Dynamically loaded self-aligning journal bearings

123 Pages·2016·2 MB·English

by  Nathan Mayer

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Mayer, Nathan, "Dynamically loaded self-aligning journal bearings: A Mobility method approach" (2004).
Thesis. Rochester Institute of Technology. Accessed from
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Dynamically Loaded Self-Aligning Journal
Bearings: A Mobility Method Approach
by
Nathan Mayer
A Thesis Submitted in
Partial Fulfillment of the
Requirement for the
MASTER OF SCIENCE
IN
MECHANICAL ENGINEERING
Approved by:
Stephen Boedo
Dr. Stephen Boedo
Department of Mechanical Engineering (Thesis advisor)
Hany Ghoneim
Dr. Hany Ghoneim
Department of Mechanical Engineering
Josef S. Torok
Dr. Josef Torok
Department of Mechanical Engineering
Edward C. Hensel
Dr. Edward C. Hensel
Department Head of Mechanical Engineering
DEPARTMENT OF MECHANICAL ENGINEERING
ROCHESTER INSTITUTE OF TECHNOLOGY
August 2004
Dynamically Loaded Self-Aligning Journal Bearings: A Mobility Method Approach
I, Nathan Mayer, hereby grant permission to the Wallace Library of the Rochester Institute of
Technology to reproduce my thesis in whole or in part. Any reproduction will not be for
commercial use or profit.
Nat han Mayer
Signature of Author:
ii
Acknowledgements
Firstand foremost I would liketothankGod forgivingthe strength andabilityto
completethiswork.
I wantto express my deep appreciation forthe supportofmy lovingwife. I don't
knowhowI couldhave made itthe pastthreeyearswithouther. I also wanttothankmy
parents forhelpingmethroughmy education and encouragingmeto do mybest.
I would liketo thankmy advisor, Dr. Boedo forstickingwith me and supportingme
throughthisprocess. I would also liketothankDr. Torokand Dr. Ghoneim fortakingthe
timeto reviewmythesis and serve onmycommittee.
Abstract
Journalbearings are a fundamental component in manypieces ofmachinery. A
properly designedbearing is capable ofsupporting large loads in rotating systemswith
minimal frictional energy losses and virtuallynoweareven afteryears ofservices. These
benefits make an understanding ofdynamic behaviorofthese devicesveryvaluable.
In applicationswherejournal bearings are subjectto misalignment (conditions where
thejournal and sleeve axes arenotparallel), ithas longbeenunderstoodthatbearing
performance canbe compromised. To eliminatethis problem, self-aligningbearings have
been designed. The sleeves ofthese bearings are capable ofmoving freelyto accommodate
misalignment. The aligningmotion ofthese bearingsunderdynamic loading is, however,
largelyunexplored. Additionally,the impactofmisalignmentonjournal midplanemotion is
unknown.
Currently, finite elementand finite difference analyses arethe onlyavailabletools for
this kind ofwork. Thisrequiresaunique and computationallycostlymathematical solution
foreverypossible bearing configuration.
It isthe goal ofthisthesis to develop acomputationally efficientmeans ofpredicting
journalmotionwithin aself-aligningbearing. This is done by creating asetof"mobility"
mapping functions from finite elementbearing modelsthatrelatethe velocity ofthejournal
tothe applied load. Such maps have previously beenbuiltand used successfully forthe
design ofperfectly aligned bearings. This expansion ofthe mobilitymethodto self-aligning
bearings provides avaluabletool forthe designerand gives valuable insight intothejournal
motion forthese devices.
IV
Table ofContents
1 Background 1
2 Problem Formulation 6
2.1 Bearing Geometry 6
2.2 Mobility Formulation: AlignedBearings 9
2.3 Mobility Formulationwith Journal Misalignment 13
2.4 Generation ofMobilityMappingFunctions 20
2.5 Application oftheMobilityMapping Functions 23
3 Application and Validation 26
3.1 Pure Squeeze 26
3.1.1 Case 1: Pure Squeeze, Zero Initial Misalignment 29
3.1.2 Cases 2aand 2b:: Pure Squeeze, Initial Misalignmentaboutthe r|-axis 30
3.1.3 Cases 3aand 3b:: Pure Squeeze, Initial Misalignmentaboutthe ^-axis 35
3.1.4 Cases 4aand 4b:: Pure Squeeze, Initial Misalignment45 from the Force
Vector 39
3.1.5 Case 5 Pure Squeeze, ArbitraryInitialJournal Location 39
3.2 Steady Rotation 47
3.2.1 Cases 6aand 6b: Steady Rotation, Zero Initial Misalignment 48
3.2.2 Cases 7a-8d:: SteadyRotation, Initial Misalignmentabouthe ^-axis
orr|-axis 51
3.2.3 Cases 9a-9d:: SteadyRotation, InitialMisalignment45 from theForce
Vector 72
3.2.4 Case 10: Steady Rotation, Arbitrary Initial Journal Location 72
3.2.5 Cases 1laand 1lb: SteadyRotation, Variable Load 72
4 Conclusions and Future Work 91
Appendices
A Finite Element BasedAlignedBearing MobilityMap 96
B MisalignmentAdjustment Functions 97
C Reference Tables ofResults 102
D Multi-Generational Curve Fitting Process 103
E FlowchartofLogic forBearing OrbitCalculation usingMobility Maps 104
F Axial Spacing forNon-UniformMeshes 105
Referencs 106
VI
List ofFigures
Figure 1.1 Spherical Socket Self-AligningJournal Bearing 3
Figure 1.2 Elastomer Supported Self-AligningJournal Bearing 5
Figure 1.3 Pivoted Sleeve Self-AligningJournal Bearing 5
Figure 2.1 BearingGeometry 7
Figure 2.2 BearingLoads andKinematics 8
Figure 2.3 Example Mobility Map: Sortbearingmodel 17
Figure 2.4 Translational Mobility Vector 19
Figure 2.5 3-D UnwrappedExample Elemental Mesh 21
Figure 2.6 3-D Representation ofExample Elemental Mesh 21
Figure 3.1 Coarse Mesh: 14 axial by 40 circumferencialnodes, spacing ratio of1.25 27
Figure 3.2 Fine Mesh: 20 axial by 60 circumferencialnodes, spacing ratio of1.15 27
Figure 3.3 AxialNode Spacing, Scheme 28
Figure 3.4 Time History ofJournal Eccentricity: Pure Squeeze, zero initialmisalignment
(Casel) 31
Figure 3.5 Time HistoryofJournal Eccentricity:Pure Squeeze, specifiedmisalignmentabout
the r|-axis (Case 2a) 32
Figure 3.6 TimeHistory ofJournal Misalignment: Pure Squeeze, specified misalignment
aboutthe r|-axis (Case 2a) 32
Figure 3.7 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment about
the r|-axis (Case 2b) 33
Figure 3.8 Time History ofJournal Misalignment: Pure Squeeze, specified misalignment
aboutthe n.-axis (Case 2b) 33
Figure 3.9 Time HistoryofJournal Eccentricity: Pure Squeeze, comparison between aligned
case and initial misalignmentaboutthe rj-axis 34
Figure 3.10 Time History ofJournalEccentricity: Pure Squeeze, comparison between aligned
case and initial misalignmentaboutthe n-axis (Case2a) 34
Figure 3.11 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment
aboutthe -axis (Case 3a) 36
VII
Figure 3.12 Time HistoryofJournal Misalignment: Pure Squeeze, specified misalignment
aboutthe ,-axis (Case 3a) 36
Figure 3.13 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment
aboutthe -axis (Case 3b) 37
Figure 3.14 Time History ofJournal Misalignment: Pure Squeeze, specified misalignment
aboutthe ^-axis (Case 3b) 37
Figure 3.15 Time History ofJournal Eccentricity: Pure Squeeze, comparisonbetween aligned
case and initial misalignmentaboutthe -axis 38
Figure 3.16 TimeHistory ofJournalEccentricity: Pure Squeeze, comparisonbetween aligned
case and initial misalignmentaboutthe ^-axis 38
Figure 3.17 TimeHistory ofJournal Eccentricity: Pure Squeeze, specified misalignment 45
fromthe load (Case 4a) 40
Figure 3.18 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment45
from the load (Case 4a) 40
Figure 3.19 Time History ofJournal Misalignment: Pure Squeeze, specifiedmisalignment
45 fromthe load (Case4a) 41
Figure 3.20 Time History ofJournal Misalignment: Pure Squeeze, specifiedmisalignment
45 fromthe load (Case 4a) 41
Figure 3.21 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment45
from the load (Case 4b) 42
Figure 3.22 TimeHistory ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment45
fromthe load (Case4b) 42
Figure 3.23 Time HistoryofJournal Misalignment: Pure Squeeze, specifiedmisalignment
45 fromthe load (Case 4b) 43
Figure 3.24 Time History ofJournal Misalignment: Pure Squeeze, specifiedmisalignment
45 fromthe load (Case 4b) 43
Figure 3.25 Time History ofJournalEccentricity: Pure Squeeze, comparison betweenaligned
case and initialmisalignment45 fromthe load iq-axis 44
Figure 3.26 Time History ofJournal Eccentricity: Pure Squeeze, comparison between aligned
case and initial misalignment45 fromthe load r|-axis 44
VIM
Figure 3.27 Time HistoryofJournalEccentricity: Pure Squeeze, specifiedmisalignmentand
eccentricity (Case 5) 45
Figure 3.28 Time History ofJournal Eccentricity: Pure Squeeze, specifiedmisalignment and
eccentricity (Case 5) 45
Figure 3.29 Time History ofJournal Misalignment: Pure Squeeze, specified misalignment
andeccentricity (Case 5) 46
Figure 3.30 Time History ofJournal Misalignment: Pure Squeeze, specifiedmisalignment
and eccentricity (Case 5) 46
Figure 3.31 Time History ofJournal Eccentricity: SteadyRotation, zero initial misalignment
(Case 6a) 49
Figure 3.32 TimeHistoryofJournal Eccentricity: SteadyRotation, zero initial misalignment
(Case 6a) 49
Figure 3.33 TimeHistory ofJournal Eccentricity: Steady Rotation, zero initial misalignment
(Case 6b) 50
Figure 3.34 Time History ofJournal Eccentricity: Steady Rotation, zero initial misalignment
(Case 6b) 50
Figure 3.35 Time History ofJournal Eccentricity: Steady Rotation, specifiedmisalignment
aboutthe r|-axis (Case 7a) 52
Figure 3.36 TimeHistory ofJournal Eccentricity: SteadyRotation, specifiedmisalignment
aboutthe r|-axis (Case 7a) 52
Figure 3.37 TimeHistory ofJournal Misalignment: SteadyRotation, specifiedmisalignment
aboutthe r|-axis (Case 7a) 53
Figure 3.38 Time HistoryofJournal Misalignment: SteadyRotation, specifiedmisalignment
aboutthe n,-axis (Case 7a) 53
Figure 3.39 Time HistoryofJournal Eccentricity: Steady Rotation, specifiedmisalignment
aboutthe iq-axis (Case 7b) 54
Figure 3.40 Time History ofJournal Eccentricity: Steady Rotation, specifiedmisalignment
aboutthe n,-axis (Case 7b) 54
Figure 3.41 Time HistoryofJournal Misalignment: SteadyRotation, specified misalignment
aboutthe r|-axis (Case 7b) 55
IX