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

2. 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
oS Robustness studies scan the design space and evaluate the sensitivities with statistical measurements.
That is in contrast to traditional (mathematical) Robustness analysis using functional analysis (gradient, differentiation,..).
The advantage of oS Robustness analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things.
Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets.
Tutorial: Complex Modal Analysis – brake squeal analysis

3. 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.
oS Robustness studies scan the design space and evaluate the sensitivities with statistical measurements.
That is in contrast to traditional (mathematical) Robustness analysis using functional analysis (gradient, differentiation,..).
The advantage of oS Robustness analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things.
Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets.
Tutorial: Complex Modal Analysis – brake squeal analysis

4. 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”).
Tutorial: Complex Modal Analysis – brake squeal analysis

5. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

6. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

7. 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 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

8. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

9. Modal Analysis (Perturbation Analysis )
Introduction
In ANSYS available methods for simulation of brake-squealing
Method
Base Static Analysis
Modal Analysis (Perturbation Analysis )
Initial Contat/Pre-stress
Force frictional sliding
(CMROTATE)
QRDAMP/UNSYMM/DAMP
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
Linear perturbation modal solve
In our example we will concentrate on the partial nonlinear perturbed modal analysis.
Tutorial: Complex Modal Analysis – brake squeal analysis

10. Workflow in ANSYS Workbench
Workflow partial nonlinear perturbed modal analysis 1 2 3 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
Tutorial: Complex Modal Analysis – brake squeal analysis

11. 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_“.
Tutorial: Complex Modal Analysis – brake squeal analysis

12. Brake squeal analysis in Workbench: parametric geometry-import1
Tutorial: Complex Modal Analysis – brake squeal analysis

13. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

14. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

15. 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…)
Tutorial: Complex Modal Analysis – brake squeal analysis

16. Simple brake example Geometry parameters I
Pad_width
Pad_thickness
Pad_position
Cooling_radius
Disc_radius
Disc_thickness
Tutorial: Complex Modal Analysis – brake squeal analysis

17. Simple brake example Geometry parameters II
Cooling_angle
Pad_angle
Tutorial: Complex Modal Analysis – brake squeal analysis

18. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

19. Brake squeal analysis in Workbench: non linear pre-stress2
Tutorial: Complex Modal Analysis – brake squeal analysis

20. Simple brake example keyopt,cid,4,3 nonlinear frictional contact
frictional coefficient as parameter for Robustness analysis.
keyopt,cid,4,3
Tutorial: Complex Modal Analysis – brake squeal analysis

21. Simple brake example Mesh
Tutorial: Complex Modal Analysis – brake squeal analysis

22. Simple brake example nropt,unsym
Prestress as static structural analysis with large deflections = on
Pressure on the brake pads parametrized for optiSLang
nropt,unsym
Tutorial: Complex Modal Analysis – brake squeal analysis

23. Brake squeal analysis in Workbench: complex modal analysis3
Tutorial: Complex Modal Analysis – brake squeal analysis

24. Simple brake example
Complex modal analysis activated via command blocks
CMROTAT, E_ROTOR, , ,ARG1 ! Rotate the selected elements
alls
ARG1 = 2 (rotational speed)
MODOPT,qrdamp,arg1,arg2,arg3,on
MXPAND,arg1
ARG1 = 30 (nmodes)
ARG2 = 0 (fmin)
ARG3 = 7500 (fmax)
Tutorial: Complex Modal Analysis – brake squeal analysis

25. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

26. Simple brake example Exicated mode Damped mode
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 j j j j j j j j j j j j j j j j
Exicated mode
Damped mode
Tutorial: Complex Modal Analysis – brake squeal analysis

27. Simple brake example
Using the RSTMAC command in the postprocessing, we‘ll get a measure for modetracking during the optiSLang run.
*** NOTE *** CP = 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 (%) E E E E E E E E E E
Tutorial: Complex Modal Analysis – brake squeal analysis

28. 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%
Tutorial: Complex Modal Analysis – brake squeal analysis

29. Robustness analysis in optiSLang4
Tutorial: Complex Modal Analysis – brake squeal analysis

30. 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

31. 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

32. 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)
Tutorial: Complex Modal Analysis – brake squeal analysis

33. Simple brake example
Overview of the 12 input Parameters in ANSYS Workbench
Contact frictional coefficients
Brake pressure
Geometry parameters
Rotational speed
Tutorial: Complex Modal Analysis – brake squeal analysis

34. 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 %
Tutorial: Complex Modal Analysis – brake squeal analysis

35. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

36. Simple brake example
Open optiSLang 3.x.x and import the previously exported project into optiSLang.
Tutorial: Complex Modal Analysis – brake squeal analysis

37. Simple brake example
Start the parameter editor to modify the parametrization and for including signal data.
Tutorial: Complex Modal Analysis – brake squeal analysis

38. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

39. Simple brake example
1.) Double click „Frictional_Solid_To_Solid_Friction_Coefficient“
2.) Rename it as Frictional_Coefficient_Pad_1
Tutorial: Complex Modal Analysis – brake squeal analysis

40. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

41. Simple brake example
1.) Now, copy the new, important signal extraction file „damp_ratio.txt“ into the optiSLang directory.
Tutorial: Complex Modal Analysis – brake squeal analysis

42. Simple brake example
1.) Open a new file – browse for damp_ratio.txt and open it
2.) Set is as an output file
Tutorial: Complex Modal Analysis – brake squeal analysis

43. Simple brake example 1.) Mark the first row.
2.) Set it as a repeated block marker
3.) Set as super marker and mark „single steps“
4.) The start is set to „2“
Tutorial: Complex Modal Analysis – brake squeal analysis

44. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

45. Simple brake example 1.) Repeat this for second and third column.
2.) Set it as a vector.
3.) Give reasonable names.
Tutorial: Complex Modal Analysis – brake squeal analysis

46. 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“.
Tutorial: Complex Modal Analysis – brake squeal analysis

47. Simple brake example
1.) 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 Function
4.) For the corresponding frequency, use the SIG_MAX_X Function
Tutorial: Complex Modal Analysis – brake squeal analysis

48. Simple brake example 1.) Double click on constraint section
2.) Add 2 constraints by clicking „New“
2.) Insert 0 <= DS_Disc_radius-DS_Cooling_Radius+25 as constraint1
3.) Insert 0 <= DS_Disc_radius-DS_Pad_Width-125 as constraint2
Tutorial: Complex Modal Analysis – brake squeal analysis

49. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

50. 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.
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"
"C:\Program Files\optiSLang_3.2.0\perl5.10.0\bin\perl" myperl.pl
Tutorial: Complex Modal Analysis – brake squeal analysis

51. Simple brake example Start the robustness workflow.
Insert 100 as a number of samples, choose „Advanced LHS“
Choose the start script if necessary
Tutorial: Complex Modal Analysis – brake squeal analysis

52. Simple brake example
Check the start set. The parameters are normal distributed.
Tutorial: Complex Modal Analysis – brake squeal analysis

53. 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)
Tutorial: Complex Modal Analysis – brake squeal analysis 53

54. Simple brake example 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

55. Simple brake example CoD/CoI/CoP Get ready for productive use.1 4 3
optiSLang Version 3
(CoI find most important variable) 2 1
optiSLang Version 3.1
(CoP quantify nonlinearity)
optiSLang Version 3.1
CoP: 0.73
MoP: MLS-Approximation
Sample Split 70/30
optiSLang Version 2
(CoD shows no importance)
Tutorial: Complex Modal Analysis – brake squeal analysis

56. Simple brake example
Start the Metamodel of optimal prognosis workflow.
Enter a reasonable workflow name
Browse for the .bin file from robustness analysis
Tutorial: Complex Modal Analysis – brake squeal analysis

57. Simple brake example
Keep the default settings for MoP and run the algorithm.
In the optiSLang command box, you can follow the algorithm.
Tutorial: Complex Modal Analysis – brake squeal analysis

58. Simple brake example Start a new result monitoring workflow.
Browse for the .bin file from MoP and start the postprocessing.
Tutorial: Complex Modal Analysis – brake squeal analysis

59. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

60. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

61. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

62. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

63. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

64. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

65. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

66. 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!
Tutorial: Complex Modal Analysis – brake squeal analysis

67. Simple brake example
There are three frequency windows to define:
1.) 2500…3000 Hz
2.) 4600…5000 Hz
3.) 6600…7200 Hz 1. 2. 3.
Tutorial: Complex Modal Analysis – brake squeal analysis

68. Simple brake example 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

69. 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“
Tutorial: Complex Modal Analysis – brake squeal analysis

70. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

71. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

72. Simple brake example
Check in the end the correct definition of the signal functions
Save and close the parametrization.
Tutorial: Complex Modal Analysis – brake squeal analysis

73. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

74. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

75. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

76. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

77. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

78. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis

79. Example: Analysis of an automotive brake
Solution in ANSYS v13 for this model most robust by using partial solution with QRDAMP
Tutorial: Complex Modal Analysis – brake squeal analysis

80. Example: Analysis of an automotive brake
Point masses on the suspension parts for simulation of bearings
Tutorial: Complex Modal Analysis – brake squeal analysis

81. Example: Analysis of an automotive brake
A torsioal spring was added between the piston and the caliper to simulate the hydraulic oil
Tutorial: Complex Modal Analysis – brake squeal analysis

82. Example: Analysis of an automotive brake
Nonlinear, frictional contact between the brake pads and the disc.
Tutorial: Complex Modal Analysis – brake squeal analysis

83. Example: Analysis of an automotive brake
Using of the command based unsymmetric partial solution for the prestress run and the qrdamp modal analysis
Tutorial: Complex Modal Analysis – brake squeal analysis

84. Example: Analysis of an automotive brake
Result of complex eigenmodes can be displayed since ANSYS 12/13
Tutorial: Complex Modal Analysis – brake squeal analysis

85. Example: Analysis of an automotive brake
First squealing Mode at 3300 Hz
Tutorial: Complex Modal Analysis – brake squeal analysis

86. Example: Analysis of an automotive brake
Second squealing mode at 5800 Hz
Tutorial: Complex Modal Analysis – brake squeal analysis

87. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

88. Example: Analysis of an automotive brake
The signal data shows the appearance of real parts
Each graph represents one design
Tutorial: Complex Modal Analysis – brake squeal analysis

89. 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 ima- ginary part of the modes
Tutorial: Complex Modal Analysis – brake squeal analysis

90. 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
Tutorial: Complex Modal Analysis – brake squeal analysis

91. 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.
Tutorial: Complex Modal Analysis – brake squeal analysis