Efficient Simulation for Strongly Coupled Noise- …

1 Efficient Simulation for Strongly Coupled Noise- vibration - harshness (NVH)R. S. Puri, D. Morrey, Oxford BrooksE. B. Rudnyi, CADFEM1 Background Joint work 2004- Over email Available online Simulation > 250 HzAir bornHigh Frequency100 250 HzStructure and air borneMid Frequency0 100 HzStructure borneLow Frequency3 Fully Coupled Finite Element Discretization FLUID29/FLUID30 in ANSYS The element size should be smaller than wavelength High dimensional models Unsymmetricmatrices = + + -asafssasafssFFpuKKKCCjMMM00002ww4 Model Order Reduction Relatively new technology Solid mathematical background: Approximation of large scale dynamic systems Dynamic Simulation .

2 Harmonic or transient Simulation Industry application level: Linear dynamic systems only5 From Finite Elements to System Simulation Electrothermal Simulation with IGBTs: From ANSYS Workbench to Caspoc(Eurosime2008)Physics &GeometrySystem ofnODEsReduced System ofr << nODEsFEMMORV1600 +-SCOPE2 FILENAMED:\caspoc2003\SomeProjects\mor\M OR30 Inputs\morSCOPE1h1h2h3h4h5h6h7h8h9h10h11 h12h13h14h15h16h17h18h19h20h21h22h23h24h 25h26h27h28h29h3050 Hzh1l1h2l2h3l30h1l10h2l2 FILENAME1h3l36 Model Reduction as Projection Projection onto low-dimensional subspace How to find subspace? Mode superposition is not the best way to do +=zxVxVz=uxxBKE=+&uzzBVKVVEVVTTT=+&EEr7 Implicit Moment Matching Pad approximation Matching first moments for the transfer function Implicit Moment Matching: via Krylov Subspace -=00)(iissmH mi=mi,red,i=0,K,r()BKsEsH1)(-+= -=00,)(irediredssmHs0=0V=span{ (K-1E,K-1b)}uxxBKE=+&8 MOR for ANSYS: filesLinear Dynamic System, ODEsCxyBuKxxExM==++&&&MOR AlgorithmSmall dimensionalmatricesCurrent version ModelSimulink, Caspoc,Simplorer, VerilogA.

3 9 Electrothermal Simulation of IGBTs Eurosime2008, Daimler, Simulation with CASPOCDDDDDDDDDDDDDDDVDC+-DDDV1600 +-SCOPE2 FILENAMED:\caspoc2003\SomeProjects\mor\M OR30 Inputs\morSCOPE1h1h2h3h4h5h6h7h8h9h10h11 h12h13h14h15h16h17h18h19h20h21h22h23h24h 25h26h27h28h29h3050 Hzh1l1h2l2h3l30h1l10h2l2 FILENAME1h3l310 HDD actuator and suspension system Prof J. S. Han. Transactions of the KSME, A, Vol. 31, No. 5, pp. 541-549, Angular Rate Sensor with Coriolis Effect Prof J. S. Han, KSME 2008. = + + lfVuKKKKVuEVuMdTzz&&&&&&00000012 Piezoelectric Angular Rate Sensor with Coriolis Effect13 Model Reduction as Fast Solver Simulation of the reduced model is a few seconds.

4 ArnoldiProcess is fast: Transient and harmonic response analysis for the cost comparable with that of a static solution. It is advantageous to use MOR even the reduced model is used only once: Design, Geometry Benchmarks in Thesis The 2D Acid-Test 3D Plate backed air filled cavity 3D Plate backed Rectangular Water Filled Cavity Cylinder enclosing an air-filled cavity Demonstrator Structure: Adhesive Bonded Joint15 Adhesive Bonded Joint Benchmark Mechanical Structure -SHELL181 Adhesive SOLID45 Fluid FLUID30 Single excitationpoint Global and localdamping16 Comparison17 Comparison Relative Error18 Error Indicator True Error Error Indicator)()()()(sHsHsHsErr-=)()()()( 1sHsHsHsErrrr+-=)( )

5 (sEsErr 19 Timing Problem in ANSYS 37988 elements, 38712 nodes, 62581 free DoFs Full solution in ANSYS for 200 frequencies 16695 s hours 83 s per frequency Proportional to the number of frequencies MOR for ANSYS Reading ANSYS files 3 s Model reduction 170 s Proportional to the number of vectors Simulation of the reduced model 4 s20 NVH Optimization21 NVH Vibro-Acoustic Optimization SHELL181 to model the layered composite Stack of eight layers To find optimal lamination22 Fluid Structure Interaction at Acoustic LevelBy courtesy of By courtesy of VoithVoithSiemens Hydro Power Generation Siemens Hydro Power Generation GmbH & Co.)

6 KGGmbH & Co. KG23 Conclusion Model reduction is an excellent tool to speed up NVH Simulation Software for ANSYS is available: MOR for ANSYS More information.