Brake Squeal Analysis -...

© 2011 ANSYS, Inc. November 23, 2014

1

Brake Squeal Analysis


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,

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


4

Reduce the noise and vibration produced by brake squeal Initiated by instability due to the friction forces leading to self-excited vibrations Predict the onset of instability

Objectives of Brake Squeal Analysis


5

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

Analysis Steps


6

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

Early Approach: Direct modeling

“Complex Eigenvalue Analysis for Reducing Low Frequency Brake Squeal” by Shih-Wei Kung, K. Brent Dunlap and Robert

S. Ballinger,Delphi Automotive Systems


7

Convert a DMIG File to an ANSYS SUB File

MATH-APDL: Transition tool

! 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


8

Practical & Consistent way

Contact

→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 !


9

Three different methods

→Full Nonlinear Perturbed Modal Analysis

→Partial Nonlinear Perturbed Modal Analysis

→Linear Non-prestressed Modal Analysis

ANSYS approach


10

Linear Perturbation Method

Full Nonlinear perturbed Modal Analysis

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


11

Linear Perturbation

Partial-Nonlinear perturbed Modal

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


12

New at R14.0

Linear Non-prestressed Modal Analysis

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


13

Parametric variations

Brake design involves study with large number of parametric variations

→Friction Coefficient

→Braking pressure

→Material strength parameters

→Velocity dependence of friction

Solution should be very fast!

Nouby & Srinivasan 2009, Journal Mekanikal


14

Summary

Method Base Static Analysis Modal Analysis

Initial Contact/Pre-stress

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

http://pghintranet/prod_docu/Daily_Builds/ans_cmd/Hlp_C_CMROTATE.html

http://pghintranet/prod_docu/Daily_Builds/ans_cmd/Hlp_C_PSOLVE.html

http://pghintranet/prod_docu/Daily_Builds/ans_cmd/Hlp_C_CMROTATE.html

http://pghintranet/prod_docu/Daily_Builds/ans_cmd/Hlp_C_PSOLVE.html


15

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

Simulation Outcome


16

Example


17

Project Schematic

Full Nonlinear Method

Partial Nonlinear Method

Linear Non-prestressed Method


18

Analysis setup


19

Results

unstable


20

New at R14.0

Squeal Damping

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.


21

Partial Nonlinear perturbed Modal Analysis

Including Squeal Damping - 1

Including Squeal Damping, introduced many modes with positive real part

Without Squeal Damping With Squeal Damping


22

Full method vs. Partial method

Including Squeal Damping

Both Full & Partial method are giving similar results with Squeal Damping


23

• Complex Eigen solve • Animate: Complex Mode Shape • Contact Status at Pads

ANSYS WB Baseline Process

CAD Mesh & Connection

Setup & solver

Post Processing

Bi-Directional CAD Connectivity

• Automated Contact Detection

• Provides for sliding contact with friction • No match mesh needed • Supports higher order elements • Automated Meshing

• Flexibility to use Linear & Non-linear solver capabilities

• Root locus plots • Correlation of modes • List Strain energy per component per mode

Friction sensitivity study • Physical prototyping time consuming and expensive

• Provide more analysis early in the design cycle • Parametric Study by changing friction coefficient

• Run set of DOE’s • Reuse symmetric modes and just run un-symmetric part • Significant time reduction

• Can Include Squeal and Contact damping • - Sliding velocity

dependent Friction


24

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

Summary


25

Appendix


26

Simple brake disc-pad set up


27

Generic model of brake disc system with brake pads and rotating disc modeled in DM and meshed in Simulation- WB1

Simple brake disc-pad set up

Nodes: 60351 Elements: 11473 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


28

• Simple model of a brake disk system with brake pads and rotating disk

Modal Analysis: Brake Squeal


29


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



30


Mode Full Nonlinear Perturbed Modal Analysis


Partial Nonlinear Perturbed Modal Analysis

19 0 4678.4 0 4678.9 0 4678.4

20 0 5187. 0 5187.3 0 5187.

21 20.018 6303.3 19.915 6304.8 19.944 6303.3

22 -20.018 6303.3 -19.915 6304.8 -19.944 6303.3

23 0 6658.1 0 6658.7 0 6658.1

24 0 6662.7 0 6663.2 0 6662.7

Comparison of unstable frequencies from the 3 methods


31

The squeal damping can be introduced through TB,Fric or/and through static-dynamic friction (real constants: FACT, DC)

TB,FRIC,matid,,,ISO ! Activate orthotropic friction model

TBFIELD,SLRV, 0.0 ! 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


TBFIELD,SLRV, 200.0 ! Define 3rd value of sliding relative 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: NMISC160-163

Squeal Damping (cont..)

Brake Squeal Analysis -...

Documents

Transcript of Brake Squeal Analysis -...