Using component modes in a system
design process.

G. Vermot, JP Bianchi, E. Balmes, SDTools, Arts et Metiers ParisTech
R....
Component design and NVH

Concept : a device that decelerates
                                      Operation




Requirem...
Component design and NVH
1. Which system features
   are important for NVH
2. Classify sensitivity and
   energy contribut...
Outline
• Motivation
• Method : a reduced model using modal
  coordinates of components
• Illustrate the use
  – Validate ...
Reduction method
• Disjoint components with interface energy




                     +

• Rayleigh-Ritz reduction of each...
Reduced model
• Reduction basis diagonal by block
• specific topologies are obtained
   – K split in elastic + interaction...
Reduction validation
• Assembled real modes are explicitly in the model

• Reduced and full models show identical real mod...
Validation – 1. Disc Young Modulus
• First terms of the reduced elastic
  matrix are varying
• E disc +10% 2% accuracy (co...
Validation – 2. Anchor Mass Modification
• 9 grams added to anchor handle
• Anchor mode frequencies up to -6%
• Error on s...
Validation – 3. Lining Transverse Young Modulus
• Lining Ezz is a common updating parameter (material
  parameters accurac...
Lining Ezz tuning
• Cross interpolation tested
• Curves are globally overlaying



• Differences are due to the reduction ...
Component Mode Tuning 1
• Analysis of energy contribution can target a
  singlecomponent mode
• Most unstable mode at 12 B...
Component Mode Tuning 2
• The first pad bending mode has no real effect on mode 55
• Decreasing its frequency by 2.5 % is ...
Sensitivity Analysis - 1
• A nominal design point does not show the
  variability of the solution
• Robustness is improved...
Sensitivity Analysis - 2
• Assembled modes are
  sensitive to a few component     Disc (c10001ds)
  modes at a time

• Pis...
Interaction Tuning
• Interaction tuning for penalized contact
• Robustness of the static computation
• Pad spring example ...
Friction Analysis
• Instability from asymmetric coupling due to friction
  forces driven by μ
• Test from 0.7 to 0.3 ; Red...
Other applications
• Multi-stage cyclic symmetry
  (SNECMA).
   – Which stage, which diameter, …
   – Mistuning (which bla...
Conclusion
• Reduced model with component modes and
  exact system modes
• Enables parametric studies
  –   Low computatio...
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Imac10 Component

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Imac10 Component

  1. 1. Using component modes in a system design process. G. Vermot, JP Bianchi, E. Balmes, SDTools, Arts et Metiers ParisTech R. Lemaire, T. Pasquet Bosch, Chassis System Brakes IMAC 28, Jacksonville
  2. 2. Component design and NVH Concept : a device that decelerates Operation Requirements & System, verification architecture & validation Component design Integration, test, verification
  3. 3. Component design and NVH 1. Which system features are important for NVH 2. Classify sensitivity and energy contributions of component modes 3. Redesign component Component redesign Sensitivity, energy analysis
  4. 4. 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
  5. 5. 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
  6. 6. 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 Disc 1 ωj2 OuterPa d Inner Pad Anchor Caliper Piston [M] [Kel] [KintS] [KintU] Knuckle Hub • Free mode amplitudes are DOFs • Change component mode frequency ⇔ change the diagonal terms of Kel
  7. 7. 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
  8. 8. 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 -20% Nom. +10% +20% +10% +20% Nom. -20%
  9. 9. 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%
  10. 10. 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= 3000 MPa Ezz= 275 MPa
  11. 11. 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
  12. 12. 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%
  13. 13. 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
  14. 14. 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
  15. 15. Sensitivity Analysis - 2 • Assembled modes are sensitive to a few component Disc (c10001ds) 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
  16. 16. 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
  17. 17. 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 0.7 0.7 0.6 0.6 0.3 0.3
  18. 18. Other applications • Multi-stage cyclic symmetry (SNECMA). – Which stage, which diameter, … – Mistuning (which blade) • Damping design (PSA) – Fixed system modes, component redesign
  19. 19. 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 www.sdtools.com/Publications.html

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