Imac10 Component
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Using component modes in a system design process.
G. Vermot, JP Bianchi, E. Balmes, SDTools, Arts et Metiers ParisTechR. Lemaire, T. Pasquet Bosch, Chassis System Brakes
IMAC 28, Jacksonville
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Requirements & architecture
Component design and NVH
Concept : a device that decelerates
Component designIntegration, test, verification
Operation
System, verification & validation
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Component design and NVH
Component redesign
Sensitivity, energy analysis
1. Which system features are important for NVH
2. Classify sensitivity and energy contributions of component modes
3. Redesign component
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Outline• Motivation• Method : a reduced model using modal
coordinates of components• Illustrate the use
– Validate the ability to do parametric analysis
– See how this can be used for design
• Conclusion
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Reduction method• Disjoint components with interface energy
• Rayleigh-Ritz reduction of each component using– free/free real modes (explicit DOFs)– trace of the assembled modes on the component
• Nominal system modes are predicted exactly
+
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Reduced model• Reduction basis diagonal by block• specific topologies are obtained
– K split in elastic + interactions– Mass is identity, Kel is diagonal– Kint has blocks ≠0 where component interaction exists
• Free mode amplitudes are DOFs• Change component mode frequency ⇔ change the
diagonal terms of Kel
Disc
OuterPad
Inner Pad
Anchor
Caliper
Piston
Knuckle
Hub
ωj21
[M] [Kel] [KintS] [KintU]
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Reduction validation• Assembled real modes are explicitly in the model
• Reduced and full models show identical real modes• High frequency precision depends on the solver
convergence• Low frequencies show an increasing difference due to a
shift in the Abaqus results
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Validation – 1. Disc Young Modulus• First terms of the reduced elastic
matrix are varying• E disc +10% 2% accuracy (compared to
Abaqus full)
• Stability diagram well predicted
Nom.+10% +20%
-20%
Nom.+10% +20%
-20%
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Validation – 2. Anchor Mass Modification• 9 grams added to anchor handle• Anchor mode frequencies up to -6%• Error on system modes
less than 1 %
1%
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Validation – 3. Lining Transverse Young Modulus• Lining Ezz is a common updating parameter (material
parameters accuracy)• Matrix stiffness interpolation between two states• 2 reduction bases possible, high or low Ezz• Same basis for both matrices• The modified matrix is not diagonal
Ezz= 275 MPa
Ezz= 3000 MPa
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Lining Ezz tuning• Cross interpolation tested• Curves are globally overlaying
• Differences are due to the reduction basis used• Using the high Ezz (+, +) is better• Low Ezz ( ) computation loses high values accuracy
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Component Mode Tuning 1• Analysis of energy contribution can target a
singlecomponent mode• Most unstable mode at 12 Bar is mode 55,
involves pad mode 7• Mode 51 is also sensitive to pad mode 7
Mode 51 @ 3560 Hz 0% Mode 55 @ 4056 Hz -2.3%
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Component Mode Tuning 2• The first pad bending mode has no real effect on mode 55• Decreasing its frequency by 2.5 % is enough to trigger
mode 51 instability• A few percent of variation is likely to append in the
production process
• Robustness studies can be easily performed
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Sensitivity Analysis - 1• A nominal design point does not show the
variability of the solution• Robustness is improved if sensitive modes
are spotted• The sensitivity is given by
• Scanning each component mode for each assembled mode is a quick computation
• Gives direction for component tuning analyses by spotting relevant modes
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Sensitivity Analysis - 2• Assembled modes are
sensitive to a few component modes at a time
• Piston has no sensitivity (excepted piston cap modes)
• Hub has very limited sensitivity
• Pad are sensitive at rather high frequencies (>4kHz)
• Knuckle show great sensitivity but mainly limited to local fixation areas contribution
Disc (c10001ds)
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Interaction Tuning• Interaction tuning for penalized contact• Robustness of the static computation• Pad spring example (Mode 55)• Involves comp. interaction AND material
compression• Some variation observed• Applicable to any interaction
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Friction Analysis• Instability from asymmetric coupling due to friction
forces driven by μ• Test from 0.7 to 0.3 ; Reduction basis at 0.6• A stiff transition is observed between
μ=0.4 to 0.5• A few modes are
sensitive
0.70.6
0.3
0.7 0.6
0.3
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Other applications• Multi-stage cyclic symmetry
(SNECMA). – Which stage, which diameter, …– Mistuning (which blade)
• Damping design (PSA)– Fixed system modes, component
redesign
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Conclusion• Reduced model with component modes and
exact system modes• Enables parametric studies
– Low computation times– Validated accuracy (vs. full Abaqus recomputation)– Access to physical and modal parameters– Sensitivity analysis– Modal energy useful to understand motion
• Illustrated for brake squeal• Lots of other possible applications
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