Modeling tire vibrations in ABS-braking - Aaltoatuonone/files/Aachen_chassis_days_2012.pdf ·...
Transcript of Modeling tire vibrations in ABS-braking - Aaltoatuonone/files/Aachen_chassis_days_2012.pdf ·...
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Modeling tire vibrations in ABS-braking
Ari Tuononen Aalto University
Lassi Hartikainen, Frank Petry, Stephan WestermannGoodyear S.A.
Tag des Fahrwerks 8. Oktober 2012
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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
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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
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Review on Rigid Ring Model (RRM)
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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
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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 )
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Resonant frequencies in car and test rig boundary conditions
CarTest rig
MyMy
MyMy
Boundary conditions affect resonant frequencies
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Vibration mode shapes - Vertical
Road input 13 Hz Road input 77 Hz
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Vibration mode shapes – Long. & torsional
Moment input 11 Hz Moment input 36 Hz Moment input 68 Hz
In-phase Anti-phase
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Light gate detector
Force hub
Brake robot
GPS antenna
Wheel speed sensorsBrake pressure sensors
Vehicle instrumentation and cleat dimensions
Cleat 20x35mm zx
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Results
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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
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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
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Tire vibrations in ABS braking -measurement
Force hub longitudinal signal (complete braking event)One ABS cycle
80Hz frequency excited during braking
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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
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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
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ABS braking simulations on rough road
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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
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ABS braking simulation on smooth roadSome Fz variation due to velocity and amplitudedependent sidewall stiffnesses
Rim Fx shows ABS control cycles• No strong vibrations
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ABS braking simulation with road excitation (77Hz, 0.25mm)
Fz resonates
Fx cross talk during high force
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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
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Measurement results from ABS braking
Force hub longitudinal force signal and its spectrogram
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Fx – Fz 78Hz crosstalk during braking
Slip ratio [-]
F x
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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
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Thank you for your attention
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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
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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