Nafems15 Technical meeting on system modeling
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Transcript of Nafems15 Technical meeting on system modeling
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Integration of reduced 3D models in vibration design processes. Examples from various 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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