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Performing a parametric Brake Squeal Analysis in ANSYS WB and optiSLang

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)

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Performing a parametric Brake Squeal Analysis in ANSYS WB and optiSLang

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  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 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. Tutorial: Complex Modal Analysis – brake squeal analysis

  4. How can we measure brake squealing? Example test setup (McDaniel1999): Measurement by laser scanning vibrometer Introduction 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. 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 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. Introduction In ANSYS available methods for simulation of brake-squealing 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 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 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-import 1 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-stress 2 Tutorial: Complex Modal Analysis – brake squeal analysis

  20. Simple brake example • 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 • 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 analysis 3 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 • 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 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 = 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 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% 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 Tutorial: Complex Modal Analysis – brake squeal analysis

  29. Robustness analysis in optiSLang 4 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 theresult 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 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 Tutorial: Complex Modal Analysis – brake squeal analysis

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