuning of the system. Employing this model, it will be possible to design driving systems and to analyse varied operating regimes of the driving unit. Acknowledgements:

The paper has been elaborated in the frame of the solution of the grant project: 1M0553

Literature

[1] SKŘIVÁNEK, J., BÍLEK, M. :The small-diameter knitting machine structure change, IV Miedzynarodowa Konferencja Mlodych Naukovcow Szkol Wyzszych Euroregionu Nysa, Jelena Gora, 2010, pp.: 243-248, ISBN 978-83-61719-86-1

[2] JULIŠ, K., BREPTA, R.,: MechanikaII, Dynamika, Volume 1, SNTL Praha 1987, L13-E1-V-41f/2270

__________________________________________________________________________ Ing. Josef Skřivánek, doc. Ing. Martin Bílek, Ph.D.

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ANALÝZA DYNAMICKÉHO MODELU POHONU MOLOPRŮMĚROVÉHO PLETACÍHO STROJE ANGE 18.1

Článek je zaměřen na dynamickou analýzu pohonného systému maloprůměrového pletacího stroje. Hlavním cílem je popis a analýza stávajícího konstrukčního uspořádání náhonu. Současné uspořádání pohonu zajišťuje svázaný pohyb jehelního válce a přístroje realizovaný jednou pohonnou jednotkou. Z technologického hlediska je nutné zajistit minimální odchylku natočení hlavních částí stroje během pracovního cyklu. Příspěvek popisuje sestavení matematického modelu. K sestavení pohybových rovnic byly použity Lagrangeovy rovnice druhého druhu. Ty byly řešeny pomocí software Matlab a jeho nadstavby Simulink. Výsledkem jsou průběhy kinematických veličin základních částí pohonného systému.

ANALYSE DES DYNAMISCHEN MODELLS DES ANTRIEBS DER

KLEINRUNDSTRICKMASCHINE ANGE 18.1

Der Artikel befasst sich mit der dynamischen Analyse des Antriebssystems der Kleinrundstrickmaschine. Das Hauptziel ist die Beschreibung und die Analyse der bestehenden Konstruktionsgestaltung des Antriebs. Die derzeitige Anordnung des Antriebs gewährleistet die gekoppelte Bewegung des Nadelzylinders und des Gerätes mittels einer Antriebseinheit. Unter dem technologischen Aspekt ist es erforderlich, eine minimale Abweichung der Drehung der Hauptteile während des Arbeitszyklus zu gewährleisten. Der Beitrag beschreibt die Erstellung eines mathematischen Modells. Zur Formulierung der Bewegungsgleichungen wurden Lagrangegleichungen zweiter Art verwendet. Diese wurden mittels der Software Matlab und ihres Überbaus Simulink gelöst. Das Ergebnis sind die Verläufe der kinematischen Größen der grundlegenden Teile des Antriebssystems.

ANALIZA MODELU DYNAMICZNEGO NAPĘDU

MAŁOŚREDNICOWEJ MASZYNY DZIEWIARSKIEJ ANGE 18.1

Artykuł jest poświęcony analizie dynamicznej układu napędowego małośrednicowej maszyny dziewiarskiej. Głównym celem jest opis i analiza obecnego układu konstrukcyjnego napędu. Obecnie układ napędu zapewnia sprzężony ruch cylindra igłowego i przyrządu wykonywany przez jedną jednostkę napędową. Z technologicznego punktu widzenia konieczne jest zapewnienie minimalnego odchylenia ustawienia głównych części maszyny w ciągu cyklu roboczego. Artykuł opisuje zestawienie modelu matematycznego. Do zestawienia równań ruchu wykorzystano równania Lagrange’a drugiego rzędu. Rozwiązywano je przy pomocy oprogramowania Matlab i jego nadbudowy Simulink. Wynikiem są przebiegi wielkości kinematycznych podstawowych części układu napędowego.

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LIST OF AUTHORS

Name E-mail

prof. Ing. Jaroslav Beran, CSc. Technical University of Liberec

doc. Ing. Martin Bílek, Ph.D. Technical University of Liberec

doc. Ing. Dana Bolibruchová, PhD. University of Žilina

Ing. Petr Dolejš Technical University of Liberec

Prof. ATH Józef Drewniak, Ph.D., D.Sc. Technical University of Bielsko-Biała

doc. Ing. Antonín Havelka Technical University of Liberec

Ing. Vojtěch Klouček Technical University of Liberec

Ing. Radoslav Koňár University of Žilina

Dr Jerzy Kopeć, Ph.D. Technical University of Bielsko-Biała

Prof. Dr. Ing. Zdeněk Kůs Technical University of Liberec

Ing. Dušan Medlen University of Žilina

doc. Ing. Miloš Mičian, PhD. University of Žilina

Ing. Jaromír Moravec, PhD. University of Žilina

M. Motawe, CSc. Technical University of Liberec

Prof. Ing. Iva Nová, CSc. Technical University of Liberec

Ing. Ondřej Novák, Ph.D. Technical University of Liberec

Ing. Karel Pejchar Technical University of Liberec

Ing. Marek Pešík Technical University of Liberec

Ing. Michal Petrů Technical University of Liberec

Prof. RNDr. Jana Přívratská, CSc. Ph.D. Technical University of Liberec

Ing. Josef Skřivánek Technical University of Liberec

Ing. Dušan Urgela University of Žilina

Dr Stanisław Zawislak, Ph.D. Technical University of Bielsko-Biała

Ing. Katarina Zelová Technical University of Liberec

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LIST OF REVIEWERS

Name Work location Andrášová Hana, PaedDr. Ph.D. Jihočeská univerzita v Českých Budějovicích

Antoch Jaromír, Prof. RNDr. CSc. Matematicko-fyzikální fakulta UK v Praze

Baraniecka Anna, Dr. Uniwersytet Ekonomiczny we Wroclawiu

Blin Jutta, Prof. Dr. phil. Hochschule Zittau/Görlitz

Brauweiler Jana, Dr. rer. pol. Internationales Hochschulinstitut Zittau

Busch-Lauer Ines Andrea, Prof., Dr. Fachhochschule Zwickau

Čech Jaroslav, Prof. Ing. CSc. Vysoké učení technické Brno

Čiháková Silvia Aguilar, Ing., Ph.D. Technická univerzita v Liberci

Daněk Ladislav, doc. Ing. CSc. Vysoké učení technické v Brně

Delakowitz Bernd, Prof.Dr.rer.nat Hochschule Zittau/Görlitz

Domosławski Zbigniew, Prof. dr hab. N. Med. Karkonoska państwowa szkoła wyższa w Jeleniej Górze

Doucek Petr, Prof. Ing. Vysoká škola ekonomická v Praze

Dynybyl Vojtěch, Prof. Ing., CSc. ČVUT Praha

Felixová Kateřina, Ing., Ph.D. Univerzita J. E. Purkyně v Ústí nad Labem

Fliegel Vítězslav, Doc. Ing. CSc. Technická univerzita v Liberci

Gerstlberger Wolfgang, Univ.-Prof.Dr.rer.pol.habil. University of Southern Denmark

Griebel Bernd, Prof. Dr. phil. Hochschule Zittau/Görlitz

Harland Peter E. Prof. Dr. Internationales Hochschulinstitut Zittau

Herzig Ingo, M.A. PhDr. Technická univerzita v Liberci

Heßberg Silke, Prof. Dr.-Ing. Westsächsische Hochschule Zwickau

Hlavatý Ivo, doc. Ing. Ph.D. Technická univerzita Ostrava

Hokr Milan, Doc. Ing. Ph.D. Technická univerzita v Liberci

Homišin Jaroslav, Prof. Ing. CSc. Technická univerzita v Košiciach

Honců Jan, Prof. Ing. CSc. Technická univerzita v Liberci

Hortel Milan, Ing., DrSc. Akademie věd ČR, Praha

Hyžík Jaroslav, Prof. Ing. CSc. Technická univerzita v Liberci

Chocholoušková Hana, Mgr. Státní archiv Liberec

Jáčová Helena, PhDr. Ing. Ph.D. Technická univerzita v Liberci

Jeleńska Kamila, mgr Karkonoska państwowa szkoła wyższa w Jeleniej Górze

Jihlavec Jan, Mgr. DiS. Technická univerzita v Liberci

Jílková Jiřina, Prof. Ing. CSc. Univerzita J. E. Purkyně v Ústí nad Labem

Jirman Pavel, Ing. Technická univerzita v Liberci

Kasper Tomáš, Doc. PhDr. Ph.D. Technická univerzita v Liberci

Klápšťová Květoslava, Mgr., Ph.D. Technická univerzita v Liberci

Klíma Radek, Ing. Cadence Innovation s.r.o., Liberec

Koláčková Ludmila, Mgr. Univerzita obrany Brno

Kretschmar Gerlinde, Prof. Dr.-Ing. Hochschule Zittau/Görlitz

Kurek Robert, dr Uniwersytet Ekonomiczny we Wroclawiu

Ładysz Jerzy, dr Uniwersytet Ekonomiczny we Wroclawiu

Lachout Martin, PhDr., Ph.D. Metropolitní univerzita Praha

Lori Willfried, Prof. Dr.-Ing. Westsächsische Hochschule Zwickau

Maroušková Marie, Prof. PhDr., CSc. Univerzita J. E. Purkyně v Ústí nad Labem

Modrlák Osvald, Doc. Ing. CSc. Technická univerzita v Liberci

Mráz Jan, Ing. Ph.D. EGAP, a.s., Praha

104

Müller Hardy, Prof. Dr. Westsächsische Hochschule Zwickau

Müller Miloš, Ing. Ph.D. LENAM s.r.o., Liberec

Nehls Uwe, Prof. Dr.- Ing. FH Oldenburg

Neuhoff Antje, M.A. TU Dresden

Norková Alena, Mgr. Magistrát města Ústí n.Labem

Nouza Jan, Prof. Ing. CSc. Technická univerzita v Liberci

Nováková Kateřina, Ing. Česká školní inspekce Liberec

Pavelka Tomáš, Ing. Ph.D. Vysoká škola ekonomická v Praze

Pawłowski Maciej, dr inż. Politechnika Wrocławska

Marzena Pełczyňska, M.D., Ph. D. Karkonoska państwowa szkoła wyższa w Jeleniej Górze

Pełka Marcin, mgr Uniwersytet Ekonomiczny we Wrocławiu

Pištěk Luděk, Ing. TOS Varnsdorf

Procházka. Martin, Ing. Okresní hospodářská komora Liberec

Radzik Tadeusz, Prof. dr Karkonoska państwowa szkoła wyższa w Jeleniej Górze

Richter Ernst, Dr.-Ing. Hochschule Zittau/Görlitz

Rozkovec Jiří, Mgr. Technická univerzita v Liberci

Seidler Christine, Dr. Internationales Hochschulinstitut Zittau

Schmidt Fritz Jochen, Prof. Dr.-Ing. habil. Hochschule Zittau/Görlitz

Schönherr Jürgen, Prof. Dr.-Ing. Hochschule Zittau/Görlitz

Skála Marek, Mgr. Ing., Ph.D. Technická univerzita v Liberci

Skrbek Jan, Doc. Dr. Ing. Technická univerzita v Liberci

Stößel Bernd, Prof. Dr.-Ing. Hochschule Zittau/Görlitz

Strahl Danuta, Prof. dr hab. Uniwersytet Ekonomiczny we Wroclawiu

Svoboda Milan, PhDr. Ph.D. Technická univerzita v Liberci

Szargot Maciej, Prof. dr hab. Uniwersytet Humanistyczno przyrodniczny

Piotrków Trybunalski Ševčík Ladislav, Prof.Ing. CSc. Technická univerzita v Liberci

Štěpánek Libor, PhDr. Mgr. Ph.D. Masarykova univerzita v Brně

Theilig Holger, Prof. Dr.-Ing. habil. Hochschule Zittau/Görlitz

Trešl Jiří, Doc. Ing. CSc. Vysoká škola ekonomická v Praze

Urbánek Václav, Doc. Ing. CSc. Vysoká škola ekonomická v Praze

Vacek Jiří, Doc. Ing. CSc. Technická univerzita v Liberci

Vašutová Jaroslava, Doc. PaedDr. Ph.D. Univerzita Karlova v Praze

Vítek Leoš, Doc.Ing. Ph.D. Vysoká škola ekonomická v Praze

Vlčková Kateřina, Mgr. et Mgr. Ph.D. Masarykova univerzita Brno

Vogt Matthias-Theodor, Prof. Dr. Hochschule Zittau/Görlitz

Walter Johann Heinrich, Prof. Dr.-Ing. Dipl.-Math. HS für Technik und Wirtschaft Dresden

Winnicki Tomasz, Prof. zw. dr hab. inż. Karkonoska państwowa szkoła wyższa w Jeleniej Górze

Winzeler Marius, Dr. Des.,lic.phil. Städtische Museen Zittau

Worlitz Frank, Prof. Dr.-Ing. Hochschule Zittau/Görlitz

Zaremba – Warnke Sabina, dr Uniwersytet Ekonomiczny we Wroclawiu

Žďánská Vladimíra, MUDr. Privátní lékař, Liberec

Žižka Miroslav, Doc. Ing. Ph.D. Technická univerzita v Liberci

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GUIDELINES FOR CONTRIBUTORS

Guidelines for contributors are written in the form of a model article, which is available as a Word document at the Secretariat of the ACC, [email protected].

MODEL ARTICLE FOR THE ACC JOURNAL

Pavel Novák *Jiří Němec





[email protected]

Abstract

In the scientific and professional ACC JOURNAL original research reviewed papers, scientific studies and reports on research projects are published. The author is responsible for the originality, as well as for the scientific and formal accuracy of the article. The author can be an academic, a specialist from a research institution or a PhD. student. Publishing a contribution from an author outside any HEI in the ERN will be charged an editorial fee of EUR 50.

Introduction

Thematically the ACC JOURNAL is subdivided into two issues. Issue A, covering natural sciences and technology, and Issue B, focusing on social sciences and economics.

Articles on natural sciences, technology and economics can be published only in English, inclusive of the introductory abstract and the name of the author’s institution. Social science topics can be dealt with in one of the ERN languages with an introductory abstract in English.

These guidelines are written in the required template for the contribution and can be used for contribution submitting. The guidelines are subdivided into two chapters called the Contents and the Form; and further on more subcategories follow.

1 Contents of the Contribution The contribution contains a headline, the author or authors´ address, introductory abstract, introduction, description of the studied problem, conclusion, literature and abstracts in the ERN languages.

1.1 Headline of the Contribution

It should be concise and clear.

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1.2 Author’s and/or Authors´ Name/s The name of the author is written without the academic degrees, similarly to co-authors, whose names are also included without the academic degrees and below each other. The names of authors or co-authors with the degrees are provided below the list of references and under a line.

1.3 The Author’s Address This piece of information includes the name of the institution and the department in English, street name, postcode number, town and the English name of the country. Below this, the e-mail address follows. The second co-author has an asterisk before the name and the address. The third co-author has two asterisks in the same positions.

1.4 Introductory Abstract

The abstract outlines the studied problem, states introductory conditions and gained results.

1.5 Introduction

In this section the author describes the current state, aims of the study, and used methods, which will be elaborated on in the following parts.

1.6 Description of the Studied Problem The content of the contribution can use not only text, but also pictures, equations, and graphs.

1.7 Conclusion

The conclusion presents a summary of gained results, presents the unique and original principle of the used methods.

1.8 Literature

The list of the used literature complements the content of the contribution and presents sources the author studied.

1.9 Abstracts in the ERN Languages

Abstracts in the ERN languages, which are Czech, German, and Polish, emphasize the character of the journal and its main type of target readers.

2 Form of the Contribution

What follows is a description of how the contribution should look. The authors can utilise the electronic form of the model contribution for their writing.

The basic style is “Normal“, Times New Roman font size 12 with single spacing. Furthermore, other styles are used according to the position and function of a piece of text in the contribution. Switch on the function “Styles“and define the following items or utilize the model contribution.

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Individual chapters and sub-chapters are separated by a blank line style”10_Gap between the lines B“, size 16. After the headline a blank line follows; it uses style”10_Gap between the lines A“, size 5.

2.4 Headline of the Article

For this, the style”01_Name of the contribution“is used (capital bold letters, size 14, aligned to the centre). Beneath the headline there is a blank line, style”10_Gap between the lines B“.

2.5 Name of the Author/Authors

For this item style”02_Name of the author/authors“is used (bold letters, size 12, aligned to the centre). Beneath the name there is a blank line, style „10_Gap between the lines B“.

Before the name of the co-author there is an asterisk, similarly to another one placed before the name of the home institution in the address section. In the case of the third co-author, in the same positions two asterisks are placed.

The name of the author and/or co-author is provided with the academic degrees below the list of the used literature; it is below a line, utilising style”06_Text“(size 12, block-justified, gap 3 behind a paragraph).

2.6 The author’s Address

The author’s address (or authors´ addresses) utilise style”03_Name and address of the institution“(size 12, aligned to the centre). The e-mail address is style”04_E-mail address“(underlined, size 12, aligned to the centre). Beneath the e-mail address of the author (authors) there is a blank line, style”10_Gap between the lines B“.

2.7 Introductory Abstract

The word Abstract is style”05_Name of a part of the contribution“(bold letters, size 12, left-aligned). Beneath the word Abstract there is a blank line, style”10_Gap between the lines A“.

On the following line there is the text of the abstract, style”06_Text“not longer than 10 lines. Beneath the text there is a blank line, style”10_Gap between the lines B“.

2.8 Form of the Introduction

The word Introduction is style”05_Name of a part of the contribution“. Beneath the word Introduction there is a blank line, style”10_Gap between the lines A“.

On the following line there is the text of the introduction, utilising style”06_Text“. Beneath the text there is a blank line, style”10_Gap between the lines B“.

2.9 Description of the Studied Problem

The name of the chapter uses style”07_Name of a chapter“(bold letters, size 12, left-aligned). After the number of the chapter there is no full stop. Beneath the name of the chapter there is a blank line, style”10_Gap between the lines A“.

On the following line there is the text of the chapter using style”06_Text“. Beneath the text there is a blank line, style”10_Gap between the lines B“.

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Names of sub-chapters use style”07_Sub-chapter names 1.x“(bold letters, size 12, left-aligned), or”07_Sub-chapter names 2.x“(bold letters, size 12, left-aligned) etc. Behind the number of the sub-chapter there is no full stop. Beneath the name of the sub-chapter there is a blank line, style”10_Gap between the lines A“. On the following line there is the text of the sub-chapter using style”06_Text“. Beneath the text there is a blank line style „10_Gap between the lines B“.

Equations and their numbers are included in a table with two cells, one to each other, of the total width 16 cm. In the first cell the equation is placed, and to the other cell the number of the equation in brackets is added. The former cell is left-aligned and centred; it is style”08_The first cell of the equation table“(size 12, left-aligned, gaps before paragraphs and behind them is 3). The latter cell is centred and uses style”08_The second cell of the equation table“(size 12, right-aligned, gap before and after the paragraph 3). The inner margins of the cells are set on 0 cm. For the table, borders are set off.

(1)

For image wrapping in the text we use style”09_Image“(centred).

The name of the image or table, its number and description is included in a table with two cells, one to each other of the total width 16 cm. The first cell includes the name and number; the other one contains the description. Both cells are left top aligned, style”09_Table cell of the image or table name“(italics, size 12, left aligned, and with gap 6 before and after the paragraph). The inner margins of the cells are set on 0 cm. For the table, borders are set off.

Fig. 1 Diagram of the dependence of the rate of inflation

The name of the table is provided above the table itself.

Tab. 1 Periodogram of time series of inflation (in %) in the CR in 2003 – 2007

Frequency Ordinates Frequency Ordinates Frequency Ordinates 0,0166667 10,7537 0,183333 1,51176 0,35 0,435943 0,0333333 12,777 0,2 2,24582 0,366667 0,331248

2.10 Form for Conclusion

The word Conclusion is style”05_Name of a part of the contribution“. Beneath the word Conclusion there is a blank line, style”Gap between lines A“. On the following line the text of the conclusion follows in style”06_Text“. The blank line follows, style”10_Gap between the lines B“.

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H

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110

Míra

infla

ce v

%

0 10 20 30 40 50 60

t

-0,4

0,6

1,6

2,6

3,6

4,6

5,6

109

2.11 Literature

Individual items are included according to the relevant norm; style”06_Text“is to be set at the beginning of typing.

2.12 Abstracts in Euroregional Languages

The last page contains only abstracts in all three languages of the ERN; the first one is the language of the author and then the remaining language of the countries according to the clockwise direction when looking at the ERN map.

Conclusion

These guidelines can be used for typing the contribution. An advantage is opening the window of styles and using the function of spell-check.

Literature

Individual sources used in the text are included here according to the relevant norm, as demonstrated below.

[1] ANDĚL, J. Statistická analýza časových řad. SNTL, Praha, 1976. L11-B3-IV-41f/11740

[2] BROWN, R. Lecture notes: harmonic analysis [online]. USA, Lexington: University of Kentucky. [cit. 2009-04-14]. Dostupný z WWW: <http://www.ms.uky.edu/~rbrown/courses/ma773/notes.pdf >

[3] CIPRA, T. Analýza časových řad s aplikacemi v ekonomii. SNTL/Alfa, Praha, 1986. ISBN 99-00-00157-X

[4] HINDLS, R.; KAŇOKOVÁ, J.; NOVÁK, I. Metody statistické analýzy pro ekonomy. Management Press, Praha, 1997. ISBN 80-85943-44-1

___________________________________________________________________________ Name of the author or co-authors including the academic degrees.

110

POKYNY PRO AUTORY PŘÍSPĚVKŮ DO ČASOPISU ACC JOURNAL

Název abstraktu je ve stylu 01_Název příspěvku. Příspěvek musí být v rozsahu 5 - 10 stran. Abstrakt musí být v rozsahu 8 - 12 řádků. Forma příspěvku v časopise ACC JOURNAL byla na základě jednání Redakční rady upravena tak, že příspěvek ve vydání „Natural Sciences and Technology“ musí být napsán v anglickém jazyce a v jeho závěru jsou uvedeny abstrakty ve třech euroregionálních jazycích. Příspěvek ve vydání „Social scienes and Economics“, který je z oblasti ekonomiky, musí být napsán v anglickém jazyce a v jeho závěru jsou uvedeny abstrakty ve třech euroregionálních jazycích. Pořadí jednotlivých euroregionálních abstraktů zahajuje abstrakt v jazyce země prvního autora.

HINWEISE FÜR AUTOREN DER BEITRÄGE

FÜR DIE ZEITSCHRIFT ACC JOURNAL

Der Titel des Abstracts ist in der Formatvorlage 01_Beitragstitel“zu verfassen. Der Umfang des Beitrages muss zwischen 5 bis 10 Seiten betragen. Der Umfang des Abstracts muss zwischen 8 bis 12 Zeilen betragen. Aufgrund des Beschlusses des Redaktionsrates wurde die Beitragsform im ACC JOURNAL wie folgt geändert: Beiträge, die in der Ausgabe „Natural Sciences and Technology“ und Beiträge in der Ausgabe „Social Sciences and Economics“ aus dem Gebiet der Wirtschaft, müssen in englischer Sprache verfasst werden und müssen im Schlusswort Abstracts in allen drei Sprachen der Euroregion enthalten. In der Reihenfolge der Abstracts steht an erster Stelle der Abstract in der Landessprache des ersten Autors.

WYMOGI EDYTORSKIE DLA AUTORÓW ARTYKUŁÓW

DO ZESZYTU NAUKOWEGO ACC JOURNAL

Tytuł streszczenia w stylu 01_Tytuł artykułu. Artykuł powinien mieć łącznie powyżej 5 stron i poniżej 10 stron. Streszczenie powinno zawierać powyżej 8 i poniżej 12 wierszy. Forma artykułu w czasopiśmie ACC JOURNAL, została zmieniona przez Radę Redakcyjną na podstawie uzgodnień, w wyniku których artykuł w numerze „Natural Sciences and Technology“ powinien być w języku angielskim a na jego końcu powinny znaleźć się streszczenia w trzech językach Euroregionu. Artykuł w numerze „Social sciences and Economics“, będący z zakresu ekonomii, powinien być napisany w języku angielskim ze streszczeniami w trzech językach Euroregionu w zakończeniu. Pierwszym w kolejności poszczególnych euroregionalnych streszczeń jest streszczenie w języku narodowym pierwszego autora.

GIDELINES FOR CONTRIBUTORS TO THE ACC JOURNAL

The name of the contribution uses the style 01_Name of the contribution. The contribution is longer than 5 pages and shorter than 10 pages. The abstract has more than 8 and less than 12 lines. The Editorial Board decided for the contributions on natural sciences and technology to be written in English with abstract in all three languages of the ERN at its end. Contributions on social sciences and economics are to be written in English with abstracts in three languages of the ERN at the end of the article. The order of the languages used in the abstract is the language of the first author and then the other ones.

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EDITORIAL BOARD

Editor in Chief

Prof. Ing. Lubomír Pešík, CSc. Technical University of Liberec

[email protected]

Deputy Editor in Chief

Ing. Vladimíra Hovorková Valentová, Ph.D. Technical University of Liberec

[email protected]

Executive editor

PaedDr. Helena Neumannová, Ph.D.


[email protected] phone:+420 485 352 318

Honorary editor

Doc. PhDr. Rudolf Anděl, CSc. Technical University of Liberec

Other Members of the Editorial Board

dr Franciszek Adamczuk Wroclaw University of Economics, [email protected]

Dr. Eckhard Burkatzki International Graduate School Zittau, [email protected]

Dr. phil. habil. Volker Dudeck Historiographer [email protected]

Prof. Dr.-Ing. Frank Hentschel University of Applied Sciences Zittau/Görlitz, [email protected]

Prof. Ing. Ivan Jáč, CSc. Technical University of Liberec [email protected]

mgr Krzysztof Mądry Karkonosze State School of Higher

Education in Jelenia Gora [email protected]

Prof. Dr. phil. Annette Muschner University of Applied Sciences Zittau/Görlitz, [email protected]

dr Maciej Pawłowski Wroclaw University of Technology in Jelenia Góra, [email protected]

Prof. Dr. phil. Dr. h. c. Peter Schmidt University of Applied Sciences Zittau/Görlitz, [email protected]

dr Agnieszka Sokołowska Wroclaw University of Economics in Jelenia Góra, [email protected]

dr Józef Zaprucki Karkonosze State School of Higher

Education in Jelenia Gora [email protected]

Assistant of the editorial office:

Jitka Pešíková , Akademic Coordination Centre at the Euregion Neiße,

Technical University of Liberec, phone: +420 485 354 232, e-mail: [email protected]

Název časopisu (Journal Tittle) ACC JOURNAL

Ročník (vol./year/issue) XVII (1/2011/Issue A)

Autor (Author) kolektiv autorů (composite authors)

Vydavatel (Published by) Technická univerzita v Liberci

Studentská 2, Liberec 1, 461 17

IČO 46747885, DIČ CZ 46 747 885

Schváleno rektorátem TU v Liberci

dne 27. 4. 2011, č. j. RE 29/11

Vyšlo (Published) 30. 6. 2011

Počet stran (Number of pages) 112

Vydání (Edition) první (first)

Číslo publikace (Number of publication) 55-029-11

Evidenční číslo periodického tisku MK ČR E 18815

(Registry reference number of periodical print)

Tištěná verze ISSN (ISSN printed version) 1803-9782

Počet výtisků (Number of copies) 100 ks (pieces)

Adresa redakce (Address of the editorial office) Tiskne (Print)

Technická univerzita v Liberci ReproArt Liberec, s.r.o.

Akademické koordinační středisko Nová 348/26,

v Euroregionu Nisa (ACC) Liberec 10

Sokolská 8 460 10

Liberec 1

461 17, Česká republika

Tel. + 420 485 354 323, Fax +420 485 354 309

e-mail: [email protected]

http://acc-ern.tul.cz

Upozornění pro čtenáře (Readers’ notice) Příspěvky v časopise jsou recenzovány a prošly jazykovou redakcí. Contributions in the journal have been reviewed and edited.

Předplatné (Subscription):

Objednávky předplatného přijímá redakce. Cena předplatného za rok je 900,-Kč a poštovné. Starší čísla lze objednat do vyčerpání zásob (cena 200,- Kč za kus).

Subscription orders must be sent to the editorial office. The price a year is 40,- € and postal charges. It is possible to order older issues only until present supplies are exhausted (8,-€ an issue).

Časopis ACC JOURNAL vychází obvykle dvakrát ročně (červen, prosinec).

The ACC JOURNAL is published usually twice per year (June, December).

© Technická univerzita v Liberci – 2011

ISSN 1803-9782

ISSN 1803-9782

acc-ern.tul.czacc-ern.tul.cz/images/journal/sbornik/acc journal_2011_a.pdfissue liber a int un wyd k...

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