EB2017-VDT-018 : Presentation slides

Full text

Squeal measurement using operational deflection
shape.
Quality assessment and analysis improvement using
FEM expansion.
Guillaume Martin, SDTools
Etienne Balmes, SDTools
Guillaume Vermot Des Roches, SDTools
Thierry Chancelier, Chassis Brakes International
EB2017-VDT-018

Introduction
Sensor positioning
Squeal
Frequency shift
Wheel revolution
Drum brake squeal measurement
Time measurement
Several time/frequency analysis
2

Main shape
extraction
Introduction
Several time/frequency analysis
Expansion
FEM
3
How to handle
•Variability ?
•Reproducibility ?
Difficult to interpret

Outline
•Expected shapes in a squeal event : numeric analysis
•Time frequency analysis : principal shape extraction
•MDRE method
•Simple disc brake
•Mode coupling : 2 shapes
•Shape variability
•Shape reproducibility
Difficult to
interpret
Easier
to exploit
4

Simple example of squeal
Normal contribution Tangential contribution
Coupling
X Y Z
X
Y
Z
Pressure application + linearization
Non symetric contact stiffness
Normal relative displacement
Tangential load
Z
XY
Vermot, 2011
5

•At first : damped modes
•Rising of : coupling and transition toward
instability
Contribution of real modes to complex modes
5.046 5.048 5.05 5.052 5.054 5.056 5.058 5.06
Frequency [kHz]
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Damping [%]
o
o
Real mode 8
Real mode 9
Complex mode 8
Real mode
amplitudes
Real mode phase
shift
6

Contribution of real modes to complex modes
5.046 5.048 5.05 5.052 5.054 5.056 5.058 5.06
Frequency [kHz]
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Damping [%]
o
o
•At first : damped modes
•Rising of : coupling and transition toward
instability
Real mode 8
Real mode 9
Complex mode 8
Real mode
amplitudes
Real mode phase
shift
7

Contribution of real modes to complex modes
5.046 5.048 5.05 5.052 5.054 5.056 5.058 5.06
Frequency [kHz]
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Damping [%]
o
o
•At first : damped modes
•Rising of : coupling and transition toward
instability
Real mode 8
Real mode 9
Complex mode 8
Real mode
amplitudes
Real mode phase
shift
8
Mainly two real shapes
with evolving relative
amplitude and phase
-> Measurement analysis

Reduction on two real modes
Mass Damping Stiffness Coupling
𝑐𝑘=2𝜁𝑘𝜔𝑘
𝑘𝑘=𝜔𝑘
2
Evolution with the friction coefficient
•Overestimation of frequency
•Very good estimation of damping
9

Suppress squeal with «frequency spreading»
Instability removal
Values without coupling
Mass Damping Stiffness Coupling
10

Outline
•Expected shapes in a squeal event : numeric analysis
•Time frequency analysis : principal shape extraction
•MDRE method
•Simple disc brake
•Mode coupling : 2 shapes
•Shape variability
•Shape reproducibility
Difficult to
interpret
Easier
to exploit
11

•Two main real shapes
•Time evolution of principal shapes during squeal
Time-frequency analysis : variability
SVD
¿
Space:
Real principal
shapes
Time:
Complex
amplitudes
Time
evolution of
complex
shapes
12

Two cycles at different frequencies
Time-frequency analysis : reproducibility
The two principal shapes
describe precisely the two
measurements
SVD on shapes from the two measurements
13

Visualization of the shapes
Shape 1 Shape 2
Test result : What do we see ?
-> Analysis difficulty, no information between sensors
How to improve the analysis ? 14

Outline
•Expected shapes in a squeal event : numeric analysis
•Time frequency analysis : principal shape extraction
•MDRE method
•Simple disc brake
•Mode coupling : 2 shapes
•Shape variability
•Shape reproducibility
Difficult to
interpret
Easier
to exploit
15

+
•Finding expanded shapes minimizing two errors -> estimation at all DOFs
MDRE expansion
𝜖𝑇𝑒𝑠𝑡 =
‖
[
𝑐
]
{
𝜙𝑗
}
−
{
𝑦𝑗,𝑇𝑒𝑠𝑡
}
‖
𝑄
Observation
Residual loads
𝜖𝑀𝑜𝑑 =
‖
{𝑅𝑗𝐷 }
‖
𝐾
16
•Test : gap between displacement at sensors
•Model : not exact

Influence of
low : response with only frequency constraint
1e1 1e5 1e10
No information to choose a specific -> sweep
𝐽=𝜖𝑀𝑜𝑑+𝛾 𝜖𝑇𝑒𝑠𝑡
intermediate : Constrained cable guide displacement
high : Not physical displacement between sensors
17
Model reduction : free mode + unit load at sensors

Localisation of error with MDRE
•Test error
18
•Residual energy

Visualization of the shapes
Shape 1 Shape 2
19

Visualization tool : expansion
Shape 1 Shape 2
Expansion :
•Better interpretation
20

Model error localization
Updating parameters :
-Geometry of the arm (A)
-Contact plate/arm (B)
-Contact plate/shoe (C)
21

Conclusion
•Interaction between two real shapes : numerical and experimental
•Good reproducibility regarding shapes despite frequency shifts
•Better interpretation of measurements using MDRE expansion
•Points out areas where model is wrong
Model updating and its impact on the expansion result is a perspective of this
work.
www.sdtools.com/Publications.html
martin@sdtools.com
22