Modeling tire vibrations in ABS-braking

Ari Tuononen Aalto University

Lassi Hartikainen, Frank Petry, Stephan WestermannGoodyear S.A.

Tag des Fahrwerks 8. Oktober 2012

Contents

1. Introduction2. Review on Rigid Ring Model (RRM)3. Results

1. Tire vibrations – Cleat excitation2. Tire vibrations – ABS braking3. Tire vibrations – Comparison to model

4. Parameter identification sequence5. ABS braking simulations on rough road

1. Influence on vibration modes in braking compared to free rolling2. Arising crosstalk Fz → Fx during braking

6. Conclusions

Introduction

Tire vibrations are excited during ABS-braking– High frequency brake pressure variations are transmitted to the wheel torque

without damping (Zanten 1989) – Rigid Ring Model (RRM) was developed to simulate dynamic response of the tire

(Zegelaar 1998)– The RRM as a suspension part changes tire vibration mode shapes (Schmeitz

2004)

1. Rigid Ring Model requires a lot of additional parameters– Typically parameters are obtained in dedicated test-rigs– Pacejka model with a longitudinal relaxation length is a more attractive option,

even if it does not include e.g. belt inertia effect

2. Published ABS braking simulation studies often assume a smooth road and neglect the belt inertia, even if the road roughness can significantly excite tire resonances

In this study:1. How in-plane RRM parameters can be obtained from simple instrumented

vehicle tests2. Shows that road roughness can significantly influence braking forces

Review on Rigid Ring Model (RRM)

Rigid ring model (Zegelaar 1998)

Undeformable ring• rotation• longitudinal motion• vertical motion

Rim• rotation• longitudinal motion(depends on boundary condition)

• vertical motion(depends on boundary condition)

Rim and Ring connected with spring damper pairs• Torsional• Longitudinal• Vertical

Vertical residual spring Tread relaxation length

Friction model acting point

Friction model

• A simple 4-parameter Magic Formula– Lateral force and combined slip not included, but they may have

significant influence on overall braking performance

• Parameters estimated from brake ramp test– A realistic road surface was the key criteria

Brake ramp test:• Brake pressure increased smoothly

→ Tire steady state behavior→ Elasto-kinematic effect to κ avoided

• Velocity dependency not properly captured• Load non-linearity captured in an approximate manner (a certain steady state Fx results in a certain Fz )

Resonant frequencies in car and test rig boundary conditions

CarTest rig

MyMy

MyMy

Boundary conditions affect resonant frequencies

Vibration mode shapes - Vertical

Road input 13 Hz Road input 77 Hz

Vibration mode shapes – Long. & torsional

Moment input 11 Hz Moment input 36 Hz Moment input 68 Hz

In-phase Anti-phase

Light gate detector

Force hub

Brake robot

GPS antenna

Wheel speed sensorsBrake pressure sensors

Vehicle instrumentation and cleat dimensions

Cleat 20x35mm zx

Results

Vehicle cleat test measurement results

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3-2000

0

2000

Fx [N

]

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

-200-100

0100

Fy [N

]

0.6 0.7 0.8 0.9 1 1.1 1.2 1.32000

4000

6000

Fz [N

]

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

-200-100

0100

My

[Nm

]

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3-4-20246

x 104

Whe

el a

ccel

erat

ion

[deg

/s]

Time [s]

Wheel hop modeLongitudinal suspension mode

In-phase mode

Vertical belt mode

Anti-phase mode

Vehicle cleat test measurement results - Influence of velocity

• Anti-phase mode not excited for 40km/h

• Velocity decreases the in-phase mode amplitude

• Velocity does not affect the peak frequencies (in these measurements)

Parameters presented in this paper are derived from the 78km/h measurements for 2.3 bar inflation pressure.

Anti-phase mode

In-phase mode

Tire vibrations in ABS braking -measurement

Force hub longitudinal signal (complete braking event)One ABS cycle

80Hz frequency excited during braking

Comparison of measurement and model outputs

• Cleat – 3 clear modes

• ABS– Spectrum

amplitude not comparable to the cleat

– In-phase mode suppressed for the measurement and the simulation

PSD of Fx

Parameter identification sequence

1. Tire component weighing

2. K&C test (if needed)

3. Vertical deflection measurement

4. Coast-down test

5. Brake ramp test

6. Cleat test resonant frequencies

7. Cleat test time domain comparison (measurement vs.

simulation)

Mass & inertia of the rigid ring

Vehicle suspension parameters

Damping parameters

Rim inertia (in-phase and anti-phase)

Steady state Pacejka parameters (B,C,D,E)

Effective rolling radius

Overall tire stiffness

Velocity dependency of the loaded radius

Rotational stiffness (mainly anti-phase mode)

Translational stiffness (vertical rigid ring mode)

Rim mass (wheel hop)

Contact length

ABS braking simulations on rough road

About influence of road roughness on ABS braking

• Simulation setup– Rigid ring model– No load transfer or suspension– ABS controller tuned to produce typical control cycles

• Smooth road and rough road compared in simulations• Measurement results on wet and dry asphalt• Impact of crosstalk Fz → Fx during braking

ABS braking simulation on smooth roadSome Fz variation due to velocity and amplitudedependent sidewall stiffnesses

Rim Fx shows ABS control cycles• No strong vibrations

ABS braking simulation with road excitation (77Hz, 0.25mm)

Fz resonates

Fx cross talk during high force

ABS braking simulation with road excitation (white noise, 0.56mm RMS)

Fz looks random, weak resonance exists

Cross-talk to Fx reduced

• Strongest Fx vibration at belt mode, not at in-phase or anti-phase modes• Strongest cross-talk during high Fx

Measurement results from ABS braking

Force hub longitudinal force signal and its spectrogram

Fx – Fz 78Hz crosstalk during braking

Slip ratio [-]

F x

Conclusions

• It is possible to derive RRM parameters from instrumented vehicle measurements

– A parameter identification sequence was identified

• Effect of longitudinal rim motion is essential– Changes vibration mode shapes and frequencies compared to test rig (fixed rim)

case

• The identified resonant frequencies from vehicle cleat and ABS-braking tests are comparable

– In-phase mode suppressed under high tire force levels

• Vertical rigid ring mode resonance may result in Fx vibrations→ may increase braking distance

Thank you for your attention

Extended model with suspension

Rim longitudinal ~ 12 Hz

Car body ~ 1 Hz

My

Ring vertical 75Hz

Mass of quarter car

Wheel hop ~ 10 Hz

Rim & Ring:In phase mode 35 HzAnti-phase mode 70Hz

Tire radii

• Unloaded radius – in static conditions without load– Circumference / 2π

• Loaded radius – wheel center distance from road– Function of load and velocity

• Effective rolling radius – Vx/Ω– Function of load and velocity

• Brake lever arm – My/Fx– Can be approximated with the effective rolling radius re