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Modelling the dynamic interactions of rolling bearings [Elektronische Ressource] / vorgelegt von Joao Henrique Diniz Guimaraes

149 pages
MODELLING THE DYNAMIC INTERACTIONS OFROLLING BEARINGSVon der Fakulät für Elektrotechnik und Informationstechnik derRheinisch-Westfälischen Technischen Hochschule Aachenzur Erlangung des akademischen Grades einesDOKTORS DER INGENIEURWISSENSCHAFTENgenehmigte Dissertationvorgelegt vonMSc.João Henrique Diniz Guimarãesaus Rio de JaneiroBerichter: Universitätsprofessor Dr. rer nat. Michael VorländerUniversitätsprofessor Dr.-Ing. Jens-Rainer OhmTag der mündlichen Prüfung: 16. Oktober 2007Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.˜ ˜Joao Henrique Diniz GuimaraesModelling the DynamicInteractionsofRolling BearingsLogos Verlag Berlin GmbHλογοςAachener Beitra¨ge zur Technischen AkustikHerausgeber:Prof.Dr.rer.nat. Michael Vorla¨nderInstitut fu¨r Technische AkustikRWTH Aachen52056 Aachenwww.akustik.rwth-aachen.deBibliografische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in derDeutschen Nationalbibliografie; detaillierte bibliografische Daten sindim Internet u¨ber http://dnb.d-nb.de abrufbar.Dissertation RWTH AachenD 82, 2008c Copyright Logos Verlag Berlin GmbH 2008Alle Rechte vorbehalten.ISBN 978-3-8325-2010-6ISSN 1866-3052Band 8Logos Verlag Berlin GmbHComeniushof, Gubener Str. 47,10243 BerlinTel.: +49 (0)30 / 42 85 10 90Fax: +49 (0)30 / 42 85 10 92http://www.logos-verlag.deiifür meine ElterniiiivContents1 Introduction 11.0.
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MODELLING THE DYNAMIC INTERACTIONS OF
ROLLING BEARINGS
Von der Fakulät für Elektrotechnik und Informationstechnik der
Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines
DOKTORS DER INGENIEURWISSENSCHAFTEN
genehmigte Dissertation
vorgelegt von
MSc.
João Henrique Diniz Guimarães
aus Rio de Janeiro
Berichter: Universitätsprofessor Dr. rer nat. Michael Vorländer
Universitätsprofessor Dr.-Ing. Jens-Rainer Ohm
Tag der mündlichen Prüfung: 16. Oktober 2007
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.˜ ˜Joao Henrique Diniz Guimaraes
Modelling the DynamicInteractions
ofRolling Bearings
Logos Verlag Berlin GmbH
λογοςAachener Beitra¨ge zur Technischen Akustik
Herausgeber:
Prof.Dr.rer.nat. Michael Vorla¨nder
Institut fu¨r Technische Akustik
RWTH Aachen
52056 Aachen
www.akustik.rwth-aachen.de
Bibliografische Information der Deutschen Nationalbibliothek
Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der
Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind
im Internet u¨ber http://dnb.d-nb.de abrufbar.
Dissertation RWTH Aachen
D 82, 2008
c Copyright Logos Verlag Berlin GmbH 2008
Alle Rechte vorbehalten.
ISBN 978-3-8325-2010-6
ISSN 1866-3052
Band 8
Logos Verlag Berlin GmbH
Comeniushof, Gubener Str. 47,
10243 Berlin
Tel.: +49 (0)30 / 42 85 10 90
Fax: +49 (0)30 / 42 85 10 92
http://www.logos-verlag.deiifür meine Eltern
iiiivContents
1 Introduction 1
1.0.1 Outline of this dissertation . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Approach adopted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Measuring System and Test Facility 12
2.1 The Test Bench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Experimental chain and its components . . . . . . . . . . . . . . . . . . . 16
2.3 Sensors and actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 The piezoelectric actuators . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Development of built-in sensors . . . . . . . . . . . . . . . . . . . 23
2.3.3 Calibration of sensors and actuators . . . . . . . . . . . . . . . . . 28
3 Machine Transfer Functions - Experimental Results 32
3.1 Measurement procedure for the determination of the Transfer Functions . . 32
3.2 Determination of the static transfer function . . . . . . . . . . . . . . . . . 34
4 Physical Model 44
4.1 Classical contact model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Rough surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Literature review on rough surfaces . . . . . . . . . . . . . . . . . 48
4.2.2 Mathematical description of rough surfaces . . . . . . . . . . . . . 50
4.2.3 Engineering surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.4 Roughness measurements of the bearing’s surfaces . . . . . . . . . 56
4.3 Rough contact model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Literature review on rough contact models . . . . . . . . . . . . . . 62
4.3.2 Description of the rough contact . . . . . . . . . . . . . . . . . . . 65
4.4 Rough rolling contact in bearings . . . . . . . . . . . . . . . . . . . . . . . 69
4.4.1 The equivalent rough surface . . . . . . . . . . . . . . . . . . . . . 69
4.4.2 Calculation procedure . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.3 Time evolution of the excitation . . . . . . . . . . . . . . . . . . . 74
v4.4.4 Results of the modelling . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.5 Auralisation of structure-borne sounds . . . . . . . . . . . . . . . . 80
4.5 Modelling bearing’s lubrication . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5.1 Basic knowledge about lubricants and lubrication . . . . . . . . . . 84
4.5.2 The elasto-hydrodynamic lubrication . . . . . . . . . . . . . . . . 85
4.5.3 Adaptation of the EHL to the previous model . . . . . . . . . . . . 87
4.5.4 The three-dimensional case . . . . . . . . . . . . . . . . . . . . . . 89
4.5.5 The software SAMBA . . . . . . . . . . . . . . . . . . . . . . . . 91
5 Measurements and simulations on rolling bearings under running conditions 93
5.1 Measurement conditions and results . . . . . . . . . . . . . . . . . . . . . 94
5.1.1 First experimental campaign . . . . . . . . . . . . . . . . . . . . . 95
5.1.2 Second experimental campaign . . . . . . . . . . . . . . . . . . . 98
5.2 Comparison between simulations and measurements . . . . . . . . . . . . 100
6 The Inverse Problem 105
6.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 De-noising measured signals . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 Summary and Outlook 114
Appendix A - FAG 6211 C3 121
Appendix B - FAG NU211E.M1 122
Appendix C - FAG 22318EK 123
Summary 124
Zusammenfassung 125
Curriculum vitae 126
Danksagung 127
Bibliography 129
viChapter 1
Introduction
Bearings are one of the most used machine elements. Their application range is very wide
and they are generally used to support moving parts in relative movement with low friction.
Countless types of bearings are available today, going from rolling bearings, to journal
bearings through magnetic bearings and others. The variety of construction forms, sizes,
geometries, applications and characteristics of this machine element is enormous. The most
common type of bearing is the rolling bearing and, even in this specific type, the complexity
and diversity of constructive forms is immense.
A rolling bearing can be very simply described as two concentric rings between which,
rollers are mounted and kept separated from each other through a cage (figure 1.1). Al-
though this simple description may lead to the conclusion that this mechanism does not
present any technological challenge, numerous questions concerning its functioning, con-
struction and use are still open. Questions like: ’How much operation time before a failure
occurs still remains?’, ’How should the bearing’s surface be constructed in order to have
low friction, but still be capable to retain lubrication?’ or ’Which factors are most relevant
for a certain dynamical behaviour?’ are not completely cleared.
Figure 1.1: Cylindrical and spherical rolling bearings. A cage keeps rollers equidistant.2 CHAPTER 1. INTRODUCTION
The idea of reducing friction through rolling movement is very old. Ancient civi-
lizations already used this principle to transport heavy loads over rolling wooden trunks.
Leonardo da Vinci (1452-1519) is considered the creator of a support over spheres. With
the invention of a grinding machine for spheres in 1883 by Friedrich Fischer, started the
mass production of rolling bearings. The last two centuries saw an incredible increase of
this industry and an immense development of the variety and use of bearings. Much of the
development of the machine industry was impulsed by the invention and improvement of
the bearing.
Nowadays, much effort is applied in better understanding and optimizing the function-
ing of bearings. Not only because they are widespread, but also because of the importance
of the equipments, machinery and plants in which they are built in.
There exist no reliable unified theory capable of handling with all different types of
bearings. Concerning specifically the calculation of the remaining operation life, much is
based on heuristics and/or experimental results for a specific case that is generalised for
other cases. However, many factors like the mounting, operational regime, contamination
etc. can lead to huge variations of the predicted remaining life. Even widely accepted
standards [ISO93a] for the calculation of rolling bearing’s lifespan are categoric to say that
the calculation methods proposed there have serious limitations and these should be taken
1into account . This makes accompanying bearing’s operation even more important since a
reliable prediction of its behaviour and development of wear is still a very complex task to
be made beforehand.
This work is inserted in the context of condition monitoring and machine diagnosis.
The importance of this two terms is increasing every day and their relevance in the industry
is related not only to reduction of maintenance costs but also to integrity of machines and
persons.
Condition monitoring is related to accompanying the operation of a machine (or ma-
chine parts) in order to spot abnormal function. It has to be based in some kind of method of
evaluation that is able to sort out which are the possibles causes of what is being observed.
Once the relation of cause and consequence is established, the diagnosis of the state of
the machine continues with the evaluation of the severity of the cause and, if possible, the
1It is interesting to read the introduction of the ISO 281 (Dynamic load ratings and rating life) and see that
the first four paragraphs of the introduction of the norm are dedicated to warnings about its limitations. They
all begin with: ’It is not possible . . . ’, ’No satisfying results . . . ’ etc.. Even actualisations like the Addendum
4 [ISO93b] are not able to cope with all possible real operation situations. See also [Cor06].