automobile engg. notes

8/12/2019 automobile engg. notes

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7.2 Steady State Cornering

wherem denotes the mass of the vehicle, Fx1,Fx2,Fy1,Fy2 are the resulting forces in longitu-dinal and vertical direction applied at the front and rear axle, andspecifies the average steerangle at the front axle.

The engine torque is distributed by the center differential to the front and rear axle. Then, in

steady state condition we obtain

Fx1=k FD and Fx2= (1 k) FD, (7.43)

whereFD is the driving force and by k different driving conditions can be modeled:

k= 0 rear wheel drive Fx1= 0, Fx2=FD

0< k 0 is needed to overcome the cornering resistanceof the vehicle.

7.2.2 Overturning Limit

The overturning hazard of a vehicle is primarily determined by the track width and the height

of the center of gravity. With trucks however, also the tire deflection and the body roll have to

be respected., Fig. 7.7.

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7 Lateral Dynamics

m g

m ay

12

h2

h1

s/2 s/2FzL

FzR

FyL FyR

Figure 7.7: Overturning hazard on trucks

The balance of torques at the height of the track plane applied at the already inclined vehicle

results in

(FzL FzR)s

2 = m ay(h1+h2) + m g [(h1+h2)1+h22], (7.47)

whereay describes the lateral acceleration, m is the sprung mass, and small roll angles of theaxle and the body were assumed,11,21.

On a left-hand tilt, the right tire raises

FTzR = 0, (7.48)

whereas the left tire carries the complete vehicle weight

FTzL = m g . (7.49)

Using Eqs. (7.48) and (7.49) one gets from Eq. (7.47)

aTyg

=

s

2h1+h2

T1

h2h1+h2

T2

. (7.50)

The vehicle will turn over, when the lateral accelerationay rises above the limitaTy. Roll of axle

and body reduce the overturning limit. The angles T1 andT2 can be calculated from the tire

stiffnesscRand the roll stiffness of the axle suspension.

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If the vehicle drives straight ahead, the weight of the vehicle will be equally distributed to both

sides

FstatzR = FstatzL =

1

2

m g . (7.51)

With

FTzL = FstatzL + Fz (7.52)

and Eqs. (7.49), (7.51), one obtains for the increase of the wheel load at the overturning limit

Fz = 1

2m g . (7.53)

Then, the resulting tire deflection follows from

Fz = cRr , (7.54)

wherecR is the radial tire stiffness.

Because the right tire simultaneously rebounds with the same amount, for the roll angle of the

axle

2r = s T1 or

T1

= 2r

s =

m g

s cR(7.55)

holds. In analogy to Eq. (7.47) the balance of torques at the body applied at the roll center of

the body yields

cW 2 = m ayh2 + m g h2(1+2), (7.56)

wherecWnames the roll stiffness of the body suspension. In particular, at the overturning limitay =aTy

T2

=aTyg

mgh2cWmgh2

+ mgh2

cWmgh2T1 (7.57)

applies. Not allowing the vehicle to overturn already at aTy = 0 demands a minimum of rollstiffnesscW > c

minW =mgh2. With Eqs. (7.55) and (7.57) the overturning condition Eq. (7.50)

reads as

(h1+h2)aTyg

= s

2 (h1+h2)

1

cR h2

aTyg

1

cW 1 h2

1

cW 1

1

cR, (7.58)

where, for abbreviation purposes, the dimensionless stiffnesses

cR = cRm g

s

and cW = cWm g h2

(7.59)

have been used. Resolved for the normalized lateral acceleration

aTyg

=

s

2

h1+h2+ h2

cW 1

1

cR(7.60)

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7 Lateral Dynamics

0 10 200

0.1

0.2

0.3

0.4

0.5

0.6

normalized roll stiffness cW*

0 10 200

5

10

15

20

T T

normalized roll stiffness cW*

overturning limit ay roll angle =1+2

Figure 7.8: Tilting limit for a typical truck at steady state cornering

remains.

At heavy trucks, a twin tire axle may be loaded with m= 13000 kg. The radial stiffness of onetire iscR= 800 000 N/m, and the track width can be set tos= 2 m. The valuesh1= 0.8 mandh2= 1.0mhold at maximal load. These values produce the results shown in Fig. 7.8. Even witha rigid body suspensioncW , the vehicle turns over at a lateral acceleration ofay 0.5g.Then, the roll angle of the vehicle solely results from the tire deflection.

At a normalized roll stiffness ofcW = 5, the overturning limit lies atay 0.45 gand so reachesalready90% of the maximum. The vehicle will turn over at a roll angle of = 1+2 10

then.

7.2.3 Roll Support and Camber Compensation

When a vehicle drives through a curve with the lateral acceleration ay, centrifugal forces willbe applied to the single masses. At the simple roll model in Fig. 7.9, these are the forces mAayandmRay, wheremAnames the body mass andmR the wheel mass.

Through the centrifugal force mAay applied to the body at the center of gravity, a torque isgenerated, which rolls the body with the angle A and leads to an opposite deflection of thetiresz1= z2.

At steady state cornering, the vehicle forces are balanced. With the principle of virtual work

W = 0, (7.61)

the equilibrium position can be calculated.

At the simple vehicle model in Fig. 7.9 the suspension forcesFF1,FF2and tire forcesFy1,Fz1,Fy2,Fz2, are approximated by linear spring elements with the constantscAandcQ,cR. The work

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FF1

z1 1

y1

Fy1Fz1

S1

Q1

zA A

yA

b/2 b/2

h0

r0

SA

FF2

z2 2

y2

Fy2Fy2

S2

Q2

mA ay

mRay mRay

Figure 7.9: Simple vehicle roll model

Wof these forces can be calculated directly or using W = V via the potentialV. At smalldeflections with linearized kinematics one gets

W = mAayyA

mRay (yA+hRA+y1)2 mRay (yA+hRA+y2)

2

12cAz21 12cAz22

12cS (z1 z2)

2

12cQ (yA+h0A+y1+r01)

2 12cQ (yA+h0A+y2+r02)

2

12cR

zA+

b2A+z1

2 1

2cR

zA

b2A+z2

2,

(7.62)

where the abbreviationhR=h0 r0has been used, andcSdescribes the spring constant of theanti roll bar, converted to the vertical displacement of the wheel centers.

The kinematics of the wheel suspension are symmetrical. With the linear approaches

y1 = yz

z1, 1 = z

1 and y2 = yz

z2, 2 = z

2 (7.63)

the workWcan be described as a function of the position vector

y = [yA, zA, A, z1, z2]T . (7.64)

Due to

W =W(y) (7.65)

the principle of virtual work Eq. (7.61) leads to

W = W

y

y = 0. (7.66)

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7 Lateral Dynamics

Because ofy= 0, a system of linear equations in the form of

K y = b (7.67)

results from Eq. (7.66). The matrixKand the vectorb are given by

K=

2 cQ 0 2 cQh0yQ

z cQ

yQ

z cQ

0 2 cR 0 cR cR

2 cQh0 0 cb2

cR+h0yQ

z cQ

b2

cRh0yQ

z cQ

yQ

z cQ cR

b2

cR+h0yQ

z cQ c

A+cS+ cR cS

yQ

z cQ

cR b

2

cRh0

yQ

z cQ

cS

cA

+cS

+ cR

(7.68)

and

b =

mA+ 2 mR

0

(m1+m2) hR

mRy/z

mRy/z

ay. (7.69)

The following abbreviations have been used:

yQ

z = y

z+r0

z

, cA = cA+cQ

yz

2, c = 2 cQh

20+ 2 cR

b2

2. (7.70)

The system of linear equations Eq. (7.67) can be solved numerically, e.g. with MATLAB. Thus,

the influence of axle suspension and axle kinematics on the roll behavior of the vehicle can be

investigated.

A

1 2

a)

roll centerroll center

A

1 20

b)

0

Figure 7.10: Roll behavior at cornering: a) without and b) with camber compensation

If the wheels only move vertically to the body at jounce and rebound, at fast cornering the

wheels will be no longer perpendicular to the track Fig. 7.10 a. The camber angles 1 > 0and2 > 0 result in an unfavorable pressure distribution in the contact area, which leads toa reduction of the maximally transmittable lateral forces. Thus, at more sportive vehicles axle

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7 Lateral Dynamics

On most passenger cars the chassis is rather stiff. Hence, front and rear part of the chassis are

forced by an internal torque to an overall chassis roll angle. This torque affects the wheel loads

and generates different wheel load differences at the front and rear axle. Due to the degressive

influence of the wheel load to longitudinal and lateral tire forces the steering tendency of avehicle can be affected.

7.3 Simple Handling Model

7.3.1 Modeling Concept

x0

y0

a1

a2

xB

yB

C

Fy1

Fy2

x2

y2

x1

y1v

Figure 7.13: Simple handling model

The main vehicle motions take place in a horizontal plane defined by the earth-fixed frame 0,Fig. 7.13. The tire forces at the wheels of one axle are combined to one resulting force. Tire

torques, rolling resistance, and aerodynamic forces and torques, applied at the vehicle, are not

taken into consideration.

7.3.2 Kinematics

The vehicle velocity at the center of gravity can be expressed easily in the body fixed framexB,yB,zB

vC,B =

v cos v sin

0

, (7.71)

wheredenotes the side slip angle, andv is the magnitude of the velocity.

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7.3 Simple Handling Model

The velocity vectors and the unit vectors in longitudinal and lateral direction of the axles are

needed for the computation of the lateral slips. One gets

ex1,B = cos sin

0

, ey1,B = sin cos

0

, v01,B = v cos v sin +a1

0

(7.72)

and

ex2,B =

10

0

, ey2,B =

01

0

, v02,B =

v cos v sin a2

0

, (7.73)

wherea1 anda2 are the distances from the center of gravity to the front and rear axle, and denotes the yaw angular velocity of the vehicle.

7.3.3 Tire Forces

Unlike with the kinematic tire model, now small lateral motions in the contact points are per-

mitted. At small lateral slips, the lateral force can be approximated by a linear approach

Fy = cSsy, (7.74)

wherecS is a constant depending on the wheel load Fz, and the lateral slip sy is defined byEq. (3.61). Because the vehicle is neither accelerated nor decelerated, the rolling condition is

fulfilled at each wheel

rD = eTx v0P . (7.75)

Here,rD is the dynamic tire radius, v0P the contact point velocity, and ex the unit vector inlongitudinal direction. With the lateral tire velocity

vy = eTy v0P (7.76)

and the rolling condition Eq. (7.75), the lateral slip can be calculated from

sy =eTy v0P

| eTxv0P |, (7.77)

withey labeling the unit vector in the lateral direction direction of the tire. So, the lateral forcesare given by

Fy1 = cS1sy1; Fy2 = cS2sy2. (7.78)

7.3.4 Lateral Slips

With Eq. (7.73), the lateral slip at the front axle follows from Eq. (7.77):

sy1 = +sin (v cos ) cos (v sin +a1 )

| cos (v cos ) + sin (v sin +a1 ) |

. (7.79)

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8 Driving Behavior of Single Vehicles

8.1 Standard Driving Maneuvers

8.1.1 Steady State Cornering

The steering tendency of a real vehicle is determined by the driving maneuver called steadystate cornering. The maneuver is performed quasi-static. The driver tries to keep the vehicle ona circle with the given radius R. He slowly increases the driving speed v and, with this alsothe lateral acceleration due ay =

v2

Runtil reaching the limit. Typical results are displayed in

Fig. 8.1.

0

20

40

60

80

lateral acceleration [g]

steeran

gle[deg]

-4

-2

0

2

4

sideslip

angle[deg]

0 0.2 0.4 0.6 0.80

1

2

3

4

rollangle[deg]

0 0.2 0.4 0.6 0.80

1

2

3

4

5

6

wheelloads[kN]

lateral acceleration [g]

Figure 8.1: Steady state cornering: rear-wheel-driven car onR= 100m

In forward drive the vehicle is understeering and thus stable for any velocity. The inclinationin the diagram steering angle versus lateral velocity decides about the steering tendency andstability behavior.

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The nonlinear influence of the wheel load on the tire performance is here used to design a vehiclethat is weakly stable, but sensitive to steer input in the lower range of lateral acceleration, andis very stable but less sensitive to steer input in limit conditions.

With the increase of the lateral acceleration the roll angle becomes larger. The overturningtorque is intercepted by according wheel load differences between the outer and inner wheels.With a sufficiently rigid frame the use of an anti roll bar at the front axle allows to increase thewheel load difference there and to decrease it at the rear axle accordingly.

Thus, the digressive influence of the wheel load on the tire properties, cornering stiffness andmaximum possible lateral force, is stressed more strongly at the front axle, and the vehiclebecomes more under-steering and stable at increasing lateral acceleration, until it drifts out ofthe curve over the front axle in the limit situation.

Problems occur at front driven vehicles, because due to the demand for traction, the front axle

cannot be relieved at will.Having a sufficiently large test site, the steady state cornering maneuver can also be carried outat constant speed. There, the steering wheel is slowly turned until the vehicle reaches the limitrange. That way also weakly motorized vehicles can be tested at high lateral accelerations.

8.1.2 Step Steer Input

The dynamic response of a vehicle is often tested with a step steer input. Methods for thecalculation and evaluation of an ideal response, as used in system theory or control technics,can not be used with a real car, for a step input at the steering wheel is not possible in practice.A real steering angle gradient is displayed in Fig. 8.2.

0 0.2 0.4 0.6 0.8 1

0

10

20

30

40

time [s]

steeringangle[deg]

Figure 8.2: Step Steer Input

Not the angle at the steering wheel is the decisive factor for the driving behavior, but the steeringangle at the wheels, which can differ from the steering wheel angle because of elasticities,friction influences, and a servo-support. At very fast steering movements, also the dynamics ofthe tire forces plays an important role.

In practice, a step steer input is usually only used to judge vehicles subjectively. Exceeds in yawvelocity, roll angle, and especially sideslip angle are felt as annoying.

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0

0.1

0.2

0.3

0.4

0.5

0.6

lateralacceleration[

g]

0

2

4

6

8

10

12

yawv

elocity[deg/s]

0 2 40

0.5

1

1.5

2

2.5

3

rollangle[deg]

0 2 4-2

-1.5

-1

-0.5

0

0.5

1

[t]

sideslipangle[deg

]

Figure 8.3: Step Steer: Passenger Car atv = 100km/h

The vehicle under consideration behaves dynamically very well, Fig. 8.3. Almost no overshootsoccur in the time history of the roll angle and the lateral acceleration. However, small overshootscan be noticed at yaw the velocity and the sideslip angle.

8.1.3 Driving Straight Ahead

8.1.3.1 Random Road Profile

The irregularities of a track are of stochastic nature. Fig. 8.4 shows a country road profile indifferent scalings. To limit the effort of the stochastic description of a track, one usually employssimplifying models. Instead of a fully two-dimensional description either two parallel tracks areevaluated

z = z(x, y) z1 = z1(s1) , and z2 = z2(s2) (8.1)

or one uses an isotropic track. The statistic properties are direction-independent at an isotropictrack. Then, a two-dimensional track can be approximated by a single random process

z = z(x, y) z = z(s) ; (8.2)

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0 10 20 30 40 50 60 70 80 90 100 01

23

45

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Figure 8.4: Track Irregularities

A normally distributed, stationary and ergodic random process z= z(s)is completely charac-terized by the first two expectation values, the mean value

mz = lims

1

2s

ss

z(s) ds (8.3)

and the correlation function

Rzz() = lims

1

2s

ss

z(s) z(s) ds . (8.4)

A vanishing mean valuemz = 0can always be achieved by an appropriate coordinate transfor-mation. The correlation function is symmetric,

Rzz() = Rzz(), (8.5)

and

Rzz(0) = lims

1

2s

ss

z(s)

2ds (8.6)

describes the variance ofzs.

Stochastic track irregularities are mostly described by power spectral densities (abbreviated bypsd). Correlating function and the one-sided power spectral density are linked by the Fourier-transformation

Rzz() =

0

Szz() cos() d (8.7)

wheredenotes the space circular frequency. With Eq. (8.7) follows from Eq. (8.6)

Rzz(0) =

0

Szz() d. (8.8)

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Thus, the psd gives information, how the variance is compiled from the single frequency shares.

The power spectral densities of real tracks can be approximated by the relation

Szz() = S0

0

w

, (8.9)

where the reference frequency is fixed to0 = 1m1. The reference psd S0 = Szz(0)actsas a measurement for unevennes and the waviness w indicates, whether the track has notableirregularities in the short or long wave spectrum. At real tracks, the reference-psdS0lies withinthe range from1106 m3 to100106 m3 and the waviness can be approximated byw = 2.

8.1.3.2 Steering Activity

-2 0 20

500

1000

highway: S0=1*10-6

m3; w=2

-2 0 20

500

1000

country road: S0=2*10-5

m3; w=2

[deg] [deg]

Figure 8.5: Steering activity on different roads

A straightforward drive upon an uneven track makes continuous steering corrections necessary.The histograms of the steering angle at a driving speed ofv = 90km/hare displayed in Fig. 8.5.The track quality is reflected in the amount of steering actions. The steering activity is often usedto judge a vehicle in practice.

8.2 Coach with different Loading Conditions

8.2.1 Data

The difference between empty and laden is sometimes very large at trucks and coaches. In thetable 8.1 all relevant data of a travel coach in fully laden and empty condition are listed.

The coach has a wheel base ofa = 6.25m. The front axle with the track width sv = 2.046mhas a double wishbone single wheel suspension. The twin-tire rear axle with the track widthssoh = 2.152m and s

ih = 1.492m is guided by two longitudinal links and an a-arm. The air-

springs are fitted to load variations via a niveau-control.

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8.2 Coach with different Loading Conditions

vehicle mass[kg] center of gravity[m] inertias[kg m2]

empty 12500 3.800|0.000|1.500 12 500 0 00 155 000 00 0 155 000

fully laden 18000 3.860|0.000|1.60015 400 0 250

0 200 550 0250 0 202 160

Table 8.1: Data for a laden and empty coach

-1 0 1-10

-5

0

5

10

suspensiontravel[cm]

steer angle [deg]

Figure 8.6: Roll steer: - - front, rear

8.2.2 Roll Steering

While the kinematics at the front axle hardly cause steering movements at roll motions, thekinematics at the rear axle are tuned in a way to cause a notable roll steering effect, Fig. 8.6.

8.2.3 Steady State Cornering

Fig. 8.7 shows the results of a steady state cornering on a 100m-Radius. The fully occupiedvehicle is slightly more understeering than the empty one. The higher wheel loads cause greater

tire aligning torques and increase the degressive wheel load influence on the increase of thelateral forces. Additionally roll steering at the rear axle occurs.

Both vehicles can not be kept on the given radius in the limit range. Due to the high position ofthe center of gravity the maximal lateral acceleration is limited by the overturning hazard. Atthe empty vehicle, the inner front wheel lift off at a lateral acceleration ofay 0.4g . If thevehicle is fully occupied, this effect will occur already atay 0.35g.

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0 0.2 0.4 0.6 0.80

50

100

steer angle LW

[deg]

0 0.2 0.4 0.6 0.80

1

2

3

4

5

roll angle [Grad]

0 0.2 0.4 0.6 0.80

2

4

6

wheel loads front [kN]

0 0.2 0.4 0.6 0.80

2

4

6

lateral acceleration ay [g]

wheel loads rear [kN]

lateral acceleration ay [g]

Figure 8.10: Steady state cornering, semi-trailing arm, - - single wishbone, trailing arm

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[32] Riepl, A.; Reinalter, W.; Fruhmann, G.: Rough Road Simulation with tire model RMOD-K and FTire. In: Proc. of the 18th IAVSD Symposium on the Dynamics of vehicles onRoads and on Tracks. Kanagawa, Japan, 2003. Taylor & Francis, London UK.

[33] Rill, G.: Instationre Fahrzeugschwingungen bei stochastischer Erregung. Stuttgart, Univ.,Diss., 1983.

[34] Rill, G.: The Influence of Correlated Random Road Excitation Processes on Vehicle Vi-bration. In: The Dynamics of Vehicles on Road and on Tracks. Ed.: Hedrik, K., Lisse:Swets-Zeitlinger, 1984.

[35] Rill, G.: Fahrdynamik von Nutzfahrzeugen im Daimler-Benz Fahrsimulator. In: Berech-nung im Automobilbau, VDI-Bericht 613. Dsseldorf: VDI-Verlag 1986.

[36] Rill, G.: Demands on Vehicle Modeling. In: The Dynamics of Vehicles on Road and onTracks. Ed.: Anderson, R.J., Lisse: Swets-Zeitlinger 1990.

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[38] Rill, G.: Modeling and Dynamic Optimization of Heavy Agricultural Tractors. In: 26thInternational Symposium on Automotive Technology and Automation (ISATA). Croydon:Automotive Automation Limited 1993.

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Index

Lateral force distribution, 34

Lateral slip, 33

Lateral velocity, 25

Lift off, 113Linear Model, 152

Loaded radius, 17, 25

Longitudinal force, 11, 32

Longitudinal force characteristics, 33

Longitudinal force distribution, 33

Longitudinal slip, 32

Longitudinal velocity, 25

Model, 39

Normal force, 11

Pneumatic trail, 34Radial damping, 28

Radial direction, 17

Radial Stiffness, 147

Radial stiffness, 28

Rolling resistance, 11, 30

Rolling resistance coefficient, 30

Self aligning torque, 11, 34

Sliding velocity, 34

Static radius, 17, 25, 27

Tilting torque, 11

Track normal, 17, 19

Transport velocity, 26

Tread deflection, 31

Tread particles, 31

Unloaded radius, 25

Vertical force, 27

Wheel load influence, 36

Tire Model

Kinematic, 135

Linear, 160

TMeasy, 39Toe angle, 4

Toe-in, 4

Toe-out, 4

Torsion bar, 82

Track, 16

Track Curvature, 140

Track Radius, 140

Track Width, 135, 147

Tracknormal, 4

Trailer, 138, 141

Understeer, 158

Vehicle, 2

Vehicle comfort, 97

Vehicle dynamics, 1

Vehicle Model, 119, 129, 138, 147, 151

Vehicle model, 97, 115

Vertical dynamics, 97

Virtual Work, 147

Waviness, 167

Wheel Base, 135

Wheel camber, 5Wheel load, 11

Wheel Loads, 119

Wheel rotation axis, 4

Wheel Suspension

Semi-Trailing Arm, 170

Single Wishbone, 170

Trailing Arm, 170

Wheel suspension

Central control arm, 79

Double wishbone, 78

McPherson, 78

Multi-Link, 78

Semi-trailing arm, 79

SLA, 79

Yaw Angle, 141

Yaw angle, 138

Yaw Velocity, 152

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Index

Ljapunov equation, 109

Load, 3

Maximum Acceleration, 122, 123Maximum Deceleration, 122, 124

Natural frequency, 101

Optimal Brake Force Distribution, 126

Optimal damping, 106, 111

Chassis, 107

Wheel, 107

Optimal Drive Force Distribution, 126

Oversteer, 158

Overturning Limit, 144

Parallel Tracks, 165

Pinion, 80

Pivot pole, 135

Power Spectral Density, 166

Quarter car model, 112, 115

Rack, 80

Random Road Profile, 165

Rear Wheel Drive, 123, 144

Reference frames

Ground fixed, 4

Inertial, 4

Vehicle fixed, 4

Relative damping rate, 102

Ride comfort, 108

Ride safety, 108

Road, 16

Roll Axis, 150

Roll Center, 150

Roll Steer, 168Roll Stiffness, 146

Roll Support, 147, 150

Rolling Condition, 152

Safety, 97

Side Slip Angle, 135, 159

Sky hook damper, 111

Space Requirement, 136

Spring rate, 103

Stability, 154

Stabilizer, 83

State Equation, 154

State matrix, 113

State vector, 113Steady State Cornering, 143, 163, 168

Steer box, 80

Steering Activity, 167

Steering Angle, 140

Steering box, 81

Steering lever, 81

Steering offset, 8, 9

Steering system

Drag link steering system, 81

Lever arm, 80Rack and pinion, 80

Steering Tendency, 151, 157

Step Steer Input, 164, 170

Suspension model, 97

Suspension spring rate, 103

System response, 87

Tilting Condition, 122

Tire

Bore torque, 11, 46

Camber angle, 17Camber influence, 43

Characteristics, 39

Circumferential direction, 17

Composites, 10

Contact forces, 11

Contact patch, 11

Contact point, 16

Contact point velocity, 24

Contact torques, 11

Deflection, 20Deformation velocity, 25

Development, 10

Dynamic offset, 34

Dynamic radius, 26

Dynamics, 49

Friction coefficient, 37

Lateral direction, 17

Lateral force, 11

Lateral force characteristics, 34

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Index

Ackermann Geometry, 135

Ackermann Steering Angle, 135, 158

Aerodynamic Forces, 121

Air Resistance, 121

Air spring, 83

All Wheel Drive, 144Anti Dive, 134

Anti Roll Bar, 148

Anti Squat, 134

Anti-Lock-Systems, 128

Anti-roll bar, 83

Axle Kinematics, 134

Axle kinematics

Double wishbone, 7

McPherson, 7

Multi-link, 7

Axle Load, 120

Axle suspension

Solid axle, 78

Twist beam, 79

Bend Angle, 142

Bend angle, 139

Brake Pitch Angle, 129

Brake Pitch Pole, 134

Camber angle, 5, 17Camber Compensation, 147, 150

Camber slip, 44

Caster, 8, 9

Climbing Capacity, 122

Coil spring, 82

Comfort, 97

Contact point, 18

Cornering Resistance, 143, 144

Cornering stiffness, 34

Critical velocity, 157

Curvature Gradient, 140

Damping rate, 101

Disturbance-reaction problems, 108

Disturbing force lever, 8

Down Forces, 121

Downhill Capacity, 122

Drag link, 80, 81

Drive Pitch Angle, 129

Driver, 2

Driving

Maximum Acceleration, 123

Driving safety, 97

Dynamic Axle Load, 120

Dynamic force elements, 87

Dynamic Wheel Loads, 119

Eigenvalues, 154

Environment, 3

First harmonic oscillation, 87

Fourier-approximation, 88

Frequency domain, 87

Friction, 122

Front Wheel Drive, 123, 144

Generalized fluid mass, 94

Grade, 120

Hydro-mount, 93

Kingpin, 7

Kingpin Angle, 8

Lateral Acceleration, 147, 158

Lateral Force, 152

Lateral Slip, 152

Leaf spring, 82, 83

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1.2 Definitions

toe-in toe-out

+

+

yF

xF

yF

xF

Figure 1.2: Toe-in and Toe-out

For minimum tire wear and power loss, the wheels on a given axle of a car should point directly

ahead when the car is running in a straight line. Excessive toe-in or toe-out causes the tires to

scrub, since they are always turned relative to the direction of travel.

Toe-in improves the directional stability of a car and reduces the tendency of the wheels toshimmy.

1.2.3 Wheel Camber

Wheel camber is the angle of the wheel relative to vertical, as viewed from the front or the rear

of the car, Fig. 1.3. If the wheel leans away from the car, it has positive camber; if it leans in

++

yF

zF

en

yF

zF

en

positive camber negative camber

Figure 1.3: Positive camber angle

towards the chassis, it has negative camber. The wheel camber angle must not be mixed up with

the tire camber angle which is defined as the angle between the wheel center plane and the local

track normalen. Excessive camber angles cause a non symmetric tire wear.A tire can generate the maximum lateral force during cornering if it is operated with a slightly

negative tire camber angle. As the chassis rolls in corner the suspension must be designed such

that the wheels performs camber changes as the suspension moves up and down. An ideal sus-

pension will generate an increasingly negative wheel camber as the suspension deflects upward.

1.2.4 Design Position of Wheel Rotation Axis

The unit vector eyR describes the wheel rotation axis. Its orientation with respect to the wheel

carrier fixed reference frame can be defined by the angles 0 and0 or0 and

0, Fig. 1.4. In

Documents

automobile engg. notes