Reduction of Vibrations in Engines using Centrifugal Pendulum Vibration Absorbers

87 Pages·2011·4.42 MB·Swedish

by  Anders Wedin

Reduction of Vibrations in Engines using
Centrifugal Pendulum Vibration Absorbers
Master’sThesisintheMaster’sprogrammeAutomotiveEngineering
ANDERS WEDIN
DepartmentofProductandProductionDevelopment
DivisionofProductDevelopment
CHALMERSUNIVERSITYOFTECHNOLOGY
Go¨teborg,Sweden2011
Master’sThesis2011

MASTER’STHESIS2011
Reduction of Vibrations in Engines using
Centrifugal Pendulum Vibration Absorbers
–aStudywithModelingandSimulationofCentrifugalPendulumVibrationAbsorbersinthe
DualMassFlywheel
Master’sThesisintheMaster’sprogrammeAutomotiveEngineering
ANDERSWEDIN
DepartmentofProductandProductionDevelopment
DivisionofProductDevelopment
CHALMERSUNIVERSITYOFTECHNOLOGY
Go¨teborg,Sweden2011
ReductionofVibrationsinEnginesusingCentrifugalPendulumVibrationAbsorbers
– a Study with Modeling and Simulation of Centrifugal Pendulum Vibration Absorbers in the
DualMassFlywheel
ANDERSWEDIN
(cid:13)c ANDERSWEDIN,2011
Master’sThesis2011
DepartmentofProductandProductionDevelopment
DivisionofProductDevelopment
ChalmersUniversityofTechnology
SE-41296Go¨teborg
Sweden
Telephone: [phone]
Cover:
Sketch of Simple, Bifilar, Roll Form, and a possible design of a Bifilar CPVA with General Path
(inblue). DrawnbyAnnaWedin.
ChalmersReproservice
Go¨teborg,Sweden2011
ReductionofVibrationsinEnginesusingCentrifugalPendulumVibrationAbsorbers
– a Study with Modeling and Simulation of Centrifugal Pendulum Vibration Absorbers in the
DualMassFlywheel
Master’sThesisintheMaster’sprogrammeAutomotiveEngineering
ANDERSWEDIN
DepartmentofProductandProductionDevelopment
DivisionofProductDevelopment
ChalmersUniversityofTechnology
Abstract
ThedevelopmentanduseofCPVAs(CentrifugalPendulumVibrationAbsorbers)started
in the beginning of the 20th century, and one of the first traces is a model by Kutzbach
in 1911. Most of the models were developed and patented during the 1930s, and those
types are still used today. CPVAs came to play a vital role in the development of radial
aircraft engines, which were used extensively in World War II. With the aid of correctly
tunedCPVAs,vibrationsofdifferentorderscouldbereducedsignificantly,ensuringreliable
operation. TheCPVAisparticularlyusefulforenginessinceitisnotdependentonfrequency,
but the order of the applied torque. The CPVA can therefore reduce vibrations in the entire
enginespeedrange.
CPVAs are now finding use in powertrains of cars, more specifically in the DMF (Dual
Mass Flywheel). The problem automotive manufacturers face today, from a vibration per-
spective, is that engines generally tend to become smaller in size and have fewer cylinders,
whilethepoweroutputtendtoincrease. TheDMFhasbeenaneffectivewayofreducingvi-
brationsfromenginetotransmissionforsometimenow,buteverincreasingvibrationlevels
fromnewlydevelopedenginescreateaneedofusingCPVAs.
The main goal of this thesis work is to, at Volvo Cars engine development department,
modelandsimulatedifferenttypesofCPVAsinthesoftwareSimdrive3DbyContecsEng,
wheresimplevibrationmodelscanbemadeforfirstinvestigations.
DifferentCPVAshavebeenmodeledthroughafullycustomizableelement,programmed
inC/C++forSimdrive. SpecialattentionhasbeengiventomodelCPVAswithcycloidaland
epicycloidalpaths,sincetheyareimportantforpracticaluse. TheCPVAunitperformanceis
analyzedinonemodelwithann:thordersine-signaltorque,andalsoinamorerealisticpow-
ertrain model with cylinders, DMF with CPVAs attached, FEAD (Front Engine Accessory
Drives),andrealisticinputtorquefromcombustionsintheenginecylinders.
Insimulationswithsine-signaltorque,allCPVAtypesconsideredseemtohavecapabil-
itiesofabsorbingvibrations. Someofthetypeswithcycloidalorepicycloidalpathsreduce
vibrationsofthedesignatedordertoalevelveryclosetozero,foramajorpartoftheengine
speedrange. Intheadvancedpowertrainmodel,wherethependulummassisrestrictedto1
kg, the CPVA units are stretched to their limit. Types with regular circular paths either fail
to reduce or amplify vibrations, while types with cycloidal or epicycloidal paths manage to
reducevibrationsforpartsoftheenginespeedrange. Withmoresimulationtime,theCPVA
parameterscouldbeoptimizedfurther.
Future work suggestions include further development of models, introduction of ”stop-
pers” in models, and introduction of multiple independent absorbers to account for non-
unisonmotion.
Keywords: Torsional Vibrations, Centrifugal Pendulum Vibration Absorbers, Dual Mass Fly-
wheel, Bifilar, Salomon, General-Path Representation, Cycloid, Epicycloid, Tautochrone, Mod-
eling,Simulation,Car,Powertrain,Crankshaft
,ProductandProductionDevelopment,Master’sThesis2011 I
Sammanfattning
I bo¨rjan av 1900-talet bo¨rjade utvecklingen och anva¨ndandet av centrifugal-pendelda¨mpare (en-
gelska: CentrifugalPendulumVibrationAbsorbers),da¨rettavdefo¨rstaspa˚rena¨renmodellfra˚n
1911avKutzbach. Deflestaavmodellernautveckladesochpatenteradesunder1930-talet,vilka
anva¨ndsa¨nnuidag. Pendelda¨mparespeladeenstorrolliutvecklingenavdemotoreravstja¨rntyp
som satt i ma˚nga flygmaskiner under andra va¨rldskriget. Med hja¨lp av pendelda¨mpare kunde
vibrationer av olika ordningar reduceras och fo¨rhindra motorhaveri. Pendelda¨mpare a¨r sa¨rskilt
va¨lla¨mpadefo¨rfo¨rbra¨nningsmotorereftersomdeda¨mparvibrationerihelavarvtalsregistret,inte
baravidenvissfrekvens.
Pendelda¨mparebo¨rjarnuanva¨ndasidrivlinanhosbilar,na¨rmarebesta¨mtitva˚massesva¨nghjul
(TMS).Idagensutvecklingtenderarmotorerattblialltmindre,hafa¨rrecylindrar,ochsamtidigt
utveckla mer effekt vilket skapar problem pa˚ vibrationssidan. TMS har anva¨nts under en tid fo¨r
attda¨mpavibrationerfra˚nmotortilltransmission,mensenaremotorermedho¨geffektskaparett
behovattanva¨ndapendelda¨mpareiTMS:et. Dethuvudsakligama˚letmeddettaexamensarbetea¨r
att,pa˚Volvopersonbilarsmotorutveckling,modelleraochsimuleraolikatyperavpendelda¨mpare
iprogramvaranSimdrive3DavContecsEng,da¨renklarevibrationsmodellerkanskapas.
Olikatyperavpendelda¨mpareharmodelleratsmanuelltiettelement,somharprogrammerats
iC/C++fo¨rSimdrive. Sa¨rskiltfokusharlagtspa˚ attmodellerapendelda¨mparemedcykloid-och
epicykloidbanor, eftersom dessa typer a¨r viktiga i praktiken. Prestandan hos pendelda¨mparna
underso¨ks i en modell med ett sinus-vridmoment som insignal, och ocksa˚ i en mer realistisk
drivlina-modell med cylindrar, TMS med pendelda¨mpare, hja¨lpapparatdrivning, och realistiskt
motor-vridmoment.
Simuleringaravmodellenmedsinus-vridmomentvisarattallatyperavpendelda¨mpareverkar
hafo¨rma˚ganattda¨mpavibrationer. Vissaavtypermedcykloid-ochepicykloidbanorda¨mparvi-
brationernasa˚ passbraattdena¨ranogelimineras,o¨verhelavarvtalsregistret. Idrivlina-modellen
med realistiskt motor-vridmoment, da¨r den totala tilla˚tna massan fo¨r pendlarna a¨r 1 kg, verkar
pendelda¨mparna befinna sig pa˚ stabilitetsgra¨nsen. De typer som har vanliga cirkula¨ra banor ly-
ckas inte da¨mpa vibrationer, vissa av modellerna fo¨rsta¨rker till och med vibrationerna. Typerna
med cykloid- eller epicykloidbanor lyckas att da¨mpa vibrationerna o¨ver vissa delar av varvtal-
sregistret. Omflersimuleringarko¨rskanparametrarnafo¨rdeolikatypernaoptimerasytterligare.
Na˚gra rekommendationer fo¨r framtida arbete a¨r fortsatt arbete med utveckling av modeller,
info¨rande av ”stopp” fo¨r pendelro¨relsen och info¨rande av modeller med flera oberoende pendlar
pa˚ sammapendelda¨mparenheteftersomdeiverklighetenintero¨rsigunisont.
II ,ProductandProductionDevelopment,Master’sThesis2011
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
Sammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II
TableofContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
ListofAbbreviationsandNotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .VIII
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 CompanyBackground–VolvoCars . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 HistoricalUseandDevelopmentofCPVAs . . . . . . . . . . . . . . . . . . . . 1
1.3 ProblemBackgroundandDescription . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 ThesisPurposeandGoals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.7 Simdrive3DandotherusedSoftware . . . . . . . . . . . . . . . . . . . . . . . 5
1.8 ThesisOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 THEORETICALFOUNDATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 VibrationsinMulticylinderEngines . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 LagrangianFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 EquationsofMotionasaSystemofFirst-OrderOrdinaryDifferentialEquations . 9
2.4 BasicFunctionandTuningofCPVAs . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Cycloids,EpicycloidsandTautochrones . . . . . . . . . . . . . . . . . . . . . . 13
2.6 StabilityandPerformanceofCPVAs . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 DescriptionofCPVAsModeledinThisWork . . . . . . . . . . . . . . . . . . . 16
2.7.1 SimpleTypewithCircularPath . . . . . . . . . . . . . . . . . . . . . . 16
2.7.2 BifilarType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7.3 RollForm(Salomon)Type . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7.4 CycloidalPathType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7.5 Epicycloidal(Cardoid)PathType . . . . . . . . . . . . . . . . . . . . . 24
2.7.6 Bifilar Type with Rollers and General-Path Representation (Epicycloid
Path) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 LITERATUREREVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 METHODOLOGY–MODELINGANDSIMULATION . . . . . . . . . . . . . . 31
4.1 CPVAModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 DerivationofEquationsofMotionforSimdriveorMatlab . . . . . . . . 31
4.1.2 C/C++ProgrammingandCompilationtodll-fileinVisualStudio . . . . 31
4.1.3 Implementationofdll-fileinSimdrive . . . . . . . . . . . . . . . . . . . 33
4.2 SimdriveModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 VerificationModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.2 ModelwithSine-signalTorque . . . . . . . . . . . . . . . . . . . . . . . 34
,ProductandProductionDevelopment,Master’sThesis2011 III
4.2.3 AdvancedModelwithDMF,FEAD,DieselEngineTorque . . . . . . . . 35
4.3 SimulationsinSimdrive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 RESULTSFROMSIMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1 ModelwithSine-signalTorque . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 AdvancedModelwithDMF,FEAD,DieselEngineTorque . . . . . . . . . . . . 43
6 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7 CONCLUSIONSANDRECOMMENDATIONSFOR
FUTUREWORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
A MatlabCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
A.1 CPVADynamicsSimulationCode . . . . . . . . . . . . . . . . . . . . . . . . . 55
A.2 Circular/Cycloidal/EpicycloidalPathCode . . . . . . . . . . . . . . . . . . . . . 56
B C/C++CodefordllSimpleTypeCPVAElementinSimdrive . . . . . . . . . . . . 58
C EquationsofMotionforBifilarTypewithRollersandGeneral-PathRepresentation
(Mathematica) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
D VisualStudioInstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
E CPVAParametersinSimdriveSimulations . . . . . . . . . . . . . . . . . . . . . . 71
IV ,ProductandProductionDevelopment,Master’sThesis2011
Preface
In this study, several types of Centrifugal Pendulum Vibration Absorbers (CPVAs) have been
modeled and simulated in the software Simdrive 3D, as a possible method to reduce vibrations
of specific orders, originating from engine combustion cycles. Simple, Bifilar, Salomon, and
General-Path type CPVAs have been considered. The work has been carried out from May to
November2010atVolvoCars–EngineTransmissionsinGo¨teborg,Sweden,withAndersWedin
as student. Supervisors have been Ph.D. Tomas Johannesson at Volvo Cars, and Senior Lecturer
Go¨ranBra¨nnareattheDepartmentofProductandProductionDevelopment,ChalmersUniversity
ofTechnologyinGo¨teborg,Sweden.
Acknowledgements
First I would like to thank my supervisor Tomas Johannesson, for initiating and giving me this
very varied and rewarding thesis, and also for being very supportive and helpful with whatever
issues duringthe work. I would alsolike to thank PeterNorin at Volvo, forstarting this thesisin
collaborationwithTomas,andforlettingmeworkonhisgroupinEngineTransmissions. Thanks
alsotomysupervisoratChalmers,Go¨ranBra¨nnare,whohasbeenveryhelpfulduringthiswork.
Further, I would like to thank Tobias Hansson at Volvo for his help with Simdrive among
other things, and hope that he will find this work useful in the future. Thanks also to Niclas
Andersson at Volvo for his comprehensive guidance on the function of Dual Mass Flywheels,
andhowtheycanbemodeled.
SpecialthankstotheguysatContecsEngineeringfortheirinvaluablesupport,especiallyfor
their help with programming issues. It would not have been possible to model the CPVA units
withouttheirhelp. ThanksalsotoAndreasKa¨llforgettingmestartedwithCprogramming,and
VictorSandgrenforbeingabrilliantstudentreviewerofthisthesis.
AveryspecialthankstofamilyfriendElisabetLeppa¨nen,forherhelpwithfindingthiswork
by spreading the word at Volvo Cars. Thanks also to Professor S. W. Shaw for sending me
previousworkinthefield,whichprovedtobemosthelpful. Iwouldalsoliketothankthepeople
atVolvothatshowedinterestinmyworkbylisteningtomypresentations.
Finally,awarmthankstofamilyandfriendsfortheirsupport. Thankstomysisterfordrawing
thenicecoverpictureforthisreport.
Go¨teborg,February2011
AndersWedin
,ProductandProductionDevelopment,Master’sThesis2011 V
List of Abbreviations and Notations
Abbreviations
CPVA(s): CentrifugalPendulumVibrationAbsorber(s)
DMF: DualMassFlywheel
FEAD: FrontEngineAccessoryDrives
ODE(s): OrdinaryDifferentialEquation(s)
Notations
t: time[s]
q : i:thgeneralizedcoordinate
i
q˙ : i:thgeneralizedvelocity
i
θ: CPVAunitrotorangle,firstgeneralizedcoordinate[rad]
φ: CPVAunitpendulumangle,secondgeneralizedcoordinate[rad]
T: kineticenergy[kg ·m2/s2]
V: potentialenergy[kg ·m2/s2]
L: Lagrangian,thedifferenceinkineticandpotentialenergy[kg ·m2/s2]
Yn2: arrayinC/C++storinggeneralizedcoordinates,velocities,andaccelerations
Ω: steadyrotaryspeedofCPVArotor
ω : naturalangularfrequencyofCPVA[rad/s]
n
m: totalpendulummass[kg]
m : massofeachpendulum[kg]
p
J: momentofinertiaforrotor[kg ·m2]
I: totalmomentofinertiapendulumforpendulums[kg ·m2]
I /I : momentofinertiaforeachpendulum[kg ·m2]
p pend
x: coordinateininertialsystemoftheCPVA[m]
y: coordinateininertialsystemoftheCPVA[m]
s: arclengthvariable,secondgeneralizedcoordinate
v: velocityvectorforpendulumcenterofmass
R: distancefromrotorcentretopendulumattachmentpointonrotor[m]
r: distancefrompendulumattachmentpointonrotor,topendulumcenterofmass[m]
k : radiusofgyrationforpendulum[m]
λ
VI ,ProductandProductionDevelopment,Master’sThesis2011