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Use of FRF-Substructures in NVH Analysis of
Powertrains in Full-Vehicle Analysis
5th International Conference: Dynamic Simulation in Vehicle Engineering
Uwe Fiedler, CDH AG
Mladen Chargin, CDH AG
Volker Kreissig, Daimler AG
Use of FRF-Substructures in NVH Analysis
Contents
2
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Introduction
3
• Finite element simulations play a
central role in full-vehicle analysis.
• Complex load cases such as:- Road excitation
- Engine excitation
- Gearbox whine
need detailed models.
• The challenge is to simulate
a wide range of excitations
over a large frequency range
in an acceptable time.
• Detailed, complex FE models
require long calculation times.
Use of FRF-Substructures in NVH Analysis
Introduction
4
Many structural derivatives and variants
must be evaluated:• Body variants: sedan, station, coupe,
cabriolet, wheelbases
influence on interior acoustics
• Chassis variants: 4x2 or 4x4,
active suspension strategies,
subframe, brakes, wheel sizes
• Powertrain variants: petrol, diesel,
parallel hybrid, plug-in hybrid,
4x2 or 4x4, 4/6/8/12 cylinder,
inline or V-engine, cylinder deactivation
Axles and powertrain are not independentMany models to evaluate
large variant matrix
Use of FRF-Substructures in NVH Analysis
Contents
5
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
FE-Model Size and Calculation Time
6
Analysis of a single subcase as an example: Gear box whine.
• Excitation between two gears of the rear axle differential.
• Frequency response up to 1000Hz.
• Evaluation at comfort points response(sound pressure),
acceleration and forces at mounts.
Use of FRF-Substructures in NVH Analysis
FE-Model Size and Calculation Time
7
Model size of Mercedes S-class:Structure:
40M DOFs
~48,000 modes < 1,500Hz
Fluid:
1M DOFs
~5,000 modes < 2,000Hz
Calculation Time:
generating matrices: 85 min
AMLS for structural modes: 225 min
AMLSF for fluid modes: 5 min
forming modal matrices: 70 min
solving modal system equation: 55 min
data-recovery: 10 min
Total calculation time 7.5 h
Current approach: full vehicle analysis is time consuming
focusing on few variants, optimisation not feasible!
Use of FRF-Substructures in NVH Analysis
Contents
8
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Reduction Methods
9
Some parts are identical for different structural
variants. The powertrain department, for example, can
use a single body for many functional assessments.
This presents an opportunity for model reduction. 1) Standard superelement method
2) New FRF-Substructure method
Use of FRF-Substructures in NVH Analysis
Contents
10
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Reduction 1: Superelement
11
An external superelement of body with:- 27M DOFs : 45,000 modes < 1,500 Hz
- 270 boundary-DOFs: coupling and response points
is impossible to generate with current HPC hardware
(1TB RAM, 500TB of disk space) within a reasonable time.
Up to 600Hz with 12,000 modes: - elapsed time 32h
- file size 4.4GB
Using a body-SE is much faster for a calculation of
full vehicle modes, but- many structure modes (huge SE-size)
- frequency response remains costly because of the same number of modes
- disadvantage: acoustic analysis is not possible
Use of FRF-Substructures in NVH Analysis
Contents
12
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Reduction 2: FRF-Substructure
13
Can we use body transfer functions only ?
Use of FRF-Substructures in NVH Analysis
Reduction 2: FRF-Substructure Theory
14
• FRF Equation of motion
• Partition Eq. (1) into 2 parts
Partition 2 contains body, output, and loaded DOFs
• is the “dynamic flexibility”
(1)
-w 2 M[ ]+ iw B[ ]+ K[ ]éë ùû u[ ] = F[ ]
A[ ] = -w 2 M[ ]+ iw B[ ]+ K[ ] A[ ] u[ ] = F[ ]
A11 A12
A21 A22
é
ëê
ù
ûú
u1
u2
é
ëê
ù
ûú =
0
F2
é
ëê
ù
ûú
A11 A12
A21 A22
é
ëê
ù
ûú
u1
H
é
ëê
ù
ûú =
0
I
é
ëê
ù
ûú
H[ ]
Use of FRF-Substructures in NVH Analysis
Reduction 2: FRF-Substructure Theory
15
• Invert Possibly ill-conditioned, especially
when it contains both structure and fluid!
• is the “dynamic stiffness”
• Any number of additional FE elements can be added or
subtracted from any DOF in
• In modal FRF generation, add residual vectors to DOFs in
to improve the accuracy of the FRF Substructure
Added Elements FD Substructure
H[ ]
H[ ] H i[ ]-1
H i[ ]-1
-w 2 M[ ]+ iw B[ ]+ K[ ] + H[ ]-1é
ëùû
u[ ] = F[ ]
Use of FRF-Substructures in NVH Analysis
Contents
16
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Example of Use
17
Mercedes S-Class FE-Model:
Generation of an FRF Substructure of a trimmed body
to couple to a chassis FE-Model:
- 42 mounting points -> 252 coupling DOFs
- 22 response DOFs
- 0 excitation DOFs
Transfer function matrix generated in 7h, file size 1.4 GB.
Use of FRF-Substructures in NVH Analysis
Example of Use
18
Use of FRF Substructure: Chassis FE-model combined
with trimmed body FRF-Substructure
Final model consists of:13M DOFs for the chassis FE model
2,100 structural modes < 1,500Hz
+ FRF-Substructure matrix of trimmed body
Total calculation time: 51 min
+
Use of FRF-Substructures in NVH Analysis
Result Quality
19
Use of FRF-Substructures in NVH Analysis
Result Quality
20
Use of FRF-Substructures in NVH Analysis
Result Quality
21
Use of FRF-Substructures in NVH Analysis
Calculation Time Comparison
22
Full FE-modell Superelement FRF-Substructure
Body Chassis Body Chassis
Model DOFs 40M 27M 13M 27M 13M
Modes < 1500Hz 48000 12000<600Hz 2100 45000 2100
One time matrix
genereation32h 7h
Combined job 7.5h 2h 51min
use of FRF-Substructures in NVH Analysis
Contents
23
1. Introduction
2. FE-model size and calculation time
3. Reduction ProcedureSuperelement method
FRF-Substructure method
4. Example
5. Conclusions
Use of FRF-Substructures in NVH Analysis
Conclusions
24
FRF-Substructure approach:
• much more efficient than use of superelements
• improved quality of results compared to superelement method
• acoustic response is possible
• FRF Substructure can represent any part of the model
• very useful for optimisation, especially mount optimisation
Thank you for kind attention!www.cdh-ag.com