Optimization for Acoustic Disciplines 4. Norddeutschen Simulationsforum 26 May Hamburg, Germany Claus B.W. Pedersen (claus.pedersen@fe-design.com) Peter M. Clausen, Peter Allinger, Jens Harder FE-Design
Topology optimization for coupled structural-acoustic interaction Goal: Design the acoustic response by changing the structural layout. Applications: Interior NVH in cabins Pumps Airplanes Loudspeakers Microphones Hearing aids Etc. Minimize noise Minimize pressure External dynamic excitation
Motivation: Examples of Applications Automotive - Pump Turbine Interior design Minimize pressure E.g. designing structural foundation pressure Excitation Old design New design Loudspeaker Microphone Hearing aids Cell phone design pressure Old design New design E.g. designing structural frame Constant - desired pressure for given excitation frequencies Excitation
Optimization Workflow with TOSCA CAD & FE Preprocessing OPTIMIZATION FE Postprocessing & CAD CAD System FE-Preprocessing ABAQUS/CAE ANSYS ANSA FEMAP Hypermesh MEDINA MSC.Patran UG NX ABAQUS ANSYS Interactive Setup MSC.NASTRAN NX.NASTRAN FE-Post ABAQUS/Viewer ANSYS meta FEMAP Hypermesh MEDINA MSC.Patran UG NX CAD System MSC.MARC PERMAS
Three different measures for the acoustic (1) Equivalent Radiated Power (ERP) is a global acoustic measure but is not accurate. {vn} Φ ERP 1 2 = cρ v nda 2 (2) Acoustic Transfer Vectors (ATV) assumes a weak coupling between the acoustic and the structure Acoustic pressure point Φ = p = ATV T { ATV} { v } n (3) Acoustic Finite Element (A-FE) assumes a strong coupling between the acoustic and the structure Acoustic pressure point Φ FE T 2 { A} { v }[ K + iωc Ω M ] 1 2 = p = Ω n f f f
Compare approaches in sequential optimization loops Equivalent Radiated Power (ERP) Acoustic Transfer Vectors (ATV) ATV - acoustic Acoustic Finite Element (A-FE) Optimization loop Optimization loop Optimization loop Modified model Modified model FE-solver Only structural model [ S ]{ u} = { f } Modified model FE-solver Only structural model [ S ]{ u} = { f } FE-solver Including acoustic elements [ S] u = p f 0 Φ ERP 1 2 T cρ v Φ { } { } n ATV p = ATV v n = da 2 = Φ FE = p TOSCA OPT TOSCA OPT TOSCA OPT
Some applications
Equivalent Radiated Power (ERP) (1) Equivalent Radiated Power (ERP) is a global acoustic measure but is not accurate. {vn} Φ ERP 1 2 = cρ v nda 2 (2) Acoustic Transfer Vectors (ATV) assumes a weak coupling between the acoustic and the structure Acoustic pressure point Φ = p = ATV T { ATV} { v } n (3) Acoustic Finite Element (A-FE) assumes a strong coupling between the acoustic and the structure Acoustic pressure point Φ FE T 2 { A} { v }[ K + iωc Ω M ] 1 2 = p = Ω n f f f
Surface velocities of node group The surface velocities as design response: 2 2 ( ) = Ω uˆ R ( Ω) + uˆ ( Ω) Φ Ω C where uˆ R 1 N N 2 ( Ω) = u ( Ω) n and uˆ ( Ω) = u ( ) n= 1 R i C 1 N N n= 1 C Ω n i Minimize the overall surface velocities by minimizing the peaks Φ( Ω) Normal to the surfaces Ω
Topology Optimization The goal of Topology Optimization is to find an optimal material distribution considering certain boundary conditions. Ω F * Ω F
Topology Optimization Design Variables Relative density of each element Large number of design variables E physical ρ physical ( ρ ( ρ relative relative ) ) ρ relative Objectives / Constraints Stiffness, Eigenfrequencies, Mass, Important: Manufacturing restrictions e.g. for casting components Possibility to transfer results to CAD Systems Large model sizes require efficient FE-solvers TOSCA Structure.topology
Motivation: Initial design Fixed domain Clamped Design domain Excitation loading: { 0 P} = { P} cos ( Ωt) Excitation frequency Surface velocities are minimized for different excitation frequencies
Quasi static dynamic - Static Optimized for minimizing surface velocities Optimized for stiffness Optimized for minimizing surface velocities Initial design Optimized for stiffness Optimized for minimizing surface velocities
Warnings!!! (1) Acoustic pressure point Minimize the acoustic pressure by changing material distribution in the structural parts Solution????? No material!!!!! Often forgotten additional requirements
Warnings!!! (2) { 0 ( ) P} cos Ωt Often optimizing the peaks in spectra Correct modeling is important, e.g. damping in both structural and acoustic K]{ u} + [ C]{ u& } + [ M ]{ u&& } = { P} cos [ 0 Small damping: Narrow peak Numerical difficult ( Ωt) Medium/high damping: Acoustic medium included Numerical good
Bead Optimization Design Variables Out-of-plane movement of the design nodes. Generating of design proposals for location and orientation of beads Objectives / Constraints Stiffness, eigenfrequencies Important: The optimization results have to be interpreted and transferred to a new sheet metal structure. Mesh independent solution TOSCA Structure.bead
What is bead optimization?? Deflection of a bending beam: d = ---------------- F l 3 3 E I moment of inertia : I = b ------------ h 3 12 The following parameters are determined Cross section b h l F d Bead location Bead orientation Under the following constraints Bead height Bead height Bead width Both have a strong influence on the manufacturing (deep drawing) Bead width
Example: Bead optimization Bead optimization of simply supported oil pan Nodal positions are design variables F( t) = F0 sin( Ωt + ϕ) Governing equation Ω 2 M u&& + iωcu& + Ku = S( Ω) u = F( Ω) Semi analytical sensitivities based on finite differences ANSYS, v11 ~ 25.000 Elements, ~ 22.000 Nodes Optimization problem: min Surface velocities s.t. Nodal movement: 5.0mm < x < 5.0mm
Solving governing equation Governing equation Direct solution High number of excitation frequencies High in CPU-time Modal decomposition solution High number of excitation frequencies Low in CPU-time High amount of output (>GB)
Bead optimization results 5 mm in positive normal direction 5 mm in negative normal direction
Bead optimization results Convergence Iteration 0 Iteration 5 Iteration 30 TOSCA s NVH response compared to SBSound (CADFEM) TOSCA, iter 0 TOSCA, iter 30 SBSound, iter 0 SBSound, iter 30
Comparison results with static and modal optimization Check against static and modal optimization frequency spectrum of optimization results Initial design max first eigenvalue min compliance min modified ERP
Acoustic Finite Element (A-FE) (1) Equivalent Radiated Power (ERP) is a global acoustic measure but is not accurate. {vn} Φ ERP 1 2 = cρ v nda 2 (2) Acoustic Transfer Vectors (ATV) assumes a weak coupling between the acoustic and the structure Acoustic pressure point Φ = p = ATV T { ATV} { v } n (3) Acoustic Finite Element (A-FE) assumes a strong coupling between the acoustic and the structure Acoustic pressure point Φ FE T 2 { A} { v }[ K + iωc Ω M ] 1 2 = p = Ω n f f f
Acoustic--Interaction Governing equations: Solid Fluid Which leads to the following system of equations (Unsymmetric equations):
Pressure measures Different pressure measures: 1. Sound Pressure Level (SPL) 3. Decibel (db) 2. Root-mean-square pressure (RMS) 4. Weighted decibels (dba) Pressure Minimize the overall pressure measure by minimizing the peaks Fluid Excitation frequencies
+ Acoustic model for optimization Harmonic force Steel Rigid air boundary condition Air Pressure Optimization problem: min Pressure s.t. Volume < 30% Central node for pressure measurement Excitation frequency
Modes in the fluid Acoustic modeshapes: Fluid BC s: n Ñp = 0 on all surfaces. (rigid wall) Conclusion: Only modes propagating in the same direction as the harmonic load results in a pressure-peak.
Acoustic Transfer Vectors (ATV) (1) Equivalent Radiated Power (ERP) is a global acoustic measure but is not accurate. {vn} Φ ERP 1 2 = cρ v nda 2 (2) Acoustic Transfer Vectors (ATV) assumes a weak coupling between the acoustic and the structure Acoustic pressure point Φ = p = ATV T { ATV} { v } n (3) Acoustic Finite Element (A-FE) assumes a strong coupling between the acoustic and the structure Acoustic pressure point Φ FE T 2 { A} { v }[ K + iωc Ω M ] 1 2 = p = Ω n f f f
First example (maybe in the world) Harmonic force Minimize the acoustic pressure by changing the structure Optimized design
Conclusions Optimization of industrial NVH-problems is possible using TOSCA Structure.bead optimization TOSCA Structure.topology optimization Optimization is using validated FE-models already being used in industrial CAE environment Optimization results can lead to new design proposals which are difficult to achieve using trial and error approach
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