Nafems15 Technical meeting on system modeling
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The document discusses the integration of reduced 3D models into vibration design processes across various industries, focusing on model reduction, system modeling, and experimental validation techniques. It highlights methodologies such as variable separation, parametric matrices, and domain decomposition to enhance simulation efficiency and accuracy while detailing tools and challenges associated with these approaches. Key elements include the use of finite element models (FEM), system response analysis, and predictive monitoring within structural dynamics.
![13
• 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 residualWithout residual
[T(p1) T(p2) … ]
Orthogonalization
[T]
[Tk] Rd
k=K-1 R(q(Tk))
Orthog [Tk Rd
k]](https://image.slidesharecdn.com/nafems15systeme-150603182808-lva1-app6892/85/Nafems15-Technical-meeting-on-system-modeling-13-320.jpg)
![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
wj
21
[M] [Kel] [KintS] [KintU]](https://image.slidesharecdn.com/nafems15systeme-150603182808-lva1-app6892/85/Nafems15-Technical-meeting-on-system-modeling-18-320.jpg)
Nafems15 Technical meeting on system modeling
- 1. 1 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
- 2. • FEM simulations • System models (model reduction, state-space, active control, SHM) • Experimental modal analysis • Test/analysis correlation, model updating Activities 2 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
- 3. Outline • Systems, models, dynamic models • Tools for model reduction – Variable separation – Parametric models – Domain decomposition • Conclusion 3
- 4. 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
- 5. Meta/reduced models 5 Full numerical model expensive Meta-model acceptable cost Learning points Responses Computation points LearningX LearningY X Estimations Yˆ 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
- 6. 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, …
- 7. 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 7
- 8. SVD on the time response • coincides with modes if isolated resonances • similar info for NL systems 8 Space / Time decomposition Squeal limit cycle PhD Vermot (Bosch) NL system with impacts, PhD Thénint (EDF)
- 9. Data/model reduction 9 • 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 t NA i=1 – Learning = full FEM static & modes (McNeal, Craig-Bampton, …) {q}N= qR Nx NR T 𝑀𝑠2 + 𝐶𝑠 + 𝐾 𝑞(𝑠) = 𝑏 𝑢(𝑠) 𝑇 𝑇 𝑍(𝑠) 𝑇 𝑁𝑅×𝑁𝑅 𝑞 𝑅(𝑠) = 𝑇 𝑇 𝑏 𝑢(𝑠)
- 10. 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 10 In Out Environment/Design point System qR Nx NR T System=IO relation System=modal series Challenge : account for environment/design change
- 11. Sample design changes • Material changes (visco damping) • Junctions (contact) • Component/system Mesh/geometry 11
- 12. 12 Ingredient 2 : parametric matrices •Viscoelastic damping 𝐾𝑣 = 𝐾 𝐸(𝜔, 𝑇) •Rotation induced stiffening 𝐾 𝐺 = 𝐾 Ω •Contact stiffness evolution with operating pressure 𝐾 𝑁 = 𝐾 p(x, 𝐹𝐺𝑙𝑜𝑏𝑎𝑙) Reduction basis T can be fixed for range of parameters Speedup : 10-1e5
- 13. 13 • 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 residualWithout residual [T(p1) T(p2) … ] Orthogonalization [T] [Tk] Rd k=K-1 R(q(Tk)) Orthog [Tk Rd k]
- 14. 1th vertical mode: Main frame and bow moving in phase 2 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 14 Concept Requirements & architecture Component design System operation AVL Hydsim
- 15. Basic component coupling Start : disjoint component models Coupling relation between disjoint states • Continuity 𝑞𝐼1 − 𝑞𝐼2 = 0 • Energy +
- 16. 16 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
- 17. 17 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
- 18. 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 wj 21 [M] [Kel] [KintS] [KintU]
- 19. CMT & design studies • One reduced model / multiple designs Examples • impact of modulus change • damping real system or component mode 19 Component redesign Sensitivity energy analysis Nom . +10 % +20 % - 20%
- 20. 20 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 www.sdtools.com/publications Ritz