Investigation of Vehicle Motion on sharp Horizontal Curves combined with steep longitudinal Grades

Stergios Mavromatis, Assistant Professor Technological Educational Institute of Athens

[email protected]

Basil Psarianos, ProfessorNational Technical University of Athens

[email protected]

Pavlos Tsekos, Research AssociateTechnological Educational Institute of Athens

[email protected]

Giorgos Kleioutis, Research AssociateTechnological Educational Institute of Athens

[email protected]

Evaggelos Katsanos, Research AssociateNational Technical University of Athens

[email protected]

Vehicle Industry

evolves technological improvements for vehicle stability

ABS

EBD

ESP

Road Design Practice

vehicle dynamics simplified

point mass

many parameters ignored

vehicle type

vehicle mass and position of gravity center

vehicle’s motion is examined independently in the tangential and lateral direction of travel

heavy vehicles dynamics

)e+f(127

V=R

maxperm,R

2

min

where

Rmin : minimum curve’s radius (m)

V : vehicle speed – usually design speed (km/h)

emax : maximum superelevation rate (%/100)

m : vehicle’s mass

fR,perm: permissible side friction factor as a portion of peak friction

Parameters Ignored

actual demand of lateral friction

roadway’s longitudinal profile

vehicle dynamics

e.g. loading, driving configuration, horse-power supply

Point Mass Model

adopted in current practice

Bicycle Model

simulates the vehicle by an axle in steady state cornering conditions

Transient Formulation of the Bicycle Model

utilized in cases of variable steering inputs (e.g. lane changes)

Full Multi–Body Vehicle Simulation

used mostly by the automotive industry for vehicle stability prediction

lflrL/R

L

fαrα

fθ

β

L/R

m VR

2

V

Vf

Vr

R

Determine the Safety Hazard

passenger cars in tractive mode

sharp horizontal curves

combined with steep

longitudinal grades

Examine Point Mass

Model’s Adequacy

to Assess

Vehicle Motion

Field Measurements

on Road Section

road geometry elements

tire – road adhesion values

speed data vs driven distance

Correlate Vehicle

Performance against

Existing Vehicle Dynamics

Model

Divided Urban Ring Road in Athens

Steep Graded and Sharp Curved

Road Section

Road Section Surveyed

via Laser Scanner

Road Section Surveyed

via Laser Scanner

median of 1.50m

Road Section Surveyed

via Laser Scanner

median of 1.50m

independent road

geometries representing

vehicle paths

(offset 4.00m from axis)

per vehicle’s

direction of travel

cross - slope

e (%)

0,00 0,00

14,62 R=○○ 2,50

14,62

13,10 A=16,90 2,50 - 5,50 35,78 6,50

27,72 43,73 8,49

48,65 R=21,80 5,50 79,51 11,00

76,37

3,51 A=8,74 2,50 - 5,50

79,87

32,02 R=○○ 2,50

111,90 111,90

upgrade section

horizontal

station (m)

distance

between (m)

horizontal geometry

(A,R) (m)

vertical

station (m)

distance

between (m)

vertical geometry

(K) (m) grade between (%)

32,3911,92

10,8735,78

cross - slope

e (%)

0,00 0,00

18,99

18,99 12,00

16,76

4,10 A=11,05 2,50 - 5,00

20,85

68,16 R=29,80 5,00

89,01

15,30 A=21,35 2,50 - 5,00 89,54 6,50

104,31

13,71 R=○○ 2,50

118,02 118,02

16,76 R=○○ 2,50

downgrade section

horizontal

station (m)

distance

between (m)

horizontal geometry

(A,R) (m)

vertical

station (m)

distance

between (m)

vertical geometry

(K) (m) grade between (%)

70,55 -6,58

28,48

-9,54

-11,04

Test Vehicle

C class passenger car, FWD

(KIA, Proceed)

ABS equipped

Test Vehicle

C class passenger car, FWD

(KIA, Proceed)

ABS equipped

Measuring Device

Accelometer, (Vericom, VC4000)

Test Vehicle

C class passenger car, FWD

(KIA, Proceed)

ABS equipped

Measuring Device

Accelometer, (Vericom, VC4000)

Dry Pavement

Runs

(performed by the same driver)

braking (friction)

driving in tractive mode

(speed vs distance)

Time, Speed and Distance Data

Time, Speed and Distance Data

Friction Data

braking runs on tangent sections

and constant grade

drag factor

drag = f + s

where

f: braking friction coefficient

s: roadway’s grade value (%/100) [(+) for upgrades, (-) for downgrades]

0.62 0.64

0.70 0.690.68

0.75 0.74

0.800.81

0.64

0.81

0.73

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

s= 13,0%KIA

s= -10,7%KIA

s= 7,0%AUDI

s= -7,0%AUDI

faverage

fmax

max drag

upgrade downgrade

s=13,0%

KIA

s=-10,7%

KIA

s=7,0% s=-7,0%

AUDI AUDI

Parameters Correlated

vehicle technical characteristics

vehicle speed, wheel drive, sprung and unsprung mass

and its position of gravity center, aerodynamic drag,

vertical lift, track width, wheel-base, roll center, vertical

suspension stiffness, cornering stiffness, etc.

Parameters Correlated

vehicle technical characteristics

vehicle speed, wheel drive, sprung and unsprung mass

and its position of gravity center, aerodynamic drag,

vertical lift, track width, wheel-base, roll center, vertical

suspension stiffness, cornering stiffness, etc.

road geometry

grade, superelevation rate,

horizontal radius

tire friction

Four - Wheel Model

Actual Wheel Load

due to

Lateral Load Transfer

Alteration of

Lateral Force

on each Wheel

Vehicle Examined at Impending Skid

Vehicle Speed Variation as a Function of Driven

Distance

Variation of Vehicle Dynamic Parameters

acceleration, horse power utilization, lateral –

longitudinal friction values for every wheel, etc.

Definition of Vsafe (dv/dt=0)

0.00

0.50

1.00

1.50

2.00

2.50

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110 120

dv/d

t(m

/se

c2)

V (

km

/h)

distance (m)

run1

run2

run3

run4

V

dv/dt

R=oo A=16.90 R=21.80 A=8.74 R=oo

Vsafe

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100 110 120

dv/d

t(m

/se

c2)

V (

km

/h)

distance (m)

run1

run2

run3

run4

V

dv/dt

R=oo A=11.05 R=29.80 A=21.35 R=oo

Vsafe

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 10 20 30 40 50 60 70 80 90 100 110 120

fric

tio

n

distance (m)

fMAX

fTfo model

fRfo model

fTfi model

fRfi model

fR pm

fRri modelR=oo A=16.90 R=21.80 A=8.74 R=oo

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 10 20 30 40 50 60 70 80 90 100 110 120

fric

tio

n

distance (m)

fMAX

fTfo model

fRfo model

fTfi model

fRfi model

fR pm

fRri modelR=oo A=11.05 R=29.80 A=21.35 R=oo

4953

77

86

0

10

20

30

40

50

60

70

80

90

s = 8% s = -8% s = 8% s = -8%

V(k

m/h

)

R=30m R=80m

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 110 120

accele

rati

on

(m

/se

c2)

ho

rse p

ow

er

uti

lizati

on

n (

%)

distance (m)

n (%)

dv/dt

R=oo A=11.05 R=29.80 A=21.35 R=oo

Friction Values

Braking Performance of Vehicles

Equipped with ABS,

on Steep Grades

average braking performance

is actually the same

peak friction coefficients higher

on downgrades

Possible Explanation

steep upgrades subject to more

intense road distortion

Determination of Vsafe (model)

Correlation against Field Measurements

model provides accurate results

vehicle drifting on certain upgrade runs

driver’s discomfort reported on downgrades

Critical Wheel for Skidding

inner to the curve

inner front prevails

Point – Mass Model Accuracy in fR

better approximation on upgrade

sections

downgrade section demand greater

portion of lateral friction

point mass model model usually

underestimates the actual friction

requirements especially

on steep grades

Steep Upgrade Road Segments

More Critical

at Impending Skid Conditions

portion of friction is engaged

in the longitudinal direction

of travel causing less friction

availability in the

lateral direction

Vehicle’s Acceleration Safety

Performance at Curve Entrance

vehicles equipped with excessive

amounts of horse power rates must

be driven very conservatively in

sharp horizontal curves combined

with steep vertical grades

previous research findings

confirmed

highlight the increased risk

associated with such alignment

combinations

Investigation in Entire Vehicle Fleet

(SUVs, Heavy Vehicles, etc.)

Analyse in More Detail

the Interaction between Driver – Vehicle

on Sharp Curves and Steep Grades

determine appropriate

horizontal and vertical

alignment combinations