Performing a parametric Brake
Squeal Analysis in ANSYS WB and
optiSLang
Outline
•
Introduction
•
Tutorial part I: Complex Modal Analysis in ANSYS Workbench 13
• Workflow in ANSYS Workbench
• Geometry Interfaces and parameters
• Simple Brake Example
• Preparations for static analysis (prestress)
• Complex modal analysis
•
Tutorial part II: Robustness analysis in optiSLang
• optiPlug plugin for ANSYS Workbench
• Parameter editor in optiSLang
• Parametrizing signals in optiSLang
• Signal objects & constraints
• Modify the predefined start script
• Robustness analysis
• Meta-model of Optimal Prognosis (MOP)
• Coefficient of Prognosis (CoP)
Applications
 Accompanying example: Analysis of an automotive brake
•
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
• The goal is to simulate brakesquealing by performing a complex
modal analysis in ANSYS Workbench. The modal analysis is based on
a static prestressed initial status (Brake pressure, contact brake discbrake pad closed) with a given frictional coefficient. It determines
apart from the eigenfrequencies the damping ratio for each mode as
a criterion for stability and squealing.
• The basic of the ANSYS FE-model is a parametric CAD model.
Model details (screws, couplings, bearing stiffnesses, and material
properties, etc.) shall be provided as well.
• Upon the ANSYS simulation model a robustness analysis in
optiSLang is perfomed in order to determine the parameters that
have a significant influence on the complex eigenfrequencies and the
damping ratio.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
How can we measure brake squealing?
• Example test setup (McDaniel1999):
• Measurement by laser scanning vibrometer
Brake system, consisting of a
brake rotor (“Bremsscheibe”)
mounted to a stationary shaft
with an attached pad
(“Bremsbelag”) and caliper
(“Bremssattel”).
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
Results (McDaniel1999)
• Magnitude of normal velocity
produced by a shaker on the
rotor and measured by a
scanning LDV (Laser Doppler
Vibrometer) for modes n=1-4
and 70 psi pad pressure.
• Lighter regions represent
larger velocity magnitudes.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
•
The vibrational instabilities that produce brake squeal have been studied
for over fifty years.
•
The sound produced by squealing brakes is a top concern of most
automotive companies due to the annoyance it causes to the customer
and the high cost of mitigating squeal for vehicles still under warrantee.
•
With a focus the theory of mode coupling instability, we will see how to
solve break applications by ANSYS QRDAMP or ANSYS UNSYM complex
modal analysis.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
•
Automobile brakes can generate several kinds of noises. Among them is
squeal, a noise in the 1-12kHz range. It is commonly accepted that brake
squeal is initiated by instability due to the friction forces, leading to selfexcited vibrations.
•
To predict the onset of instability, you can perform a modal analysis of the
prestressed structure. An unsymmetric stiffness matrix is a result of the
friction coupling between the brake pad and disk; this may lead to complex
eigenfrequencies. If the real part of the complex frequency is positive, then
the system is unstable as the vibrations grow exponentially over time.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
•
Brake squealing is a complex (damped and/or unsymmetric) eigenvalue
problem.
[M ]{u}  [C]{u}  [Ksym  Kunsymm ]{u}  {0}
•
•
•
8
The eigenvalues (i.e., frequencies) will have real and imaginary parts if
damping [C] and/or an unsymmetric [K] matrix are present. The
imaginary component reflects the damped frequency. The real component
indicates whether or not the mode is stable – unstable modes will have a
large, positive real eigenvalue.
The eigenvectors will also be complex in either case. The real and
imaginary eigenvectors represent the ‘motion’ of the mode shape – if the
imaginary eigenvector is non-zero, this means that a phase difference is
present, analogous to harmonic analysis output.
In brake squeal analyses (in the kHz range), the effect of the coefficient of
friction MP,MU (as well as other parameters) can be varied to see the
effects on different modes and the coupling between modes. This can help
to determine which modes (frequencies) will be unstable and a source of
audible discomfort.
Tutorial: Complex Modal Analysis – brake squeal analysis
Introduction
In ANSYS available methods for simulation of brake-squealing
Method
Base Static Analysis
Initial Contat/Prestress
Modal Analysis
(Perturbation
Analysis )
Force frictional
sliding
(CMROTATE)
QRDAMP/UNSYMM/DAM
P
Partial Nonlinear
Perturbed Modal
Analysis
Full nonlinear
solution
N/A
Force frictional sliding
(CMROTATE command)
and perform a Linear
perturbed modal solve
(SOLVE)
Full Nonlinear
Perturbed Modal
Analysis
Full nonlinear
solution
Full nonlinear
solution
Linear perturbation
modal solve
In our example we will concentrate on the partial nonlinear perturbed modal
analysis.
9
Tutorial: Complex Modal Analysis – brake squeal analysis
Workflow in ANSYS Workbench
Workflow partial nonlinear perturbed modal analysis
2
3
1
4
1. Parametric geometry-import of CATIA V5/ProE/Design Modeler using the
bidirectional interface (e.g. CADNexus)
2. Non linear prestress (large deflection + non linear contact)
3. Complex modal analysis
4. Parameter study in optiSLang
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Tutorial: Complex Modal Analysis – brake squeal analysis
Workflow in ANSYS Workbench
Workflow partial nonlinear perturbed modal analysis
Some additional macros are necessary to realize brake squealing in
Workbench an postprocess the results.
These macros are just some single commands.
aktivates UNSYM Solver
enforces “sliding-contact“ between disc and pad
aktivates partial nonlinear perturbed – modal analysis
Postprocessing:
extrction of the damped eigenfrequencies with the damping ratio
and define them as output parameter „mypar_“.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Brake squeal analysis in
Workbench: parametric geometryimport
1
12
Tutorial: Complex Modal Analysis – brake squeal analysis
Geometry interfaces and parameters
• ANSYS provides several bidirectional geometry interfaces,
importing a CAD geometry into workbench.
• The CATIA v5 Geometry import is realized by the CAD NEXUS
CAPRI Interface that allows a bidirectional use of parametric
geometries in CATIA
CAD / PDM
ANSYS Workbench
Structural Mechanics - Fluid Dynamics - Heat Transfer - Electromagnetics
An adaptable multi-physics design and analysis system that
integrates and coordinates different simulation tasks
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
•
•
•
•
The simple break example is created in ANSYS DesignModeler.
This enables us to create a parametric geometry in a simple way.
The brake consist of an internal ventilated disc and two brake pads.
The parametrization consist either geometry and simulation
parameters.
14
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Material for brakepads
• Due to the anisotropic behavior of the brake pad, these values are
inserted as a new material.
• The anisotropic material parameters cannot be parametrized for
optiSLang. If this is necessary, use a command block (TB,ANEL…)
15
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Geometry parameters I
Pad_thickness
Disc_thickness
16
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Geometry parameters II
Cooling_angle
Pad_angle
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Geometry conditions:
1.) DS_Disc_radius >= DS_Cooling_Radius+25
This ensures that the internal ventilation will remain.
2.) DS_Pad_Width <= DS_Disc_radius-125
This ensures that the pad will not be bigger than the disc.
These constraints will be inserted into the optiSLang
parametrization.
18
Tutorial: Complex Modal Analysis – brake squeal analysis
Brake squeal analysis in
Workbench: non linear pre-stress
2
19
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• nonlinear frictional contact
• frictional coefficient as parameter for Robustness analysis.
keyopt,cid,4,3
20
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Mesh
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Prestress as static structural analysis with large deflections = on
• Pressure on the brake pads parametrized for optiSLang
nropt,unsym
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Tutorial: Complex Modal Analysis – brake squeal analysis
Brake squeal analysis in
Workbench: complex modal
analysis
3
23
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Complex modal analysis activated via command blocks
CMROTAT, E_ROTOR, , ,ARG1
alls
! Rotate the selected elements
ARG1 = 2 (rotational speed)
MODOPT,qrdamp,arg1,arg2,arg3,on
MXPAND,arg1
ARG1 = 30
(nmodes)
ARG2 = 0
(fmin)
ARG3 = 7500 (fmax)
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Calculation Time (inkl. meshing): ~1min.
Postprocessing via classic commands.
The modelist with the damping ratio is printed into a textfile.
The damping and frequency of the squealing modes are
extracted and can be parametrized in workbench.
Frequencies
Damping ratio
25
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Extracted output of frequencies and damping for creating
signal objects in optiSLang (modelist.txt)
*****
INDEX OF DATA SETS ON RESULTS FILE
SET
1
2
3
4
5
6
7
8
TIME/FREQ(Damped)
0.0000
722.08
0.0000
-722.08
0.0000
748.65
0.0000
-748.65
0.0000
1166.1
0.0000
-1166.1
0.0000
1190.2
0.0000
-1190.2
0.0000
1454.1
0.0000
-1454.1
0.0000
1529.6
0.0000
-1529.6
21.836
2799.8
21.836
-2799.8
-21.836
2799.8
-21.836
-2799.8
*****
TIME/FREQ(Undamped)
j
722.25
j
j
748.16
j
j
1165.8
j
j
1189.9
j
j
1454.0
j
j
1529.6
j
j
2793.2
j
j
2802.3
j
LOAD STEP
1
CUMULATIVE
1
1
2
2
1
3
3
1
4
4
1
5
5
1
6
6
1
7
7
1
8
8
Exicated mode
Damped mode
26
SUBSTEP
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Using the RSTMAC command in the postprocessing, we‘ll get a
measure for modetracking during the optiSLang run.
*** NOTE ***
CP =
14.938
TIME= 17:56:44
Solutions matching in RSTMAC command succeeded.
26 pairs of solutions have a Modal Assurance Criterion (MAC) value
greater than the smallest acceptable value (.9).
********************************** MATCHED SOLUTIONS **********************************
Substep in
Substep in
MAC value
Frequency
Frequency
D:\Schulungen\Bremsefile.rst
difference (Hz)
error (%)
1
1
1.000
-0.34E-12
0.0
2
2
1.000
-0.26E-10
0.0
3
3
1.000
-0.14E-11
0.0
4
4
1.000
-0.18E-10
0.0
5
5
1.000
-0.77E-11
0.0
6
6
1.000
-0.59E-11
0.0
7
7
1.000
0.27E-11
0.0
8
8
1.000
0.27E-11
0.0
9
9
1.000
0.00E+00
0.0
10
10
1.000
-0.36E-11
0.0
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Using a little script, we get also a list of the damping ratio in % out
of the results. This damping ratio is a real indicator, in fact how
instable the mode is.
Real Part
0.000
0.000
0.000
0.000
0.000
0.000
21.836
-21.836
0.000
0.000
0.000
0.000
0.000
43.852
-43.852
0.000
0.000
17.451
-17.451
28
Frequency
722.080
748.650
1166.100
1190.200
1454.100
1529.600
2799.800
2799.800
3064.300
3088.000
4255.700
4583.100
4593.300
4833.400
4833.400
4972.400
5134.900
6211.300
6211.300
Damping Ratio in%
0.000
0.000
0.000
0.000
0.000
0.000
0.780
-0.780
0.000
0.000
0.000
0.000
0.000
0.907
-0.907
0.000
0.000
0.281
-0.281
Tutorial: Complex Modal Analysis – brake squeal analysis
Robustness analysis in optiSLang
4
29
Tutorial: Complex Modal Analysis – brake squeal analysis
Why performing robustness analysis
• Analysis models become increasingly detailed
• Numerical procedures become more and more complex
• Substantially more precise data are required for the
analysis
• Deterministic optimum design is frequently pushed to the
design space boundary
• Optimized designs lead to high imperfection sensitivities
• Optimized designs tend to loose robustness
30
How to define robustness of a design
• Intuitively: The performance of a robust design is
largely unaffected by random perturbations
• Variance indicator: The coefficient of variation (CV)
of the objective function and/or constraint values is
smaller than the CV of the input variables
• Sigma level: The interval mean+/- sigma level does
not reach an undesired performance
(e.g. design for six-sigma)
• Probability indicator: The probability of reaching
undesired performance is smaller than an acceptable
value
31
Statistical Measures
• Evaluation of robustness with statistical
measures
• Variation analysis (histogram,
coefficient of variation,
standard variation, distribution fit,
probabilities)
• Correlation analysis (linear,
quadratic, nonlinear) including
principal component analysis
• Evaluation of coefficients of
determination (CoD),
coefficient of importance (CoI) and
Coefficient of Prognosis (CoP)
32
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Overview of the 12 input Parameters in ANSYS Workbench
Contact frictional coefficients
Brake pressure
Geometry parameters
Rotational speed
33
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Overview of the 20 output Parameters in ANSYS Workbench
• 10 complex frequencies and 10 corresponding damping ratio are
parametrized in the postprocessor
Complex frequencies
Damping ratio in %
34
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Export the brake project to optiSLang by pressing the optiPlug
button; switch to stochastic problem and keep the default settings
and close ANSYS.
35
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Open optiSLang 3.x.x and import the previously exported project
into optiSLang.
36
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Start the parameter editor to modify the parametrization and for
including signal data.
37
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• What is to be done now:
1.) Change of the parameter names for frictional coefficient
2.) Addition of signal data and parameters
3.) Creating of geometry constraints according to page 14
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Double click „Frictional_Solid_To_Solid_Friction_Coefficient“
2.) Rename it as Frictional_Coefficient_Pad_1
39
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Copy the two provided files myperl.pl and start_perl.bat into the
result file directory of the complex modal analysis.
2.) Execute it by double click on start_perl.bat
3.) A sorted and cleaned textfile for parametrising (damp_ratio.txt) is
created.
40
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Now, copy the new, important signal extraction file
„damp_ratio.txt“ into the optiSLang directory.
41
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Open a new file – browse for damp_ratio.txt and open it
2.) Set is as an output file
42
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.)
2.)
3.)
4.)
43
Mark the first row.
Set it as a repeated block marker
Set as super marker and mark „single steps“
The start is set to „2“
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Double-click on the first value in the first column.
2.) Set it as a vector.
3.) Give a reasonable name.
44
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Repeat this for second and third column.
2.) Set it as a vector.
3.) Give reasonable names.
45
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.) Double click on signal section
2.) Create a Signal Object.
3.) Choose the Frequency channel for absicissa
4.) Choose Real part and damping ratio as ordinate by clicking „Add
channel“.
46
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.)
2.)
3.)
4.)
47
Double click on signal section and create a Signal Function.
Give a reasonable name and click „Add signal Function“
For the maximum of damping, use the SIG_MAX_Y Function
For the corresponding frequency, use the SIG_MAX_X Function
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
1.)
2.)
2.)
3.)
48
Double click on constraint section
Add 2 constraints by clicking „New“
Insert 0 <= DS_Disc_radius-DS_Cooling_Radius+25 as constraint1
Insert 0 <= DS_Disc_radius-DS_Pad_Width-125 as constraint2
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Save & close the parameter editor.
•The parametrization is now finished.
• See the overview of the input/output/signal parameters. Last
changes of values can be made now.
49
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The optiPlug created start script has to be updated to some lines.
• These lines will ensure that the signal text files are copied back to
the design directory and the perl script is executed.
• So insert the copy commands. Check your folder names carefully!
• Create a folder, where you put the start_perl.bat and the script
myperl.pl so that it can be copied into every design directory.
REM ------------------------------------------------------------------REM Insert your commands here
copy "Brake_squeal_parametrized_robust_files\dp0\SYS-8\MECH\*.txt" .
copy "D:\Schulungen\Bremse\Brake_Parametrized\Perl\*.*" .
call "start_perl.bat"
REM -------------------------------------------------------------------
• The start_perl.bat consist the following command line:
(modify if necessary)
"C:\Program Files\optiSLang_3.2.0\perl5.10.0\bin\perl" myperl.pl
50
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Start the robustness workflow.
• Insert 100 as a number of samples, choose „Advanced LHS“
• Choose the start script if necessary
51
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Check the start set. The parameters are normal distributed.
52
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
•What proportion of the variation of a response can be forecasted
with identified arbitrary non-linear correlations to the input
parameters?
• CoP has three benefits
• We reduce the variable space
with different filter
= best subspace
• We check multiple non linear
correlations by checking multiple
MLS/Polynomial regression
= best Meta Model
• We split the sample set and
check the forecast (prognosis)
quality at the test samples.
= Metamodel of optimized
Prognosis (MoP)
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
Coefficient of prognosis
• Correlation between sample points and model predictions
using an additional independent test data set
2
 E[Y  Yˆ ] 
Test
Test 
CoP = 
; 0  CoP  1.
  ˆ

 YTest YTest 
Splitting of data sets
• If no second data set is available for testing, input data set
is split into training and test data
• Samples are selected in that way that in each data set the
variable ranges are represented with uniform distribution
54
Simple brake example
CoD/CoI/CoP Get ready for productive use.
1
4
3
optiSLang Version 3
2
(CoI find most important
variable)
1
optiSLang Version 3.1
(CoP quantify nonlinearity)
optiSLang Version 2
(CoD shows no importance)
55
optiSLang Version 3.1
CoP: 0.73
MoP: MLS-Approximation
Sample Split 70/30
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Start the Metamodel of optimal prognosis workflow.
• Enter a reasonable workflow name
• Browse for the .bin file from robustness analysis
56
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Keep the default settings for MoP and run the algorithm.
• In the optiSLang command box, you can follow the algorithm.
57
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Start a new result monitoring workflow.
• Browse for the .bin file from MoP and start the postprocessing.
58
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The Correlation Matrix indicates that only some of the varied
parameters had a significant influence on the result.
• optiSlang was able to extract results for the 2nd to 5th frequency
and 1st to 5th damping ratio.
59
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Regarding the frequencies, we can see three significant peaks.
• The first significant sqealing point is about 3 kHz, the second
about 5000 kHz and a third area is about 6 kHz.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The damping ratio at 3 kHz is influenced by
the disc radius and the disc thickness.
• The bigger the radius and the thickness
are, the smaller is the damping ratio.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The damping ratio at 5 kHz is influenced by
the disc radius and the disc thickness.
• The bigger the radius and the thickness
are, the smaller is the damping ratio.
• The maximum occuring damping ratio is
higher than at 3 kHz (1.87 % vs. 1.3%)
• The CoP is low
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The damping ratio at 3 kHz is influenced by
the disc radius and the pad thickness.
• The bigger the radius and the
thinner the pad thickness is,
the smaller is the damping ratio.
• The maximum damping ratio is about 3.4%
• The CoP is very low.
63
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Regarding the signal data, it is clear that there are three ranges
where squealing can occour. They are about 3, 5 and 6.5 kHz.
• The higher the frequency is, the higher is the occuring damping
ratio.
• Even the variation of the input variables is only 5%, the squealing
frequencies change significantly the higher the frequency is.
64
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The robustness analysis of this simple brake example leads to the
following result:
• Although the variation of the input parameters is rather small,
the variation of the squealing frequencies is very high.
• The disc radius and disc thickness are the most important
variables in this system.
• The instable frequencies move quite widely
65
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Why are the CoPs so low?
• The CoPs of second and especially third damping ratio is
extremely low! (20% and 5%)
• The reason can be seen in the signal plot.
• The APDL Macro extracts the first, second, third,… instable mode
but this does not take care on any modenumber etc.
• To make a check, it is now recommended to define frequency
windows in which we will extract the peaks!
66
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• There are three frequency windows to define:
1.) 2500…3000 Hz
2.) 4600…5000 Hz
3.) 6600…7200 Hz
1.
67
2.
Tutorial: Complex Modal Analysis – brake squeal analysis
3.
Simple brake example
•
•
•
•
68
Start a new parametrization workflow.
Choose „Create a copy and modify it“.
Choose the problem specification of the robustness analysis.
Enter a reasonable new name and start the parametrization.
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• We have to define 6 signal functions now to extract the peak
value of the damping ratio and the corresponding frequency.
• Double-click on the signal section and now click on „Signal
Function“
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• At first click on „Add Signal Function“, enter a reasonable name
and click into the function part.
• Chose the appropiate signal function for extracting a peak value in
a certain window.
• This function is SIG_MAX_Y_SLOT
• Choose the signal damping ratio and enter the window borders.
• Repeat this for the other two frequency windows.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Now click again on „Add Signal Function“, enter a reasonable
name and click into the function part.
• Chose the appropiate signal function for extracting the abscissa
value of a peak value in a certain window.
• This function is SIG_MAX_X_SLOT
• Choose the signal damping ratio and enter the window borders.
• Repeat this for the other two frequency windows.
71
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Check in the end the correct definition
of the signal functions
• Save and close the parametrization.
72
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• To get these new results, it is now necessary to start an optiSLang
revlauation run.
• Choose the robustness folder as directory for revaluation run.
• Choose the just defined parametrization .pro file as specification.
• Start the revaluation.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Just after the revaluation, run
again the MoP flow and start the
postprocessing.
• The correlation matrix indicates
that this extraction leads to a
better explainability of the
damping ratio.
• The cooling radius has now
a bigger influence on the results
of the damping ratio and
frequency.
74
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The peak in the frequency range 2500 … 3000 Hz is still most
influenced by the disc radius and the disc thickness.
• The third important parameter here is the cooling radius
75
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The CoP of the peak in the second frequency range is much higher
than in the first run. It is now 42% instead of 26%
• The damping ratio is still most influenced by the disc radius but
the second important variable is now the cooling radius
76
Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• The CoP of the peak in the third frequency range is much higher
than in the first run. It is now 47% instead of 5%
• The damping ratio is still most influenced by the disc radius but
the second important variable is now the cooling radius
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Tutorial: Complex Modal Analysis – brake squeal analysis
Simple brake example
• Regarding peaks in a certain frequency window leads to a better
explainability than regarding only the first/second/third/… instable
mode.
• Taking the frequency windows, the results become much more
reliable.
• This is usually the method of choice to extract results from modal
analyseses.
• The reason is that a real mode tracking is much more complicated
to include, so a frequency window is much more easy to
implement.
• Also the important parameters can change, e.g. here, the cooling
radius becomes important in the second way of extracting the
results.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Solution in ANSYS v13 for this model most robust by using partial
solution with QRDAMP
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Point masses on the suspension parts for simulation of bearings
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• A torsioal spring was added between the piston and the caliper to
simulate the hydraulic oil
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Nonlinear, frictional contact between the brake pads and the disc.
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Using of the command based unsymmetric partial solution for the
prestress run and the qrdamp modal analysis
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Result of complex eigenmodes can be displayed since ANSYS 12/13
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• First squealing Mode at 3300 Hz
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Second squealing mode at 5800 Hz
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• optiSLang DoE:
• 35 Input variables
• 4 Output variables (real- / imaginary parts of the Modes
38/39/55/56)
• Taking the whole real- and imaginary parts into a vector
and link the vector to a signal object to get graphical
results of all real parts
• Variation according to presumptions
*There is no re-meshing
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• The signal data shows the appearance of real parts
• Each graph represents one design
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• The coefficient of importance shows the important parameters
with
the largest effect on the output variables
• Determination coefficient (R²) has
to be on a high level (> 70%)
• The anthill-plot shows the
coherence between real and imaginary part of the modes
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Important parameters are:
• Bearing 4, axial stiffness
• Contact stiffness cont. 2
• Contact stiffness cont. 1
• Bearing 3, torsional stiffness
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Tutorial: Complex Modal Analysis – brake squeal analysis
Example: Analysis of an automotive brake
• Challenges and chances of simulating brake squealing in FE-Models:
• Tuning of a model to the measured values takes
• Implementation of several – and also – nonlinear contacts
between the single brake parts
• Bearings can be simulated as bushing joints. This feature is
a new feature in ANSYS 13 and replaces the bearing macros
in ANSYS 12 as they were used here
• Since ANSYS 13, the complex modal analysis is performed by
a partial nonlinear solution in 2 steps as in the example.
Contacts and Settings have to be adapted to the new way of
simulation.
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Tutorial: Complex Modal Analysis – brake squeal analysis