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

Requirements & architecture

Component design and NVH

Concept : a device that decelerates

Component designIntegration, test, verification

Operation

System, verification & validation

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

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

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

+

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]

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

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%

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%

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

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

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%

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

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

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)

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

+

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

Other applications• Multi-stage cyclic symmetry

(SNECMA). – Which stage, which diameter, …– Mistuning (which blade)

• Damping design (PSA)– Fixed system modes, component

redesign

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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