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Chapter 2: Fundamentals of Vehicle Mechanics

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1. Rotation: Ψ Yaw Angle

2. Rotation: Θ Pitch Angle

3. Rotation: φ Angle of Roll

(XE,YE,ZE)Inertial Coordinate system

(X,Y,Z)Horizontal coordinate system

(XV,YV,ZV)Vehicle fixed Coordinate

system

2.1 Longitudinal Dynamics of the Vehicle I

vz Z,Ez

vy

y

Eyx

vx

Ex

ψ

θ

ϕθ

ψ

ψ θ

ϕ

Direction of travel

ϕ

Coordinate Systems

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2.1 Longitudinal Dynamics of the Vehicle II

Refer lecture “Mechatronik”bzw. “Computergestützte Verfahren”

HebenGieren

Nicken

SchiebenZucken

WankenRollen

X Y

Z

VX VY

VZ

ϕ

ψ

θ

LiftYaw

Pitch

Lateral PushJerk

Roll

For representing spatial motions in rigid bodies:

Rigid body Motions of a Vehicle Chassis

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2.1 Longitudinal Dynamics of the Vehicle III

Longitudinal Dynamics:Planar Motion in the x,z-plane

Fahrtrichtung

vordereNickachse

hintereNickachse

Direction of travel

Front BackPitch Axis Pitch Axis(Nickachse) Nickachse

Anti-Dive System of a Motor Vehicle

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2.1 Longitudinal Dynamics of the Vehicle IV

Direction of travel

Pitch pole

Pitchpole

Braking

Acceleration/Starting

Pitch pole of the chassis

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2.2 Lateral Dynamics of Vehicles I

2.2 Querdynamik von Fahrzeugen I

Ψ – Yaw Angle (XE,XV)

β - Side Slip Angle (Xν,ν)

ν – Tracking angle = Ψ - β

Direction of travelEY

EX

VY

VX

βa

A

lδ

rδ

βv

ψ

ν

All angles are respresented inthe positive direction.

(XE,YE,ZE) Inertial Coordinate

System

(XV,YV,ZV) Vehicle Coordinate

System

Motion Parameters for Lateral Dynamics

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2.2 Lateral Dynamics of Vehicles II

Instantaneous Centre (Momentanpol) hRβ+αh h90 α−o

hvhl

l

hα

R

vR

v

SP

vv

δ

β

vα

)( hv α−α−δ

β Side Slip Angle

αν,αh Slip angle

δ Steering Angle

δ - (αν - αh) Ackermann steering angle

Definition of the Ackermann Steer Angle (based on the Single-Track model)

.

.

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2.2 Lateral Dynamics of Vehicles III

Understeer Gradient of Motor Vehicles

vα vα

vαhα hα hα

M M M

hv

Neutral Understeer Oversteer

hv hvvv vv

vv

αV = αh αV > αh αV < αh

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2.2 Lateral Dynamics of Vehicles IV

Understeer gradient by equal statistical steering sensitivity.

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2.3 Parameters of Wheel Position I

Fahrtrichtung

B

C

Y

XV

V

Felgenhorn

δVSδVS

s

γ

VY

VZ vsδ vsδ

Bs

C

VY

VX

Direction of TravelRim Flange/Rim Edge

Camber Angle γ :The tilt of the wheel plane away from the vertical (z-Richtung); the camber angle issaid to be positive if the wheel tilts away from the vehicle at the top.

Track Width s , Toe-in/ Toe-out:The track width is defined as the distancebetween the wheel contact points of an axle.The track describes the difference of the distances between the rim flanges (B-C), thedistance being measured at the wheel centre height. A toe-in exists when the wheel is directed to the vehicle centre at thefront (B>C).

Wheel Parameters I

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2.3 Parameters of Wheel Position II

Wheel Parameters II

Transverse Offset at Ground rr :It is the distance between the intersection of the kingpin axis with the track and the point of contact of the wheel on the track, measured along theplane of the track. If A lies within the track: rr>0

Kingpin Inclination angle σ :It is the projection of the angle formed between the vertical and the line passing through the steering axis measured in they-z plane; the rotating axle of the steering knukle pivot is also called the Kingpinaxle.

Lenkachse Lenkachse

rr

A

VY

VZ

VY

VZ

σ

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2.3 Parameters of Wheel Position III

Castor n :Distance between the point of intersection of the axis of the steering knuckle with the track and the point of contact of the wheel, projected on the x-z plane. It is assumed tobe negative if the intersecting point is infront the wheel contact point measured along the x axis. In the given case, it is said to be a negative castor (Vorlauf).

Direction of travel

τ

E D

nln

vX

vZ

Wheel Parameters III