Efficient Simulation for Strongly Coupled Noise-

Vibration-Harshness (NVH)R. S. Puri, D. Morrey, Oxford Brooks

E. B. Rudnyi, CADFEM

1

Background

§ Joint work 2004-

§ Over email

§ Available online§ ModelReduction.com/

contrib/Srinivasan.Puri/

2

NVH Simulation

> 250 HzAir bornHigh Frequency

100 – 250 HzStructure and air borne

Mid Frequency

0 – 100 HzStructure borneLow Frequency

3

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

4

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

5

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

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

6

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

7

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 =+&

8

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,…

9

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

10

HDD actuator and suspension system

§ Prof J. S. Han. Transactions of the KSME, A, Vol. 31, No. 5, pp. 541-549, 2007.

11

Piezoelectric Angular Rate Sensor with Coriolis Effect

§ Prof J. S. Han, KSME 2008.

=

+

+

lf

Vu

KKKK

VuE

VuM

dTz

z

&

&

&&

&&

000

000

12

Piezoelectric Angular Rate Sensor with Coriolis Effect

13

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.

14

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

15

Adhesive Bonded Joint Benchmark

§ Mechanical Structure - SHELL181§ Adhesive – SOLID45§ Fluid – FLUID30§ Single excitation point§ Global and local damping

16

Comparison

17

Comparison – Relative Error

18

Error Indicator

§ True Error

§ Error Indicator

)()()(

)(sH

sHsHsE r

r−

=

)()()()(ˆ 1

sHsHsHsE

r

rrr

+−=

)(ˆ)( sEsE rr ≈

19

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

20

NVH Optimization

21

NVH Vibro-Acoustic Optimization

§ SHELL181 to model the layered composite§ Stack of eight layers§ To find optimal lamination

22

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

23

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