Nonlinear Analysis of Rotors Supported by Air Foil Journal Bearings

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Nonlinear Analysis of Rotors
Supported by Air Foil Journal
Bearings – Theory and Experiments
Larsen, Jon Steffen
Publication date:
2014
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Citation (APA):
Larsen, J. S. (2014). Nonlinear Analysis of Rotors Supported by Air Foil Journal Bearings – Theory and
Experiments. DTU Mechanical Engineering. DCAMM Special Report No. S177

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Nonlinear Analysis of Rotors
Supported by Air Foil Journal
Bearings – Theory & Experiments
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Jon Steff en Larsen
DCAMM Special Report No. S177
February 2015

Nonlinear Analysis of Rotors
Supported by Air Foil Journal
Bearings – Theory & Experiments
Jon Steffen Larsen
Kongens Lyngby 2014
DCAMM Special Report No. S177
PhD student:
Jon Steffen Larsen
[email protected]
Principal supervisor:
Ilmar Ferreira Santos
[email protected]
Industrial supervisor:
Frans Pløger
[email protected]
Technical University of Denmark
Department of Mechanical Engineering, Section of Solid Mechanics
Building 404, DK-2800 Kongens Lyngby, Denmark
Phone [phone], Fax [phone]
[email protected]
www.mek.dtu.dk
MEK-PHD: ISBN 978-87-7475-402-2
Summary (English)
Direct driven compressors supported by air foil bearings (AFB) are gaining
increasing popularity, for example within the waste water treatment industry
where the demand for larger machines up to 250 kW is growing. In order
to keep production costs low, the shaft and bearing design need to be simple
and allow manufacturing using conventional materials and production facilities.
As a consequence, the assembled rotor weight can be up to 50 kg. The com-
pressors are operated at variable speed and load and are subjected to several
starts and stops per day. Therefore, the rotor bearing design must be robust
with a good margin of rotordynamical stable operation. To ensure this, good
mathematical models, capable of accurately predicting the dynamic behaviour
of the rotor-bearing system, are required at the design stage. This thesis fo-
cuses on developing and improving existing mathematical models for predicting
the nonlinear dynamic behaviour of AFBs, both isolated and coupled with the
rotor. Large emphasis is put on the experimental validation of the obtained
theoretical results. Two experimental test rigs were designed and manufactured
specifically for this purpose. With the first rig, the isolated nonlinear mechani-
cal behaviour of the bump foils was carefully examined. A mathematical model
capable of predicting this nonlinear behaviour was developed and compared to
the experimental results with good agreement. With the second test rig, the
overall nonlinear behaviour of the rotor-bearing system was investigated exper-
imentally, and the linearised stiffness and damping coefficients of the bearings
wereidentified. Resultsobtainedtheoreticallywerecomparedtotheselinearised
coefficients with reasonably good agreement. Furthermore, the sensitivity to ro-
tor unbalance and the nonlinear response were analysed experimentally and a
coupled rotor-bearing mathematical model was compared to these results with
very good agreement in terms of the nonlinear rotor unbalance response.
ii
Resum´e (Dansk)
Direkte drevne kompressorer med folielejer bliver stadig mere populære i f.eks.
industrien for spildevandsrensning. Samtidig stiger efterspørgslen p˚a større
maskiner p˚a op til 250 kW motoreffekt. Aksel og lejedesign skal være simpelt for
at holde produktionsomkostninger nede. Et simpelt design muliggør fremstilling
i standard materialer samt brug af standard produktionsapparater. Det simple
design medfører rotorer med egenvægt p˚a op til 50 kg. Kompressorerne opereres
ved variabel last samt hastighed, og de er udsat for flere start og stop per døgn.
Der stilles derfor krav til et robust design med en god margin til rotordynamisk
ustabilitet. Dermed nødvendiggøres nøjagtige matematiske modeller, som i de-
signstadiet kan forudsige rotor-leje systemets dynamiske opførsel. Denne afhan-
dling omhandler arbejdet med udvikling og forbedring af eksisterende matema-
tiske modeller til forudsigelse af den ikkelineære dynamiske opførsel af folielejer
isoleret set, men ogs˚a sammenkoblet med en rotor. Der er lagt vægt p˚a den
eksperimentelle validering af de teoretiske resultater. S˚aledes blev der designet
ogbyggettoeksperimentelleteststandespecifikttilform˚alet. Denisoleredeikke-
lineære opførsel af bølgefolierne blev grundigt undersøgt ved hjælp af den første
teststand. Samtidig blev en matematisk model for disse bølgefolier udviklet for
at forudsige deres ikkelineære opførsel, og resultaterne blev sammenholdt med
m˚alingerne med god overensstemmelse. Den overordnede ikkelineære opførsel af
rotor-leje systemet blev eksperimentelt undersøgt ved hjælp af den anden test-
stand, og de lineariserede stivheds- og dæmpningskoefficienter blev identificeret.
Teoretiske resultater for disse lineariserede koefficienter blev sammenlignet med
de eksperimentelle med en relativ god overensstemmelse. Endvidere blev sen-
sitiviteten til rotorubalance samt det ikkelineære transiente rotorrespons un-
dersøgt eksperimentelt og sammenlignet med teoretiske resultater fra en koblet
matematisk rotor-leje model med meget god overensstemmelse.
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Preface
This thesis is submitted as a partial fulfilment of the requirements for obtaining
theDanishPhDdegree. Thethesisconsistsofasummaryreportandacollection
of six research papers written during the period 2011–2014, and elsewhere pub-
lished. The work was founded by Siemens A/S, Aeration Competence Centre
(Siemens-ACC)andtheDanishMinistryofResearchandInnovationandcarried
out from September 2011 to November 2014 at the Section of Solid Mechanics
(FAM), Department of Mechanical Engineering (MEK), Technical University
of Denmark (DTU). The project was supervised by the university-supervisor
Professor, Dr.-Ing., Dr.techn. Ilmar Ferreira Santos and the industry-supervisor
PhD Frans Pløger, to both I would express my sincere gratitude. I thank my
industry-supervisor for establishing the infrastructure in Siemens-ACC and for
allocating the resources necessary for me to focus entirely on the project work.
A special thanks goes to my university-supervisor for his general support, guid-
ance and the ever-inspiring weekly meetings, meetings that I will miss upon
finalising this project. I also thank the managing director of Siemens-ACC,
Mr. Jan Olsen, for his support during a hard transition period of our company.
From Siemens-ACC, I also wish to thank Mr. Jørgen Lyquist and Mr. Asger
Jørgen Thor Hansen for their help related to the design and construction of the
experimental test facilities at Siemens. Regarding the test facilities at DTU, I
owe a special thanks to Kristian Bjarklev, Niels Toftdahl Christensen and Peter
Kjær Svendsen.
Thanks to my closest PhD student colleagues within the machinery dynamic
researchgroupatDTU,AlejandroV.Cerda, AndreasV.Jauernik, EmilBureau,
BoB.Nielsen,SørenEnemark, JorgeA.G.Salazar,Fabi´anG.P.V´asquez, Jonas
Lauridsen, Cesar Fonseca and Geraldo Rebouc¸as for sharing countless hours at
the office, and for exchanging ideas, opinions and knowledge. I also thank Mrs.