Efficient Simulation for Strongly Coupled Noise- Vibration...
Transcript of Efficient Simulation for Strongly Coupled Noise- Vibration...
Efficient Simulation for Strongly Coupled Noise-
Vibration-Harshness (NVH)R. S. Puri, D. Morrey, Oxford Brooks
E. B. Rudnyi, CADFEM
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Background
§ Joint work 2004-
§ Over email
§ Available online§ ModelReduction.com/
contrib/Srinivasan.Puri/
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NVH Simulation
> 250 HzAir bornHigh Frequency
100 – 250 HzStructure and air borne
Mid Frequency
0 – 100 HzStructure borneLow Frequency
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Fully Coupled Finite Element Discretization
§ FLUID29/FLUID30 in ANSYS
§ The element size should be smaller than wavelength § High dimensional models
§ Unsymmetric matrices
=
+
+
−
a
s
a
fss
a
s
afs
s
FF
pu
KKK
CC
jMM
M00
002 ωω
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Model Order Reduction
§ Relatively new technology
§ Solid mathematical background:§ Approximation of large scale
dynamic systems
§ Dynamic simulation:§ Harmonic or transient simulation
§ Industry application level:§ Linear dynamic systems only
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From Finite Elements to System Simulation
§ Electrothermal Simulation with IGBTs: § From ANSYS Workbench to Caspoc (Eurosime 2008)
Physics &Geometry
System ofn ODEs
Reduced System of
r << n ODEsFEM MOR
V1 600
+
-
SCOPE2
FILENAME
D:\caspoc2003\Som eProjects\mor\M OR30Inputs\mor
SCOPE1
h1
h2
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h23
h24
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h26
h27
h28
h29
h30
50Hz
h1 l1 h2 l2 h3 l3
0
h1
l1
0
h2
l2
FILENAME1
h3
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Model Reduction as Projection
§ Projection onto low-dimensional subspace
§ How to find subspace?§ Mode
superposition is not the best way to do it.
ε+= zx V
x V
z
=
uxx BKE =+&
uzz BVKVVEVV TTT =+&
E
Er
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Implicit Moment Matching
§ Padé approximation§ Matching first moments for the
transfer function
§ Implicit Moment Matching:§ via Krylov Subspace
∑∞
−=0
0 )( ii ssmH
mi = mi,red , i = 0,K,r
( ) BKsEsH 1)( −+=
∑∞
−=0
0, )( iredired ssmH
s0 = 0
V = span{ℑ(K−1E,K−1b)}
uxx BKE =+&
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MOR for ANSYS: http://ModelReduction.com
FULL files
Linear Dynamic System, ODEsCxy
BuKxxExM=
=++ &&&MOR Algorithm
Small dimensionalmatrices
Current version 2.5
ANSYS ModelSimulink, Caspoc,
Simplorer, VerilogA,…
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Electrothermal Simulation of IGBTs
§ Eurosime 2008, Daimler, simulation with CASPOC
DDD DDD DDD
D D DD D D
VDC
+
-
DDD
V1 600 +
-
SCOPE2
FILENAME
D:\caspoc2003\SomeProjects\mor\MOR30Inputs\mor
SCOPE1
h1
h2
h3
h4
h5
h6
h7
h8
h9
h10
h11
h12
h13
h14
h15
h16
h17
h18
h19
h20
h21
h22
h23
h24
h25
h26
h27
h28
h29
h30
50Hz
h1 l1 h2 l2 h3 l3
0
h1
l1
0
h2
l2
FILENAME1
h3
l3
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HDD actuator and suspension system
§ Prof J. S. Han. Transactions of the KSME, A, Vol. 31, No. 5, pp. 541-549, 2007.
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Piezoelectric Angular Rate Sensor with Coriolis Effect
§ Prof J. S. Han, KSME 2008.
=
+
+
lf
Vu
KKKK
VuE
VuM
dTz
z
&
&
&&
&&
000
000
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Piezoelectric Angular Rate Sensor with Coriolis Effect
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Model Reduction as Fast Solver
§ Simulation of the reduced model is a few seconds.
§ Arnoldi Process 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 optimization.
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NVH 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 Joint
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Adhesive Bonded Joint Benchmark
§ Mechanical Structure - SHELL181§ Adhesive – SOLID45§ Fluid – FLUID30§ Single excitation point§ Global and local damping
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Comparison
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Comparison – Relative Error
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Error Indicator
§ True Error
§ Error Indicator
)()()(
)(sH
sHsHsE r
r−
=
)()()()(ˆ 1
sHsHsHsE
r
rrr
+−=
)(ˆ)( sEsE rr ≈
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Timing
§ Problem in ANSYS§ 37988 elements, 38712 nodes, 62581 free DoFs
§ Full solution in ANSYS for 200 frequencies§ 16695 s – 4.6 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 s
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NVH Optimization
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NVH Vibro-Acoustic Optimization
§ SHELL181 to model the layered composite§ Stack of eight layers§ To find optimal lamination
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Fluid Structure Interaction at Acoustic Level
By courtesy of By courtesy of VoithVoith Siemens Hydro Power Generation Siemens Hydro Power Generation GmbH & Co. KGGmbH & Co. KG
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Conclusion
§ Model reduction is an excellent tool to speed up NVH simulation
§ Software for ANSYS is available:§ MOR for ANSYS
§ More information:§ http://ModelReduction.com