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