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Intégration de modèles 3D réduits dans le processus de conception vibratoire. Exemples de différentes industries.

Etienne Balmes SDTools Arts et Métiers ParisTech NAFEMS Simulation des systèmes 3 Juin 2015

• FEM simulations • System models (model reduction, state-space, active control, SHM) • Experimental modal analysis • Test/analysis correlation, model updating

Activities

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CAD/Meshing

FEM

Simulation

Testing

CATIA, Workbench, …

NASTRAN, ABAQUS, ANSYS,...

Adams, Simulink,...

LMS TestLab, ME-Scope, …

Simulation

Validation

SDT : MATLAB based toolbox Commercial since 1995 > 700 licenses sold

Pantograph/catenary Modal test correlation Track dynamics

Outline

• Systems, models, dynamic models

• Tools for model reduction – Variable separation

– Parametric models

– Domain decomposition

• Conclusion

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A system = I/O representation

Prototype Virtual prototype All physics (no risk on validity) limited physics (unknown & long CPU)

in operation response design loads limited test inputs user chosen loads measurements only all states known few designs multiple (but 1 hour, 1 night,

several days, … thresholds)

Cost : build and operate Cost : setup, manipulate

In Out

Environment/Design point

System

Meta/reduced models

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Full numerical model

expensive

Meta-model

acceptable cost

Learning points

Responses

Computation points

LearningX LearningY

X

Estimations Y

Validity ? • Regular relation • Band-limited • Spatial position

of inputs • …

Predictive monitoring of fuel circuit Ph.D. of B. Lamoureux

~500 parameters

~100 indicators ~20 Inputs Data from in operation measurements

System models of structural dynamics

Simple linear time invariant system

Extensions • Coupling (structure, fluid,

control, multi-body, …) • Optimization, variability,

damping, non linearity, …

When Where

Sensors

Large/complex FEM

Historical keywords : Modal analysis Superelements, CMS, …

Ingredient 1 : variable separation

• General transient but – limited bandwidth

– time invariant system

• Modal Analysis response well approximated in spatial sub-space

𝑞(𝑥, 𝑡) = 𝜙𝑗 𝑥 𝑎(𝑡)

𝑁𝑀

𝑗=1

• Space shapes =modes

• Time shapes = generalized coordinates

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SVD on the time response

• coincides with modes if isolated resonances

• similar info for NL systems

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Space / Time decomposition

Squeal limit cycle

PhD Vermot (Bosch)

NL system with impacts, PhD Thénint (EDF)

Data/model reduction

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• SVD = data reduction through variable separation – Extension to higher dimension variable separation see Chinesta (afternoon)

• Ritz analysis : build reduced dynamic models – Reduced model = differential/analytic equation for qR(𝑡)/qR(𝑠)

– States qR allow restitution

– Assumptions on loading : band limited 𝑢 𝑡 restricted loads in space 𝑏𝑖 𝑥

F x,t = bi x u tNA

i=1

– Learning = full FEM static & modes (McNeal, Craig-Bampton, …)

{q}N= qR

Nx NR

T

𝑀𝑠2 + 𝐶𝑠 + 𝐾 𝑞(𝑠) = 𝑏 𝑢(𝑠)

𝑇𝑇 𝑍(𝑠) 𝑇 𝑁𝑅×𝑁𝑅 𝑞𝑅(𝑠) = 𝑇𝑇𝑏 𝑢(𝑠)

Validity of reduced system models

Test & FEM system models assume

• Input restrictions – Frequency band (modes)

– Localization (residual terms)

• System – Time invariant

– Linear

Implemented in all major FEM & Modal Testing software

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In Out

Environment/Design point

System

qR

Nx NR

T

System=IO relation

System=modal series

Challenge :

account for environment/design change

Sample design changes • Material changes (visco damping)

• Junctions (contact)

• Component/system Mesh/geometry

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Ingredient 2 : parametric matrices

•Viscoelastic damping 𝐾𝑣 = 𝐾 𝐸(𝜔, 𝑇)

•Rotation induced stiffening 𝐾𝐺 = 𝐾 Ω

•Contact stiffness evolution with operating pressure

𝐾𝑁 = 𝐾 p(x, 𝐹𝐺𝑙𝑜𝑏𝑎𝑙) Reduction basis T can be fixed for range of parameters Speedup : 10-1e5

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• Multi-model

• Other + residue iteration

• Example : strong coupling With heavy fluids : modes of structure & fluid give poor coupled prediction

Bases for parametric studies

Example water filled tank

With residual Without residual

[T(p1) T(p2) … ]

Orthogonalization

[T]

[Tk] Rdk=K-1 R(q(Tk))

Orthog [Tk Rdk]

1th vertical mode: Main frame and

bow moving in phase

2nd vertical mode: Main frame and

bow moving in phase opposition

3rd vertical mode: Upper arm

flexion and phase opposition between

the main frame and the bow

Co-simulation SDToos/OSCAR

MSC/Motion (VSD 2014)

Ingredient 3 : domain decomposition • 1D models coupled by few in/out :

hydraulic circuits, shaft torsion • 3D FEM : classical uses

– Component Mode Synthesis/ Craig-Bampton – Multibody with flexible superelements

• For each component base assumptions remain

– LTI, few band-limited I/O

Two challenges • Performance problems for large interfaces • Component/system relation

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Concept

Requirements & architecture

Component design

System operation

AVL Hydsim

Basic component coupling Start : disjoint component models Coupling relation between disjoint states • Continuity 𝑞𝐼1 − 𝑞𝐼2 = 0 • Energy

+

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Coupling + reduction Classical CMS • Reduced independently • All interface motion (or interface modes) • Assembly by continuity Difficulties • Mesh incompatibility • Large interfaces • Strong coupling (reduction requires knowledge of coupling)

Physical interface coupling • Assembly by computation of interface energy

(example Arlequin) Difficulties • Use better bases than independent reduction

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Squeal example : trace of system modes

CMS with trace of system modes • No reduction of DOFs internal to contact area • Reduction : trace of full brake modes on

reduced area & dependent DOFs (no need for static response at interface)

Reduced model with exact system modes Very sparse matrix for faster for time

integration

Component mode tuning method • Reduced model is sparse • Component mode amplitudes are DOFs

• Reduced model has exact nominal modes

(interest 1980 : large linear solution, 2015 : enhanced coupling)

• Change component mode frequency change the diagonal terms of Kel

Disc

OuterPad

Inner Pad

Anchor

Caliper

Piston

Knuckle

Hub

wj2 1

[M] [Kel] [KintS] [KintU]

CMT & design studies

• One reduced model / multiple designs

Examples

• impact of modulus change

• damping real system or component mode

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Component redesign

Sensitivity energy analysis

Nom

.

+10

% +20

%

-

20%

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Conclusion Reduced 3D models combine • Variable separation • Solve using generalized/reduced DOFs

–u(t) just assumed band-limited –Restitution is possible

• Parametric matrices • Domain decomposition

– Craig-Bampton is very costly – Generalized coordinates can make sense

Challenges • Engineering time to manage experiments • Control data volume (>1e3 of NL runs) • Control accuracy : develop software / train

engineers

In Out

Environment Design point

System

qR

Nx NR

T

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Ritz