enhancing structural dynamics of a v10 crankshaft using ... · enhancing structural dynamics of a...

Enhancing structural dynamics of a V10 crankshaft using multi-criterial numerical optimisation

Thomas Hinderer, BMW M GmbH

Gerald Hofmann, Intec GmbH

November, 20 2007

Bad Godesberg

Thomas Hinderer20.11.2007Seite 2

Ambition

S85, M5 engine

10 cylinders, V-90°

507 HP (~8000 rpm)

Optimisation objectives

Optimum balancing mass distribution

Radial bearing force peaks reduction

Shaft tilting and displacement reduction

Total mass and inertia minimisation

Thomas Hinderer20.11.2007Seite 3 Crank shaft

Flexible body, combined rigid and flexible body

Main bearingsHydrodynamic model (Impedance, Online-EHD)

Manual optimisationStrategyObjectivesProceedingResults

Numerical Optimisation (PSO)RequirementsJob definitionProcedureResults

Agenda


Crank shaftCombined rigid and flexible body


Crank shaftFlexible shaft without counterweights


Force applicationPoint mass counterweights


0 DOF joint

Mass

Inertia tensor

Center of mass

Mass, inertia, center of gravity = f (geometric properties)

RBE3

Point mass counterweightsAttachment of the point mass to the flexible structure

mi


( )2

22 ρbαRR=m Öia

GGW

⋅⋅⋅−

( )( )22

33

32

sin4

iaÖ

Öia

GGWS, RRα

αRR

=r−⋅⋅

⋅−⋅

( )4

44iaÖ

GGWxx,

RRbαρ=I

−⋅⋅⋅

GGW : Gegengewicht (counterweight)Ö : Öffnungswinkel (apex angle)

Varying counterweight geometry Geometry parameters


1st bending, flexible 1st bending, combined

Eigenmodes and Eigenfrequencies Flexible shaft compared to combined shaft


Crank shaftFlexible body, semi-flexible body




Agenda


Time integration

Input parameter

Position / Velocity

(Shaft, Sleeve)

Output

Bearing forces

Minimal gap

Maximal pressure

Interpolation Impedance Charts

Hydrodynamic forces

Oil gap and states

So So= ( , )ε ϑ

TO

WER

MK

S h

yd

rod

yn

am

ics

• Kinematics

• Kinetics

• Elasticity

External load

Integration

Str

ukt

ur

SIM

PA

CK

Width

Diameter

Play

Viscosity

Rev.speed

NodesTim

e in

dep

end

ent

par

am

eter

s

Solving Reynolds differential equations for

every integration timestep

( ) ( )

3 3

1 2

12 12

1( )

2

+ =

+ +

h p h p

x x z z

u u h hx t

∂ ρ ∂ ∂ ρ ∂∂ η ∂ ∂ η ∂

∂ ∂ρ ρ∂ ∂

Hydrodynamic bearings


Crank shaftFlexible body, combined rigid and flexible body




Agenda


Tilting

Max. radial fo

rce

Max. lateral force

DisplacementBearing forces

“Schiefex-Wert“

Combined Displacement-Tilting rating

Optimisation evaluation parametersBearing forces, tilting, displacement


Displacement Tilting Schiefex

Optimisation evaluation parametersSchiefex-rating


Optimisation evaluation parametersCounterweight relative angle


FGGW,3

FGGW,2

FGGW,2

FGGW,3

FRes,2&3

FRes,2&3

Frot,GGW2

Frot,GGW3

Counterweight relative anglesConcept


Hubzapfen 2

Displacement GGW3

Displacement GGW2

Reference angle GGW3

Reference angle GGW2

pivot 1

pivot 2

Counterweight relative angle variationsUnified setup


Hz 1

GGW 2

Hz 2

GGW 3

Hz 2Hz 3

GGW 4

GGW 5

GGW 6

GGW 7

Hz 3

Hz 4 Hz 4Hz 5

GGW 8

GGW 9

Counterweight arrangementReference design

Hz : Hubzapfen (Pivot)GGW : Gegengewicht (counterweight)


αÖ,GGW1, αMitte,GGW1

αÖ,GGW2 - ΔαÖαÖ,GGW3 - ΔαÖαÖ,GGW4 - ΔαÖαÖ,GGW5 - ΔαÖαÖ,GGW6 - ΔαÖαÖ,GGW7 - ΔαÖαÖ,GGW8 - ΔαÖαÖ,GGW9 - ΔαÖ



αÖ,GGW2 - ΔαÖαÖ,GGW3 - ΔαÖαÖ,GGW4 - ΔαÖαÖ,GGW5 - ΔαÖαÖ,GGW6 - ΔαÖαÖ,GGW7 - ΔαÖαÖ,GGW8 - ΔαÖ

αÖ,GGW9



αÖ,GGW2 - ΔαÖαÖ,GGW3 - ΔαÖαÖ,GGW4 - ΔαÖαÖ,GGW5 - ΔαÖαÖ,GGW6 - ΔαÖαÖ,GGW7 - ΔαÖ

αÖ,GGW8αÖ,GGW9 - ΔαÖ


Variation 1 - 3 (of 28 = 256)

Manual optimisationDesign of experiments

ΔαÖ = „Optimisation stepsize“ (!)

resulting from balancing

ΔαÖ not appliedΔαÖ applied



αÖ,GGW2αÖ,GGW3αÖ,GGW4αÖ,GGW5αÖ,GGW6αÖ,GGW7

αÖ,GGW8 - ΔαÖαÖ,GGW9



αÖ,GGW2αÖ,GGW3αÖ,GGW4αÖ,GGW5αÖ,GGW6αÖ,GGW7αÖ,GGW8

αÖ,GGW9 - ΔαÖ



αÖ,GGW2αÖ,GGW3αÖ,GGW4αÖ,GGW5αÖ,GGW6αÖ,GGW7αÖ,GGW8αÖ,GGW9


Variation 254 - 256 (of 256)

Manual optimisationDesign of experiments


Manual optimisation3D-plot of maximal bearing force of one iteration

Only 60 of 256 displayed


Manual optimisationResult evaluation after one iteration step

„Manual Hill-climbing“


Design of experiments

(Maple)

Evaluation of paramererised model

(SIMPACK)

Results visualisation

(Matlab)

Ref

ere

nce

de

sig

n

Ce

nte

r a

ngle

dis

trib

utio

n

Ape

x a

ng

le d

istr

ibut

ion

Manual evaluation

Pick optimum from 256 solutions

Manual optimisationSemi-automatic optimisation loop


Massenverläufe

20,620,8

2121,221,421,621,8

2222,222,422,622,8

2323,223,423,623,8

2424,224,4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Optimierungsschleife [-]

Ku

rbel

wel

len

mas

se [

kg]

Vierteldrehung (Kraftorientiert)

Halbdrehung (Kraftorientiert)

Serienmasse

Nulldrehung

ViertelHalbdrehung

Manual optimisationFinal results

Crank shaft total mass

Various manual approaches to set up counterweigh angles

Reference


Lagerkraftverläufe

4200043000440004500046000470004800049000500005100052000530005400055000560005700058000590006000061000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Optimierungsschleife [-]

Ma

xim

ale

La

ge

rkrä

fte

[N

]

Halbdrehung (Kraftorientiert)

Vierteldrehung (Kraftorientiert)

Serienlagerkraft

Nulldrehung

ViertelHalbdrehung

Bearing radial force

Manual optimisationFinal results

Reference

Selected solution


Crank shaftFlexible body, combined rigid and flexible body




Agenda


Numeric optimisationConditions and requirements

Conditions

Highly nonlinear system characteristics

Parameter space constraints

Reference design of unknown quality

Parameter space of dimension 16

8 optimisation objectives to minimise

Time for one evaluation ~15min

Requirements

No gradient based algorithm (Jabobian matrix, time complexity)

Quick convergence, (semi-) heuristic method

Not vulnerable to local minima

Parallel function evaluation

No predefined weighting or „magic“ factors


Particle swarm optimisationHistory and features

Idea / Functional principle

Agent-based, stochastic method

Simple rules of decision, basing on common knowledge

Distributed artificial intelligence

Self-organising collective intelligence

Emerging behaviour

History

First implemented 1995 by J. Kennedy and R. C. Eberhart

Optimiser used

www.gpsopt.de


Particle swarm optimisationParameters and settings

Swarm

Given number of particles (dynamically de-/activated to save CPU time)

Particles

Parameter vector („Position in the parameter space“)

Velocity vector („Search direction“)

Swarm knowledgeOver-all best solution for every

single objective

Over-all best solution for the

global optimum


Particle swarm optimisationParticle movement model

v=f(k)


Particle swarm optimisationExample: Three poles in a cubic parameter space


Particle swarm optimisationResult visualisation

Example: Three dimensions (of 16) selected for visualisation

Total 3D parameter space snapshots: 16! / ( 3! * (16-3)! ) = 560


Result evaluationMulti-objective result comparison


Result evaluationMulti-objective result comparison

selected


Update parameter files

Run time integration

Update optimum mapDe-/activate particles

Update direction pointersUpdate positions / velocity

Check break conditions

Check parameter constraints

Evaluate resultsCalculate fitness values

Static balancing

per

part

icle

mul

ti-th

read

ed e

valu

atio

n

Particle swarm optimisationProcedure


9°18°0°36°9351°342°0°324°818°0°36°324°754°72°36°108°6

162°144°180°108°5198°216°180°252°4225°234°216°252°3207°198°216°180°2

Achtel-drehung

Viertel-drehung

Halb-drehung

Null-drehungGGW

24.7°174.46°107.14°93.51°9

343.76°71.52°810.26°38.02°748.81°33.09°6

165.22°36.01°5195.25°28.17°4216.88°55.45°3199.23°116.37°2-165.02°131.89°1

Mitten-winkel

Öffnungs-winkelGGW

Result evaluationConfiguration found by PSO compared to manual approaches

Manual design approaches Solution found by PSO

PSO solution not related to any manual approach


Total mass reduction

Max. bearing force peak reduction

Number of iterations

Works without user interaction

Manual gpsopt

14,85% 14,8%

+/- 0 % -14 %

20000 5000

No Yes

Multi-criterial evaluation No Yes

Result summary

PSO found new designs, not covered by classic (manual) design rules.


Thank you for your attention !Thank you for your attention !

enhancing structural dynamics of a v10 crankshaft using ... · enhancing structural dynamics of a...

Documents