audi optimization

New methods for optimization and correlation NVH in the Full Vehicle Analysis

Dr. Eckhard Plank, AUDI AGAntoine Guellec, AUDI AG

Willem van Hal, MSC Software

Dr. E. Plank AUDI AG, A. Guellec AUDI AG, W. Van Hal MSC Software – NVH Symposium, Detroit, 10.10.20072


Optimization and correlation with nastran has been d one since a few decades

– Optimizing and correlating multi-millions of design variables in dynamics is of interest in European automotive

– Optimizing large assemblies puts extra strain on op timizer and solver and hardware

The Challenge


New methods for optimization and correlation NVH in the Full Vehicle AnalysisThe optimization / correlation process

Meshing

Design Variables

Optimization/Correlation Goal and Constraints Solving

Postprocessing

CAD Redesign



– Topology optimization has been used since a decade to determine optimal constructions within a given design space i n static and nlstatic loadcases in competitive products on a part level.

– Topology optimization in the area of modal/frequenc y/acoustics has been extended since Nastran sol 200 was enhanced wi th topology functionality and a new optimizer: BIGDOT as well a s powerfullsolvers.

– The method shown in this presentation is the start to extend theclassical topology optimization from „parts“ toward s assemblies in the area of modes, frequency response and acoustic s for optimizing as well as correlating models with test data.

Topology Optimization in a nutshell

?



– Topometry is a way to optimize each single reference d element values like thickness, damping, youngs modulus, density.

– Topometry helps to correlate analysis models with te st data when E,Ge or T is defined

– Topometry can also help to improve the design by def ining where the element thickness can be increased or reduced on an element level

Topometry Optimization in a nutshell



– Topology can be used within the designspace, the no n-designed part of the structure

– Topometry can be used on the designed part of the st ructure

Topology vs. Topometry

T

E=f(rho)



– Topology (Topvar), Topometry (Tomvar) are a conveni ent way to define millions of design variables in sol 200 by j ust a few lines of input, no preprocessor support is needed

– New responses (frmass,compliance) and manufacturing constraints (extrusion, cast, member thickness and symmetry) ha ve been implemented

– Output can be written to a p2.5 asci file which can be read by many 3rd party software like Fegraph, Animator, Meta Pos t and MSC products, SimX and Patran

Topology / Topometry implementation in nastran



– Topology optimization of the AUDI TT threshold prof ile (extruded Al.)

– BIW model correlation : application of topometry opt imization

– Concept investigations with application of large to pology and topometry optimization – body structure design

– Example of topology optimization for an acoustic ap plication

Application of topology and topometry optimization w ithin nastran sol 200 in AUDI projects



Aluminum casting parts

Aluminum extruded profiles

panels load path investigation

AUDI TT- Roadster Use of topology optimization in TT’s space frame des ign

AUDI TT-Roadster full car model



result of the optimization

last design (serie)

► the functional benefit to the previous design is a reduction of the BIW mass of 2 kg while increasing the entire car to rsion mode of 0,8Hz

optimization model

previous design

Targeting

• increase global torsion mode

• constraint on global mass

Conditions

• 650.000 variables

• extrusion and symmetry design constraint

AUDI TT- Roadster topology optimization of the threshold profile (ext ruded Al.)






– Example of topology for an acoustic application

Application of topology and topometry optimization w ithin nastran sol. 200 in AUDI projects



Description

FE-Modell

Test-Modell FRAC Criterion

0,472

0,346

0,4900,888

0,716

0,488

0,631

0,471

0,557

0,291

0,492

0,359

0,598

0,222

Sum Shaker 1

Sum Shaker 2

Sum Shaker 3

MAC Criterion

AUDI TT- Roadster BIW model correlation / application of topometry opt imization

► Very good correlation of the modes frequency range. Bad correlation of vectors and amplitudes

TestFE



{ } { }{ } { }( ){ } { }( )H

XT

XH

AT

A

HX

TA

HHHH

HHFRAC

2

=

{ }AH - the analytical frequency responsefunction matrix

{ }XH - the experimental frequency responsefunction matrix

Targeting of the topometry optimization


► Optimization of the joint stiffness as a way invest igating which are the sensitive parts of the structure to differences between test and

simulation

Variables : Young-Modulus of the joints

Objective : maximization of FRAC

Results : Sensitivities to a better correlation of FRFs



Results of the Optimization


►joint optimization shows main discrepancies around the aluminum casting parts. The modelization inconsistencies of t he casting parts

were investigated more in detail in a second optimi zation of shell thicknesses. A refinement of the mesh confirmed this result.

Aluminum casting parts in the AUDI TT

body structure

First step : joint stiffness optimization

2nd step : shell thicknesses optimization






– Example of topology for an acoustic application




0,01

0,1

1

10 12 14 16 18 20 22 24 26 28 30

frequency (Hz)

Sum

func

tion

body

base variant

rigid body

AUDI A3 Concept investigations – body structure design

Strategy / load case

►The important influence of the body elasticity on c omfort relevant vibrations in a low frequency range in combination with light weight

requirements dictate to track the right energy flow s in the structure in order to design a robust body.

road excitation: body acceleration

A3 full car NVH model

Excitation

Response

influence of body

elasticity

Res

pons

e



0,01

0,1

1

10 12 14 16 18 20 22 24 26 28 30

frequency (Hz)

Sum

func

tion

body

base variant

result optimization

rigid body

AUDI A3 Concept investigations – body structure design

Strategy / target Topology

Combination topology and topometry

Topometry

► The goal of the optimization is a reduction of the maximal amplitude of a sum function on a relevant frequency range.

Comparison of 3 optimization strategies (topometry, topology, both combined)


New methods for optimization and correlation NVH in the Full Vehicle AnalysisAUDI A3 Concept investigations – body structure design

Results

topology

topometry

combination of topology and topometry


New methods for optimization and correlation NVH in the Full Vehicle AnalysisAUDI A3 Concept investigations – body structure design

Results – comparison of the 3 strategies

– Topology and topometry optimization provide good res ults, fast convergence and easy interpretation

– Best strategy would be combination of topology and topometryoptimization: it allows to investigate the best cho ice between shear fields and profile structure

– Bad convergence of a combined topometry and topology optimization. Results are still difficult to be int erpreted



1,00E-02

1,00E-01

1,00E+00

1,00E+01

80 83 86 89 92 95 98

Example of beta optimization in low frequency acous tics

Sou

nd p

ress

ure

leve

l (dB

)Frequency (Hz)

Trimmed body acoustic model

Result topology optimization

Structure enhancement around the critical panel

Acoustic cavity

Sensitive panel



First step, focus on the right solver

Second step, focus on the right parallel method

Solver method selection



0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

1 10 100 1000 10000 HzHz

Statics:

– Sparse (assemblies)

– Casi, element based iterative solver (solid parts, red uced assembliesdmig)

Modes, Modal frequency response:

– SMP Lanczos, single shift

– DMP dof domain Lanczos

Acoustics / Driving point responses:

– DFreq DMP

– Mfreq ACMS

Solving methods selection, Topology

AU

TO

MO

TIV

E A

SS

EM

BLY

AU

TO

MO

TIV

E A

SS

EM

BLY

LanczosLanczos

ACMSACMS

DFREQDFREQ



– The decision should be made upon amount of subcases and conditioning of the K matrix

– The type of sensitivities can influence the solver selecti on

Statics: Sparse Decomp vs Iterative methods



– In statics we can choose between a 2 Iterative solve rs and a sparse solver

– In Nastran the sparse solver is default. The Iterat ive solver can be chosen in the case control section by:

– SMETHOD= ELEMENT $ For the CASI element based itera tive solver

– SMETHOD= MATRIX $ For the matrix based iterative so lver

______________________________________________________________

Due to the mix between shells and solids we used th e sparse solver for the Audi TB.

When the just the design space is run, 6mil element s can be run in 20min/SC on IT2 with casi.

Solver method selection STATICS



– Modal methods are needed if modes need to be tracked

– Modal methods may run into numerical side effects due to ch angesin modal densities:

ρρρρ = ρρρρo x

E = Eo xp

– Direct can be an advantage if little excitations have to be calculatedand/or if dmp is possible

MODAL vs DIRECT Methods



Modal method selection

– In modes calculation, there are 2 general economic possibilities: ACMS and Lanczos

– The decision which solver to choose will be depende nt on 2 variables: amount of solids, amount of modes.

– In general below 70-100 Hz or upto 70 modes, the Lan czos solver will be as good as acms and will outperform acms for the c ase the amount of solids increases.

– ACMS will be the choice when many modes are calcula ted and a limited amount of very dense solids.

– A Full Vehicle up to 50 hz with 3 mil solid topo vari ables is done best by Lanczos whereas an acoustic model with a double l ayer of shells (for stiffness or damping) for acoustics is handled faster by ACMS.

– High frequency domain with acoustics and solids mig ht be covered by sol 108 as well.

______________________________________________________________

Most Audi models shown, were run with the SMP varia nt from lanczos. This choice was made based on robustness and perfor mance and modal density.

Solver method selection MODES / MFREQ



– Lanczos: the choice for problems with little modal d ensity and increasingly dense problems

– Lanczos can be run in SMP,DMP (dof,freq,geom) mode.

– SMP (2 cpu) mode is economical when 1 shift can be used and most time is spend in decomp.

– Factorization cost go up if many dense solids are ad ded

– 50-70% speedup is possible on 2 cpu´s for the situat ion that factorization is the major cost factor

– DMP: DOMAINSOLVER MODES (partopt=dof) could be an alternative as well as ACMS and is a working solutio n for most TB/GFZ Models.

Lanczos Performance



Avoiding changes in the modal density in order to a void performance problems:

– When K drops faster then M, the modal density might increase at once resulting in a dramatic performance decrease (SQRT( K/M)).

– K and M can be influence by:

A) Topvar , power variable (field 8).

B) E and Rho on the mat1 card.

Under the assumption that we will add little mass, a material with reduced rho is beneficial for the performance AND wh en you want to know where you could add material without adding a significant amount of mass then the assumption be valid.

C) Dynamic dampers can be avoided by this assumptio n

DFREQ (sol 108) wouldn't show this problem and is a viable option for the higher frequency domain.

Modal (lanczos and acms) Performance (2)



– Modes up to 50hz,

– 8 frequencies, 1 subcase sum over max of acceleration of 10 grids.

– Determine where to stiffen between 2 spring struts

– 6.2 Mil design elements (12.4 mil desvar)

– 12 mil dof (G), 8 mil dof (A)

– 20H/ cycle 85% solving 15% optimizing

– I8 with 14gb memory used in SMP mode

– Extremely dense design space

Example MFREQ, TB (not shown) + Design Space Topolo gy in dynamics



Dfreq can be a economical choice if:

– The modal density get’s too high as design elements go down the highest request frequency

– DFREQ can be run in DMP with an almost linear speed up

– DFREQ can be used economical to combine Topology wi th acoustics.

Direct frequency response: DFREQ



Mostly shell based, or dominated structures, no extra d of are added ornumerical difficulties are not to be expected

Statics

– Sparse, Sparse smp/dmp

Modes, Dynamics / Acoustics

– ACMS > 100 Hz in both smp or dmp mode

– Single shot lanczos (1 shift) < 70 Hz

– I8 might be beneficial for mfreq with many excitation frequ encies forspeeding up adjoint sensitivities

– Dfreq

Solving methods selection, Topometry



– Large assemblies can be optimized with multi millio n desvar due to efficient solvers for various problems and efficien t optimizers

– Topology optimization can be used to determine load path within the non-designed structure

– Topometry can be used to define model improvements w ithin the designed structure

– Topometry can be used to easily define design variab les for correlation

Conclusion



– Glueing might be a good way to easily define design space s as congruent meshes are not needed

– Frac and Mac values should be considered as responses in nastran as well as a more simplified test data input.

– Relative/percentage output

– Ease of use topometry interface: TOMVAR (MD2.1) to b e released

Outlook and possible enhancements



– Special thanks to ..

Ludger Lagerman, EDAG for the meshing efforts and

Nastran Devl: Xiaoming Yu, Shenghua Zhang, Joe Cole, Peter Schartz, Mike Reymond and Erwin Johnson for enhancing Nastran in t he area of performance and functionality.

– The credits, for the correlation data method, go to Andreas von Mach / Von Mach engineering.

Credits



Thank you !! Questions?

audi optimization

Documents

guellec audi

plank audi

full vehicle

aluminum casting

biw model

designed structure

solving methods

audi a3