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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