Performing a parametric Brake Squeal Analysis in ANSYS WB and optiSLang.

Performing a parametric Brake Squeal Analysis in ANSYS WB and

optiSLang

2 Tutorial: Complex Modal Analysis – brake squeal analysis

• 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

Outline


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 disc-brake 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.


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”).

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.

Introduction


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.


• 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 self-excited 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.

Introduction


Introduction• Brake squealing is a complex (damped and/or unsymmetric) eigenvalue

problem.

• 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.

}0{}]{[}]{[}]{[ unsymmsym uKKuCuM


Introduction

In ANSYS available methods for simulation of brake-squealing

In our example we will concentrate on the partial nonlinear perturbed modal analysis.


Workflow in ANSYS Workbench

Workflow partial nonlinear perturbed modal analysis

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 analysis4. Parameter study in optiSLang

11

22 33

44


Workflow in ANSYS Workbench

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_“.

Workflow partial nonlinear perturbed modal analysis


Brake squeal analysis in Workbench: parametric geometry-

import

11


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

ANSYS WorkbenchStructural Mechanics - Fluid Dynamics - Heat Transfer - Electromagnetics

An adaptable multi-physics design and analysis system that integrates and coordinates different simulation tasks

CAD / PDMCAD / PDM


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.


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…)


Simple brake example• Geometry parameters I

Disc_radius Disc_thickness

Pad_thickness

Pad_width

Pad_position

Cooling_radius


Simple brake example• Geometry parameters II

Pad_angle

Cooling_angle


Simple brake example

• Geometry conditions:

1.) DS_Disc_radius >= DS_Cooling_Radius+25This ensures that the internal ventilation will remain.

2.) DS_Pad_Width <= DS_Disc_radius-125This ensures that the pad will not be bigger than the disc.

These constraints will be inserted into the optiSLangparametrization.


Brake squeal analysis in Workbench: non linear pre-stress

22


Simple brake example• nonlinear frictional contact• frictional coefficient as parameter for Robustness analysis.

keyopt,cid,4,3


Simple brake example• Mesh


Simple brake example• Prestress as static structural analysis with large deflections = on• Pressure on the brake pads parametrized for optiSLang

nropt,unsym


Brake squeal analysis in Workbench: complex modal

analysis

33


Simple brake example• Complex modal analysis activated via command blocks

CMROTAT, E_ROTOR, , ,ARG1 ! Rotate the selected elementsalls

MODOPT,qrdamp,arg1,arg2,arg3,on MXPAND,arg1

ARG1 = 30 (nmodes) ARG2 = 0 (fmin) ARG3 = 7500 (fmax)

ARG1 = 2 (rotational speed)


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 areextracted and can be parametrized in workbench.

Frequencies

Damping ratio


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 TIME/FREQ(Damped) TIME/FREQ(Undamped) LOAD STEP SUBSTEP CUMULATIVE 1 0.0000 722.08 j 722.25 1 1 1 0.0000 -722.08 j 2 0.0000 748.65 j 748.16 1 2 2 0.0000 -748.65 j 3 0.0000 1166.1 j 1165.8 1 3 3 0.0000 -1166.1 j 4 0.0000 1190.2 j 1189.9 1 4 4 0.0000 -1190.2 j 5 0.0000 1454.1 j 1454.0 1 5 5 0.0000 -1454.1 j 6 0.0000 1529.6 j 1529.6 1 6 6 0.0000 -1529.6 j 7 21.836 2799.8 j 2793.2 1 7 7 21.836 -2799.8 j 8 -21.836 2799.8 j 2802.3 1 8 8 -21.836 -2799.8 j

Exicated modeDamped mode


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


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 Frequency Damping Ratio in% 0.000 722.080 0.000 0.000 748.650 0.000 0.000 1166.100 0.000 0.000 1190.200 0.000 0.000 1454.100 0.000 0.000 1529.600 0.000 21.836 2799.800 0.780 -21.836 2799.800 -0.780 0.000 3064.300 0.000 0.000 3088.000 0.000 0.000 4255.700 0.000 0.000 4583.100 0.000 0.000 4593.300 0.000 43.852 4833.400 0.907 -43.852 4833.400 -0.907 0.000 4972.400 0.000 0.000 5134.900 0.000 17.451 6211.300 0.281 -17.451 6211.300 -0.281


Robustness analysis in optiSLang

44

30

• 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

Why performing robustness analysis

31

• 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

How to define robustness of a design


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)


Simple brake example• Overview of the 12 input Parameters in ANSYS Workbench

Contact frictional coefficients

Brake pressure

Geometry parameters

Rotational speed


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

Damping ratio in %

Complex frequencies


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.


Simple brake example• Open optiSLang 3.x.x and import the previously exported project into optiSLang.


Simple brake example• Start the parameter editor to modify the parametrization and for including signal data.


Simple brake example• What is to be done now:1.) Change of the parameter names for frictional coefficient2.) Addition of signal data and parameters3.) Creating of geometry constraints according to page 14


Simple brake example1.) Double click „Frictional_Solid_To_Solid_Friction_Coefficient“2.) Rename it as Frictional_Coefficient_Pad_1


Simple brake example1.) Copy the two provided files myperl.pl and start_perl.bat into theresult file directory of the complex modal analysis.2.) Execute it by double click on start_perl.bat3.) A sorted and cleaned textfile for parametrising (damp_ratio.txt) is created.


Simple brake example1.) Now, copy the new, important signal extraction file „damp_ratio.txt“ into the optiSLang directory.


Simple brake example1.) Open a new file – browse for damp_ratio.txt and open it2.) Set is as an output file


Simple brake example1.) Mark the first row.2.) Set it as a repeated block marker3.) Set as super marker and mark „single steps“4.) The start is set to „2“


Simple brake example1.) Double-click on the first value in the first column.2.) Set it as a vector.3.) Give a reasonable name.


Simple brake example1.) Repeat this for second and third column.2.) Set it as a vector.3.) Give reasonable names.


Simple brake example1.) Double click on signal section2.) Create a Signal Object.3.) Choose the Frequency channel for absicissa 4.) Choose Real part and damping ratio as ordinate by clicking „Add channel“.


Simple brake example1.) Double click on signal section and create a Signal Function.2.) Give a reasonable name and click „Add signal Function“3.) For the maximum of damping, use the SIG_MAX_Y Function4.) For the corresponding frequency, use the SIG_MAX_X Function


Simple brake example1.) Double click on constraint section2.) Add 2 constraints by clicking „New“2.) Insert 0 <= DS_Disc_radius-DS_Cooling_Radius+25 as constraint13.) Insert 0 <= DS_Disc_radius-DS_Pad_Width-125 as constraint2



• 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.



• The optiPlug created start script has to be updated to some lines.• These lines will ensure that the signal text files are copied back tothe 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 scriptmyperl.pl so that it can be copied into every design directory.

• The start_perl.bat consist the following command line: (modify if necessary)

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 -------------------------------------------------------------------

"C:\Program Files\optiSLang_3.2.0\perl5.10.0\bin\perl" myperl.pl


• Start the robustness workflow.• Insert 100 as a number of samples, choose „Advanced LHS“• Choose the start script if necessary



• Check the start set. The parameters are normal distributed.



• 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)

•What proportion of the variation of a response can be forecasted with identified arbitrary non-linear correlations to the input parameters?


54

Coefficient of prognosis

• Correlation between sample points and model predictions using an additional independent test data set

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

1.0;]ˆ[

=

2

ˆ

CoP

YYCoP

TestYTestY

TestTest

E



CoD/CoI/CoP Get ready for productive use.

optiSLang Version 3.1CoP: 0.73MoP: MLS-ApproximationSample Split 70/30

optiSLang Version 2(CoD shows no importance)

optiSLang Version 3(CoI find most important variable)

1

2

1

4

3

optiSLang Version 3.1(CoP quantify nonlinearity)



• Start the Metamodel of optimal prognosis workflow.• Enter a reasonable workflow name• Browse for the .bin file from robustness analysis



• Keep the default settings for MoP and run the algorithm.• In the optiSLang command box, you can follow the algorithm.



• Start a new result monitoring workflow.• Browse for the .bin file from MoP and start the postprocessing.



• 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.



• 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.



• The damping ratio at 3 kHz is influenced bythe disc radius and the disc thickness.

• The bigger the radius and the thicknessare, the smaller is the damping ratio.



• The damping ratio at 5 kHz is influenced bythe disc radius and the disc thickness.

• The bigger the radius and the thicknessare, 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



• The damping ratio at 3 kHz is influenced bythe 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.



• 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.



• 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



• 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!



• There are three frequency windows to define:1.) 2500…3000 Hz2.) 4600…5000 Hz3.) 6600…7200 Hz


1. 2. 3.


• 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.



• 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“



• 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.



• 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.



• Check in the end the correct definitionof the signal functions

• Save and close the parametrization.



• 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.



• Just after the revaluation, run again the MoP flow and start thepostprocessing.

• The correlation matrix indicates that this extraction leads to a better explainability of the damping ratio.

• The cooling radius has nowa bigger influence on the resultsof the damping ratio andfrequency.



• 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



• 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



• 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



• 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.



Example: Analysis of an automotive brake• Solution in ANSYS v13 for this model most robust by using partial

solution with QRDAMP


Example: Analysis of an automotive brake• Point masses on the suspension parts for simulation of bearings


Example: Analysis of an automotive brake• A torsioal spring was added between the piston and the caliper to

simulate the hydraulic oil


Example: Analysis of an automotive brake• Nonlinear, frictional contact between the brake pads and the disc.


Example: Analysis of an automotive brake• Using of the command based unsymmetric partial solution for the

prestress run and the qrdamp modal analysis


Example: Analysis of an automotive brake• Result of complex eigenmodes can be displayed since ANSYS 12/13


Example: Analysis of an automotive brake• First squealing Mode at 3300 Hz


Example: Analysis of an automotive brake• Second squealing mode at 5800 Hz


• 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

Example: Analysis of an automotive brake


• The signal data shows the appearance of real parts• Each graph represents one design



• The coefficient of importance shows the important parameters withthe largest effect on the output variables

• Determination coefficient (R²) hasto be on a high level (> 70%)

• The anthill-plot shows the coherence between real and ima-ginary part of the modes



• Important parameters are:

• Bearing 4, axial stiffness• Contact stiffness cont. 2 • Contact stiffness cont. 1• Bearing 3, torsional stiffness



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 contactsbetween the single brake parts

• Bearings can be simulated as bushing joints. This feature isa new feature in ANSYS 13 and replaces the bearing macrosin ANSYS 12 as they were used here

• Since ANSYS 13, the complex modal analysis is performed bya partial nonlinear solution in 2 steps as in the example.Contacts and Settings have to be adapted to the new way of simulation.

Performing a parametric Brake Squeal Analysis in ANSYS WB and optiSLang.

Documents

Transcript of Performing a parametric Brake Squeal Analysis in ANSYS WB and optiSLang.