SAE 2007-NVC-180

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1 SAE Noise and Vibration Conference May 15-17, 2007 A Simple Model for the A Simple Model for the Simulation of Low-Frequency Simulation of Low-Frequency Disc Brake Noise Disc Brake Noise Ragnar Ledesma and Shan Shih Ragnar Ledesma and Shan Shih Advanced Engineering Advanced Engineering Commercial Vehicle Systems Commercial Vehicle Systems

Transcript of SAE 2007-NVC-180

Page 1: SAE 2007-NVC-180

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SAE Noise and Vibration ConferenceMay 15-17, 2007

A Simple Model for the Simulation of A Simple Model for the Simulation of Low-Frequency Disc Brake Noise Low-Frequency Disc Brake Noise

Ragnar Ledesma and Shan ShihRagnar Ledesma and Shan ShihAdvanced EngineeringAdvanced Engineering

Commercial Vehicle SystemsCommercial Vehicle Systems

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SAE Noise and Vibration ConferenceMay 15-17, 2007

ObjectiveObjective

• The objective of this study is to develop a simple multi-body dynamics model that can simulate low-frequency disc brake noise• Verify the hypothesis that low-frequency brake noise can be

caused by the coupling of 2 vibration modes through a friction interface

• A second objective is to determine the effect of various design parameters on brake noise propensity• brake pad/brake rotor sliding friction coefficient

• brake pad stiffness (pad compressibility)

• bushing stiffness (suspension lateral stiffness)

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Modeling AssumptionsModeling Assumptions

• Brake noise is a manifestation of friction-induced mode coupling

• The friction interface is characterized by 2 parameters: normal contact stiffness and sliding friction coefficient

• Mode coupling is an instability phenomenon that occurs when

enn kF * e

nf kF **

)2/()2sin( nkK )tan(

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Multi-Body Dynamics ModelMulti-Body Dynamics Model

• Disc brake assembly• Torque plate (flexible – use FE model)• Caliper (rigid)• Rotor and brake pads (rigid)• Push rods/pistons (rigid)• Pad/Rotor normal contact – Hertz contact model• Friction model: constant sliding friction coefficient

• Typical suspension system for heavy-duty bus/coach• Upper and lower torque rods• Air springs/shock absorbers• Beam axle• Truck tires

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ADAMS Model (Disc Brake Assembly)ADAMS Model (Disc Brake Assembly)

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Model VerificationModel Verification

• Baseline model: stiff pads – noise occurs at 185 Hz• Consistent with vehicle test

data (noise measured at 180 Hz)

• Modified model: soft pads – no noise

• Trends are consistent with results of vehicle tests

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Designed Numerical ExperimentsDesigned Numerical Experiments

• Determine the effect of design parameters on the propensity of low-frequency disc brake noise

• 3-factor, 3-level design (27 runs)

Design Factor Assigned Values

A. Coefficient of Friction (0.2, 0.3, 0.4)

B. Pad Stiffness (1.0, 5.5, 10.0) x 105 N/mm

C. Bushing Stiffness (1.0, 5.5, 10.0) x 104 N/mm

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DOE ResultsDOE Results

Run No.

Torque Rod Bushing Stiffness

Brake Pad Stiffness

Brake Pad Friction

Std. Deviation of Caliper

Displacement

Std. Deviation of Axle Pitch Rotation

(N/mm) (N/mm) (no units) (mm) (deg) 1 10000 100000 0.2 0.0225 0.00742 10000 100000 0.3 0.0209 0.00753 10000 100000 0.4 0.0264 0.00824 10000 550000 0.2 0.0364 0.00745 10000 550000 0.3 0.0503 0.00846 10000 550000 0.4 0.0435 0.00947 10000 1000000 0.2 0.3807 0.03598 10000 1000000 0.3 0.0540 0.00879 10000 1000000 0.4 0.1540 0.0190

10 55000 100000 0.2 0.0180 0.007311 55000 100000 0.3 0.0217 0.007812 55000 100000 0.4 0.0230 0.008413 55000 550000 0.2 0.0364 0.007514 55000 550000 0.3 0.0544 0.008915 55000 550000 0.4 0.0408 0.009316 55000 1000000 0.2 0.3586 0.031217 55000 1000000 0.3 0.3584 0.043618 55000 1000000 0.4 0.0553 0.011519 100000 100000 0.2 0.0188 0.007320 100000 100000 0.3 0.0231 0.007921 100000 100000 0.4 0.0237 0.008522 100000 550000 0.2 0.0340 0.007623 100000 550000 0.3 0.0358 0.008824 100000 550000 0.4 0.0464 0.010525 100000 1000000 0.2 0.3553 0.028126 100000 1000000 0.3 0.3803 0.032927 100000 1000000 0.4 0.6265 0.0622

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ANOVA Table: Inverse of the Vibration ANOVA Table: Inverse of the Vibration Amplitude of the Caliper (Side-to-Side Mode)Amplitude of the Caliper (Side-to-Side Mode)

Sum of Mean FSource Squares DF Square Value Prob > FModel 7347.51 6 1224.59 54.70 < 0.0001A - Friction Coeff 41.13 1 41.13 1.84 0.1904B - Pad Stiffness 7030.79 1 7030.79 314.07 < 0.0001C - Bushing Stiffness 0.74 1 0.74 0.03 0.8577A*B 189.91 1 189.91 8.48 0.0086A*C 14.33 1 14.33 0.64 0.4330B*C 70.60 1 70.60 3.15 0.0910Residual 447.73 20 22.39Cor Total 7795.24 26

Std. Dev. 4.73 R-Squared 0.94Mean 25.63 Adj R-Squared 0.93C.V. 18.46 Pred R-Squared 0.90

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Predicted Response: Inverse of the Vibration Predicted Response: Inverse of the Vibration Amplitude of the Caliper (Side-to-Side Mode)Amplitude of the Caliper (Side-to-Side Mode)

DESIGN-EXPERT Plot

1.0/(Std. Dev . - Caliper Disp.)X = A: Friction Coef f icientY = B: Pad Stif f ness

Actual FactorC: Bushing Stif f ness = 55000.00

3.40172

15.2726

27.1435

39.0143

50.8852

1.0

/(Std

. Dev

. - C

alip

er D

isp.)

0.20

0.25

0.30

0.35

0.40

100000.00

325000.00

550000.00

775000.00

1000000.00

A: Friction Coefficient

B: Pad Stiffness

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ANOVA Table: Inverse Squared of the Axle ANOVA Table: Inverse Squared of the Axle Pitch Rotation (Spring Wrap-Up Mode)Pitch Rotation (Spring Wrap-Up Mode)

Sum of Mean FSource Squares DF Square Value Prob > FModel 7.37E+09 5 1.47E+09 25.85 < 0.0001A - Friction Coeff. 3.69E+08 1 3.69E+08 6.47 0.0189B - Pad Stiffness 5.88E+09 1 5.88E+09 103.09 < 0.0001C - Bushing Stiffness 1.76E+08 1 1.76E+08 3.09 0.0934B*B 6.87E+08 1 6.87E+08 12.03 0.0023A*B 2.60E+08 1 2.60E+08 4.56 0.0447Residual 1.20E+09 21 5.71E+07Cor Total 8.57E+09 26

Std. Dev. 7553.80 R-Squared 0.86Mean 29161.60 Adj R-Squared 0.83C.V. 25.90 Pred R-Squared 0.77

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Predicted Response: Inverse Squared of the Predicted Response: Inverse Squared of the Axle Pitch Rotation (Spring Wrap-Up Mode)Axle Pitch Rotation (Spring Wrap-Up Mode)

DESIGN-EXPERT Plot

(Std. Dev . - Axle Wrap-Up) -̂2.2X = A: Friction Coef f icientY = B: Pad Stif f ness

Actual FactorC: Bushing Stif f ness = 55000.00

7388.71

18755.9

30123

41490.1

52857.3

(St

d. D

ev. -

Axle

Wra

p-Up

)̂-2

.2

0.20

0.25

0.30

0.35

0.40

100000.00

325000.00

550000.00

775000.00

1000000.00

A: Friction Coefficient

B: Pad Stiffness

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Sample Results: Effect of Friction on Brake Sample Results: Effect of Friction on Brake Noise FrequencyNoise Frequency

Time History

Frequency Spectrum

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ConclusionConclusion

• A simple multi-body dynamics model was developed to simulate low-frequency disc brake noise

• The assumed mechanism for noise generation is the friction-induced mode coupling (axle wrap-up mode and caliper transverse mode)

• Rigid body models (with a few flexible components) are sufficient to simulate the low-frequency noise

• Designed numerical experiments show that the primary design parameter is the brake pad stiffness

• Modeling of brake squeal will require FE model of brake rotor in order to capture nodal diameter modes