Brake Squeal Analysis ANSYS, Inc. November 23, 2014

Transcription

1 Brake Squeal Analysis 1

2 Introduction Brake squeal has been under investigation by the automotive industry for decades due to consistent customer complaints and high warranty costs. Although the real mechanism is still unknown, many engineering approaches have been implemented to attack the problem. One documented example is the complex eigenvalue method by which squeal propensity is quantified by the dynamic instability of a certain system mode. Complex Eigenvalue Analysis for Reducing Low Frequency Brake Squeal by Shih-Wei Kung, K. Brent Dunlap and Robert S. Ballinger, 2 Delphi Automotive Systems

3 Sneaker Squeals? FEA techniques are applicable to other sectors Martyn Shorten & Xia Xi, The squeaks in your sneaks: Vibrations at the shoe-surface interface but we will focus on Brakes 3

4 Objectives of Brake Squeal Analysis Reduce the noise and vibration produced by brake squeal Initiated by instability due to the friction forces leading to selfexcited vibrations Predict the onset of instability 4

5 Analysis Steps Pre-stressed static analysis to establish contact between the pads and disc Forced frictional sliding between pads and disc to generate non symmetric stiffness matrix Pre-stressed modal analysis to generate complex eigen frequencies Positive real part of the eigen frequencies indicates unstable mode 5

6 Early Approach: Direct modeling Standard FE Model provides M and K Discrete 2 node (springs) elements are used to provide Friction stiffness (MATRIX27) Drawbacks Requires matching nodes at the sliding interface Tedious, Time consuming Rotor-pad interface is not treated consistent Impractical for parametric studies Complex Eigenvalue Analysis for Reducing Low Frequency Brake Squeal by Shih-Wei Kung, K. Brent Dunlap and Robert S. Ballinger,Delphi Automotive Systems 6

7 MATH-APDL: Transition tool Convert a DMIG File to an ANSYS SUB File! IMPORT A STIFF MATRIX FROM A DMIG FILE. *DMAT,K,D,IMPORT,DMIG,K.DMIG,,! In the input file, Fields are separated by,! IMPORT A MASS MATRIX FROM ANOTHER DMIG FILE *DMAT,M,D,IMPORT,DMIG,M.DMIG! In the input file, Fields are separated by spaces (default)! PRINT THESE MATRICES *PRINT,K *PRINT,M! GENERATE AN ANSYS.SUB FILE THAT CONTAINS THESE TWO MATRICES *EXPORT,K,SUB,newfile.sub,STIFF,,WAIT *EXPORT,M,SUB,newfile.sub,MASS,,DONE 7

8 Contact Practical & Consistent way Rotor-Pad interface is a contact pair Matching mesh is no longer required Unsymmetric matrices are generated when sliding occurs Lower & higher order elements Allows study of squeal damping ANSYS Workbench at its best with Contact Modeling! 8

9 ANSYS approach Three different methods Full Nonlinear Perturbed Modal Analysis Partial Nonlinear Perturbed Modal Analysis Linear Non-prestressed Modal Analysis 9

10 Full Nonlinear perturbed Modal Analysis Linear Perturbation Method Most Accurate Method Uses Newton-Raphson for all static solutions Most Expensive Method Not suited for Parametric Studies Computation cost Convergence issues? Better suited for detailed singular studies 10

11 Partial-Nonlinear perturbed Modal Linear Perturbation Include nonlinear Stress stiffening effects Non-uniform contact pressure Frictional effects, other loads Nonlinear iterations not required for rotational velocity Less expensive than Full Nonlinear analysis sequence Faster than FULL method Better suited for DOE studies 11

12 Linear Non-prestressed Modal Analysis New at R14.0 Assumptions Ignore Stress stiffening effects Neglect squeal damping Nonlinear iterations not required, No Convergence issues Contact stiffness based on initial contact status Fast run times Allows for large DOE studies 12

13 Parametric variations Brake design involves study with large number of parametric variations Friction Coefficient Braking pressure Material strength parameters Velocity dependence of friction Nouby & Srinivasan 2009, Journal Mekanikal Solution should be very fast! 13

14 Summary Method Base Static Analysis Modal Analysis Initial Contact/Prestress Force frictional sliding (CMROTATE) QRDAMP/UNSYMM Linear N/A N/A Force frictional sliding (CMROTATE command) and perform a Linear modal solve (SOLVE) Partial Nonlinear Full nonlinear solution N/A Force frictional sliding (CMROTATE command) and perform a Linear perturbed modal solve (SOLVE) Full Nonlinear Full nonlinear solution Full nonlinear solution Linear perturbation modal solve 14

15 Simulation Outcome Complex Eigen value analysis Real & imaginary part Complex Eigen vector Damping ratio Animate Complex Mode Shape Contact status at Pads Root locus plots Frequency vs. coefficient of friction Correlation of modes RSTMAC Strain energy per component per mode 15

16 Example 16

17 Project Schematic Full Nonlinear Method Partial Nonlinear Method Linear Non-prestressed Method 17

18 Analysis setup 18

19 Results unstable 19

20 Squeal Damping New at R14.0 In R14.0, we introduce ability to study the effects of Squeal damping for Brake instability analysis Based on defined frictions vs sliding velocities relation ANSYS will compute the squeal damping When negative friction-velocity gradient is used (the usual case) it typically triggers instabilities. 20

21 Including Squeal Damping - 1 Partial Nonlinear perturbed Modal Analysis Without Squeal Damping With Squeal Damping Including Squeal Damping, introduced many modes with positive real part 21

22 Including Squeal Damping Full method vs. Partial method Both Full & Partial method are giving similar results with Squeal Damping 22

23 ANSYS WB Baseline Process Automated Meshing Provides for sliding contact with friction No match mesh needed Supports higher order elements Complex Eigen solve Animate: Complex Mode Shape Contact Status at Pads CAD Mesh & Connection Setup & solver Post Processing 23 Bi-Directional CAD Connectivity Automated Contact Detection Flexibility to use Linear & Non-linear solver capabilities Friction sensitivity study Physical prototyping time consuming and expensive Provide more Can analysis Include early Squeal in the design and cycle Contact damping Parametric Study by changing friction coefficient - Sliding velocity Run set of DOE s dependent Friction Reuse symmetric modes and just run unsymmetric part Significant time reduction Root locus plots Correlation of modes List Strain energy per component per mode

24 Summary Quick setup to solution time Higher Quality Ability to generate quick variations Reduced Costs 24

25 Appendix 25

26 Simple brake disc-pad set up 26

27 Simple brake disc-pad set up Generic model of brake disc system with brake pads and rotating disc modeled in DM and meshed in Simulation- WB1 Nodes: Elements: Contact: 3D standard surface to surface contact between brake disc and pads Pre-stress load: Surface pressure applied on the pads Constraints: Fixed support on inner radius of brake disc 27

28 Modal Analysis: Brake Squeal Simple model of a brake disk system with brake pads and rotating disk 28

29 Modal Analysis: Brake Squeal Linear Non-prestressed Modal Analysis Mode shape at frequency 6304, unstable mode (1,21) Command Snippets /solu antype,static nropt,unsym! Unsymmetric matrices ematwrite,yes! Write element matrices esel,s,type,,30 esel,a,type,,32 cm,rotor,elem! Select target elements on brake rotor allsel,all cmrot,rotor,,,2,! Rotate along Z axis nsubst,1,1,1 allsel,all psolve,elform,cndi! Partial solve ****************************************** /solu antype,modal modopt,qrdamp,50! Qrdamp solver mxpand,50 psolve,eigqrda! Partial solve psolve,eigexp 29

30 Modal Analysis: Brake Squeal Comparison of unstable frequencies from the 3 methods Mode Full Nonlinear Perturbed Modal Analysis Linear Non-prestressed Modal Analysis Partial Nonlinear Perturbed Modal Analysis

31 Squeal Damping (cont..) The squeal damping can be introduced through TB,Fric or/and through static-dynamic friction (real constants: FACT, DC) TB,FRIC,matid,,,ISO TBFIELD,SLRV, 0.0! Activate orthotropic friction model! Define 1st value of sliding relative velocity TBDATA,1,0.5.! define friction at Sliding velocity 0.0 TBFIELD,SLRV, 50.0! Define 2nd value of sliding relative velocity TBDATA,1,0.3.! define friction at Sliding velocity 50.0 TBFIELD,SLRV, 200.0! Define 3rd value of sliding relative velocity TBDATA,1,0.2.! define friction at Sliding velocity Based on defined frictions vs sliding velocities relation ANSYS will compute the squeal damping (usually a negative damping). The squeal damping can be posted through ETABLE quantities: NMISC