The Dynamics of Road Vehicles Werner Krantz Workshop „Piloten- / Fahrermodelle“ Manching, 10./11. Mai 2011

Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Introduction Driving Dynamics – Basics and Models Driving Characteristics

Control Systems Driver-Vehicle Interaction Summary

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Introduction

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Introduction

Demands on the Driving Characteristics: The vehicle‘s control response shall be reasonable, adequate and predictable. It shouldn’t overburden the driver or put an unneeded workload on him. The vehicle’s stability limit shall be perceptible early enough. The response to disturbances (ambient winds, road irregularities) shall always be moderate. In case compensatory steering action is required from the driver, this should be perceptible early and in a distinct way. Variations in the driving dynamics characteristics because of loading, tire and road properties, etc. should be as small as possible.

 Ride comfort  Active driving safety

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Introduction

Driving Characteristics Development: Large number of open-loop criteria Closed-loop evaluation by expert drivers  Correlation to customer’s subjective assessment Closed-loop evaluation in simulation requires driver models and assessment criteria

Quelle: Mitschke, M., Wallentowitz, H.: Dynamik der Kraftfahrzeuge Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Driving Dynamics – Basics and Models

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Driving Dynamics – Basics and Models

Side Force Generation Mechanism

Fy vT

vV v C =

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Fy

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Driving Dynamics – Basics and Models

Side Force Generation Mechanism

Fy v

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Driving Dynamics – Basics and Models vx

’Spring’

Yawing dynamics vx

’Damper’ vy

Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Driving Dynamics – Basics and Models

Full vehicle

Steering system Compliance

Bicycle model

Fy

F

Steering

Axle (concept dependent)

F

Fy

Elastokinematics Roll steer

Overall cornering stiffness



CG

Axle

Left tire SideRight forcetire Fy stiffness Side force Fy stiffness Fz

R Fz

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Driving Dynamics – Basics and Models

Detailed MBS Model

Detailed dynamics Body motion

~ 1 to 3 Hz

(with flexible body) ~ 30 Hz Engine

~ 8 Hz

Unsprung mass

~ 12 Hz

Detailed nonlinearities

Kinematics / elastokinematics Friction (steering / damper) Power steering assist force Tire  Conceptual design

 Characteristics development  Large parameterization effort

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Driving Dynamics – Basics and Models

(Linear) Bicycle Model

Simple modeling approach 2 DOF in the road plane

F

Minimum set of parameters (7 lateral dyn., 3 aerodyn.) Parameterization from simulation or road test data Linear model valid up to approximately 0.4 g



CG

 Basic analysis  Control system design

R

Other modeling approaches: Enhanced single track models 5-mass models

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Driving Characteristics

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Driving Characteristics

A

lF

lR r

lF

lR

r Steady state cornering, ay

P

0

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Driving Characteristics

A

EG a y

FFF

EG:R C Steering l F C Gradient lR , Neutral steer:Self F EG > 0: Understeer C steer lR , Understeer: EGC= 0:l FNeutral F R Oversteer:

F

R

F

R

EG < 0: Oversteer C

EG

F

lF

m (C ( lF

C

R

R

lR ,

lR C

lR ) C

F

F

F

C

R

lF ) R

R

r

P

Steady state cornering, ay > 0 Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Driving Characteristics

Steering angle

Yaw rate Steering angle

Steady State Vehicle Response

EG = 0 (Neutral steer) A

Max. steady state yaw gain EG > 0 (Understeer)

vcrit

Lateral acc. ay

Critical Velocity vcrit

( lF m (C

lF

vcrit

Velocity v

Characteristic Velocity

l R )2 C F

vch

C

F

C

R

R

lR )

Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

vch

( lF m (C

l R )2 C R

C

F

lR C

F

R

lF )

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Driving Characteristics

Magnitude of frequency response of lateral acceleration due to steering wheel angle [m/s²rad]

Magnitude of frequency response of yaw rate due to steering wheel angle [1/s]

Dynamic Vehicle Response

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 Limited accuracy of 2 DOF bicycle model

Frequency response criteria: Yaw damping (overshoot) Amplitude response drop at higher frequencies Phase margin

…

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Driving Characteristics

Dynamic Vehicle Response T  ,max

Peak-Response-Time

T  ,max

SW ,0

1

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2

 ay = 4 m/s²

SW ,0

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Driving Characteristics

Driving Characteristics Development: Large number of open-loop criteria Closed-loop evaluation by expert drivers  Correlation to customer’s subjective assessment Closed-loop evaluation in simulation requires driver models and assessment criteria

Quelle: Mitschke, M., Wallentowitz, H.: Dynamik der Kraftfahrzeuge Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Control Systems

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Control Systems

Linear region (up to 4 m/s²): ‘Normal driving’ Lateral / longitudinal dynamics usually controlled by driver only

 Latest assistance systems: Lane keeping Crosswind compensation Vertical dynamics: CDC, ABC

High lateral acceleration levels: Highly nonlinear behavior

Fy

Rear axle Rear axle * E.g. with 50:50 load distribution

Saturation of tire forces Possible loss of controllability / spinout

Front axle

 Electronic Stability Control  Wheel slip control (ABS, ASR)

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Control Systems

ESC (Electronic Stability Control)

CG

Oversteer:  brake front outer wheel Understeer:  brake rear inner wheel

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Control Systems

Trajectory Control Nonlinear ‘virtual test driver’  Autonomous testing  Future crash avoidance systems?

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Driver-Vehicle Interaction

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Driver-Vehicle Interaction

Navigation level

Path planning

Velocity planning

Lateral control

Longitudinal control

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Guidance level

Stabilization level

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Driver-Vehicle Interaction

Driver Model Partly conscious to the driver

Not conscious to the driver

Preview time Effective delay time  Control performance  Workload  Subjective evaluation Quelle: Donges, E. in Winner, H., Hakuli, S., Wolf, G.: Handbuch Fahrerassistenzsysteme Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

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Driver-Vehicle Interaction

Crosswind Compensation: Processing of near field / far field information

,  , 

y ,v y , a y

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Driver-Vehicle Interaction

Closed-loop Yaw Response to Crosswind

2 vres

2.5

Magnitude of frequency response of yaw rate to wind excitation [10-4 s/m²]



With driver

Without driver

2.0



1.5

2 vres

max

1.0



2 vres 2 vres max

0.5 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Frequency [Hz]

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Driver-Vehicle Interaction

Driver-Vehicle Interaction under Natural Crosswind

+ Objective assessment criteria

 , ,...

Closed loop system model

SW

Virtual driver • Realistic control behavior • Realistic adaptation to different vehicles

Digital design process Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart

Vehicle model

• Accurate lateral dynamics • Accurate aerodynamics RESEARCH IN MOTION

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Summary

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Summary Large number of open-loop criteria for a vehicle’s driving characteristics

Closed-loop evaluation is done by expert drivers  Correlation to customer’s subjective assessment The driver is in full control of the vehicle motion in the road plane  full responsibility

In critical situations control systems assist the driver by maintaining vehicle controllability Latest assistance systems also aim on increasing ride comfort (reducing workload) during normal driving

Appropriate driver models and assessment criteria would allow evaluating general driving characteristics as well as assistance systems in simulation

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