Modeling tire vibrations in ABS-braking Ari Tuononen Aalto University Lassi Hartikainen, Frank Petry, Stephan Westermann Goodyear S.A. Tag des Fahrwerks 8. Oktober 2012
Contents 1. Introduction 2. Review on Rigid Ring Model (RRM) 3. Results 1. Tire vibrations Cleat excitation 2. Tire vibrations ABS braking 3. Tire vibrations Comparison to model 4. Parameter identification sequence 5. ABS braking simulations on rough road 1. Influence on vibration modes in braking compared to free rolling 2. Arising crosstalk F z F x 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 tests 2. 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 Friction model acting point Tread relaxation length
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 avoided Velocity dependency not properly captured Load non-linearity captured in an approximate manner (a certain steady state F x results in a certain F z )
Tire radii Unloaded radius in static conditions without load Circumference / 2 Loaded radius wheel center distance from road Function of load and velocity Effective rolling radius V x / Function of load and velocity Brake lever arm M y /F x Can be approximated with the effective rolling radius r e
Extended model with suspension Car body ~ 1 Hz Mass of quarter car Rim & Ring: In phase mode 35 Hz Anti-phase mode 70Hz Rim longitudinal ~ 12 Hz M y Wheel hop ~ 10 Hz Ring vertical 75Hz
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
Resonant frequencies in car and test rig boundary conditions Test rig Car M y M y Boundary conditions affect resonant frequencies
Vehicle instrumentation and cleat dimensions Light gate detector Brake robot GPS antenna Cleat 20x35mm z x Force hub Wheel speed sensors Brake pressure sensors
Results
Vehicle cleat test measurement results 2000 Wheel hop mode Longitudinal suspension mode Fx [N] 0-2000 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Vertical belt mode Fy [N] 100 0-100 -200 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 6000 Fz [N] 4000 2000 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 My [Nm] Wheel acceleration [deg/s] 100 0-100 -200 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 x 10 4 6 4 2 0-2 -4 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Time [s] In-phase mode Anti-phase mode
Vehicle cleat test measurement results - Influence of velocity Anti-phase mode not excited for 40km/h Velocity decreases the inphase mode amplitude Velocity does not affect the peak frequencies (in these measurements) In-phase mode Anti-phase mode Parameters presented in this paper are derived from the 78km/h measurements for 2.3 bar inflation pressure.
Tire vibrations in ABS braking - measurement One ABS cycle Force hub longitudinal signal (complete braking event) 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 F x
Parameter identification sequence 1. Tire component weighing Mass & inertia of the rigid ring 2. K&C test (if needed) Vehicle suspension parameters 3. Vertical deflection measurement Overall tire stiffness Contact length 4. Coast-down test Effective rolling radius Velocity dependency of the loaded radius 5. Brake ramp test Steady state Pacejka parameters (B,C,D,E) Rim mass (wheel hop) 6. Cleat test resonant frequencies Translational stiffness (vertical rigid ring mode) Rim inertia (in-phase and anti-phase) Rotational stiffness (mainly anti-phase mode) 7. Cleat test time domain comparison (measurement vs. simulation) Damping parameters
ABS braking simulations on rough road
Simulation setup Rigid ring model About influence of road roughness on ABS braking 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 F z F x during braking
ABS braking simulation on smooth road Some F z variation due to velocity and amplitude dependent sidewall stiffnesses Rim F x shows ABS control cycles No strong vibrations
F z resonates ABS braking simulation with road excitation (77Hz, 0.25mm) F x cross talk during high force
ABS braking simulation with road excitation (white noise, 0.56mm RMS) F z looks random, weak resonance exists Cross-talk to F x reduced Strongest F x vibration at belt mode, not at in-phase or antiphase modes Strongest cross-talk during high F x
Measurement results from ABS braking Force hub longitudinal force signal and its spectrogram
Fx Fz 78Hz crosstalk during braking F x Slip ratio [-]
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 ABSbraking tests are comparable In-phase mode suppressed under high tire force levels Vertical rigid ring mode resonance may result in F x vibrations may increase braking distance
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