This document summarizes a study that developed a simple multi-body dynamics model to simulate low-frequency disc brake noise. The model treats the brake assembly as rigid bodies and assumes noise is generated through friction-induced coupling of the axle wrap-up and caliper transverse vibration modes. A numerical experiment was conducted varying pad stiffness, friction coefficient, and bushing stiffness. The results showed that pad stiffness was the primary factor affecting noise, with higher stiffness correlated to greater vibration amplitude. The model provides a method for exploring the effects of design parameters on brake noise propensity.

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

2. 2
SAE Noise and Vibration Conference
May 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)

3. 3
SAE Noise and Vibration Conference
May 15-17, 2007
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
e
nn kF δ*= e
nf kF δµ **=
)2/()2sin( nkK∆>γ µγ =)tan(

4. 4
SAE Noise and Vibration Conference
May 15-17, 2007
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

5. 5
SAE Noise and Vibration Conference
May 15-17, 2007
ADAMS Model (Disc Brake Assembly)ADAMS Model (Disc Brake Assembly)

6. 6
SAE Noise and Vibration Conference
May 15-17, 2007
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

7. 7
SAE Noise and Vibration Conference
May 15-17, 2007
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

8. 8
SAE Noise and Vibration Conference
May 15-17, 2007
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 0.0074
2 10000 100000 0.3 0.0209 0.0075
3 10000 100000 0.4 0.0264 0.0082
4 10000 550000 0.2 0.0364 0.0074
5 10000 550000 0.3 0.0503 0.0084
6 10000 550000 0.4 0.0435 0.0094
7 10000 1000000 0.2 0.3807 0.0359
8 10000 1000000 0.3 0.0540 0.0087
9 10000 1000000 0.4 0.1540 0.0190
10 55000 100000 0.2 0.0180 0.0073
11 55000 100000 0.3 0.0217 0.0078
12 55000 100000 0.4 0.0230 0.0084
13 55000 550000 0.2 0.0364 0.0075
14 55000 550000 0.3 0.0544 0.0089
15 55000 550000 0.4 0.0408 0.0093
16 55000 1000000 0.2 0.3586 0.0312
17 55000 1000000 0.3 0.3584 0.0436
18 55000 1000000 0.4 0.0553 0.0115
19 100000 100000 0.2 0.0188 0.0073
20 100000 100000 0.3 0.0231 0.0079
21 100000 100000 0.4 0.0237 0.0085
22 100000 550000 0.2 0.0340 0.0076
23 100000 550000 0.3 0.0358 0.0088
24 100000 550000 0.4 0.0464 0.0105
25 100000 1000000 0.2 0.3553 0.0281
26 100000 1000000 0.3 0.3803 0.0329
27 100000 1000000 0.4 0.6265 0.0622

9. 9
SAE Noise and Vibration Conference
May 15-17, 2007
ANOVA Table: Inverse of the VibrationANOVA Table: Inverse of the Vibration
Amplitude of the Caliper (Side-to-Side Mode)Amplitude of the Caliper (Side-to-Side Mode)
Sum of Mean F
Source Squares DF Square Value Prob > F
Model 7347.51 6 1224.59 54.70 < 0.0001
A - Friction Coeff 41.13 1 41.13 1.84 0.1904
B - Pad Stiffness 7030.79 1 7030.79 314.07 < 0.0001
C - Bushing Stiffness 0.74 1 0.74 0.03 0.8577
A*B 189.91 1 189.91 8.48 0.0086
A*C 14.33 1 14.33 0.64 0.4330
B*C 70.60 1 70.60 3.15 0.0910
Residual 447.73 20 22.39
Cor Total 7795.24 26
Std. Dev. 4.73 R-Squared 0.94
Mean 25.63 Adj R-Squared 0.93
C.V. 18.46 Pred R-Squared 0.90

10. 10
SAE Noise and Vibration Conference
May 15-17, 2007
Predicted Response: Inverse of the VibrationPredicted Response: Inverse of the Vibration
Amplitude of the Caliper (Side-to-Side Mode)Amplitude of the Caliper (Side-to-Side Mode)
3.40172
15.2726
27.1435
39.0143
50.8852
1.0/(Std.Dev.-CaliperDisp.)
0.20
0.25
0.30
0.35
0.40
100000.00
325000.00
550000.00
775000.00
1000000.00
A: Friction C oefficient
B: Pad Stiffness

11. 11
SAE Noise and Vibration Conference
May 15-17, 2007
ANOVA Table: Inverse Squared of the AxleANOVA Table: Inverse Squared of the Axle
Pitch Rotation (Spring Wrap-Up Mode)Pitch Rotation (Spring Wrap-Up Mode)
Sum of Mean F
Source Squares DF Square Value Prob > F
Model 7.37E+09 5 1.47E+09 25.85 < 0.0001
A - Friction Coeff. 3.69E+08 1 3.69E+08 6.47 0.0189
B - Pad Stiffness 5.88E+09 1 5.88E+09 103.09 < 0.0001
C - Bushing Stiffness 1.76E+08 1 1.76E+08 3.09 0.0934
B*B 6.87E+08 1 6.87E+08 12.03 0.0023
A*B 2.60E+08 1 2.60E+08 4.56 0.0447
Residual 1.20E+09 21 5.71E+07
Cor Total 8.57E+09 26
Std. Dev. 7553.80 R-Squared 0.86
Mean 29161.60 Adj R-Squared 0.83
C.V. 25.90 Pred R-Squared 0.77

12. 12
SAE Noise and Vibration Conference
May 15-17, 2007
Predicted Response: Inverse Squared of thePredicted Response: Inverse Squared of the
Axle Pitch Rotation (Spring Wrap-Up Mode)Axle Pitch Rotation (Spring Wrap-Up Mode)
7388.71
18755.9
30123
41490.1
52857.3
(Std.Dev.-AxleWrap-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 C oefficient
B: Pad Stiffness

13. 13
SAE Noise and Vibration Conference
May 15-17, 2007
Sample Results: Effect of Friction on BrakeSample Results: Effect of Friction on Brake
Noise FrequencyNoise Frequency
Time History
Frequency Spectrum

14. 14
SAE Noise and Vibration Conference
May 15-17, 2007
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