safety assessment of control design parameters …...s. mavromatis, «safety assessment of control...

Stergios Mavromatis1, Alexandra Laiou2

1Technological Educational Institute of Athens, Greece

School of Civil Eng. and Surveying & Geoinformatics Eng.2National Technical University of Athens, Greece

Department of Transportation Planning and Engineering

email: stemavro@teiath.gr

The Hague, October 2017

Safety Assessment

of Control Design Parameters

through Vehicle Dynamics Model

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Background

• Design speed• key parameter for defining critical geometric elements

• Road design practice• simplified approach

• failure to assess interactions between parameters

)e+f(127

V=R

maxperm,R

2

min

whereRmin : minimum curve’s radius (m)

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

emax : maximum superelevation rate (%/100)

m : vehicle’s massfR,perm: permissible side friction factor as a portion of peak friction

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Point Mass Deficiencies

• Steady state cornering is assumed• acceleration effect is ignored

• Key vehicle parameters ignored• type, mass and position of gravity (mass) center,

loading - driving configuration, horse-power supply, etc.

• Vehicle motion is examined independently in tangential - lateral direction of travel• respective friction components interact

• Utilized lateral friction based on empirical vehicle accident considerations• assumed as fixed portion of the relevant peak (40%-50%)

• Longitudinal profile disregarded

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Necessity for More Sophisticated Models

• Current control grade values • based mostly on experience

• limitations from the operational point of view

and not an outcome of a safety assessment

• Simulate vehicle’s cornering process• especially in cases of steep grades

(reduction of safety margin)

• upgrade road sections more critical in terms of horizontal radii requirements

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Objective

• Lift restrictions imposed

by point mass model

• Assess the ability of a typical passenger car

to maintain design speed values

for the corresponding

control design parameters• critical upgrade values

• various tire – road friction values

• Investigate the safety impact of vehicle’s peak attainable constant speed against design parameters imposed by design speed

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Vehicle Dynamics Model

• Moving 3D coordinate system

• Parameters correlated• vehicle technical characteristics

• road geometry

• tire friction

• 4-wheel model• lateral load transfer

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

• Output: Vsafe

vehicle’s peak attainable constant speed

• C class passenger car utilized (KIA Proceed)

• assessment for AASHTO-2011 design guidelines (Vd =50km/h – Vd =90km/h)

• 3 pavement friction values (0.35, 0.50, 0.65)

• definition of critical wheel (impending skid conditions)

Methodology

road

parameters

vehiclefriction

V0

define

critical wheel

dV/dt=0

V=V+Vstep

dV/dt>0

Vsafe , n

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

92.490.4

87.9

84.7

81.0

76.3

70.2

0.11

0.15

0.19

0.22

0.26

0.28

0.310.33

0.32

0.29

0.27

0..24

0.20

0.16

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

60

65

70

75

80

85

90

95

0.0 2.0 4.0 6.0 8.0 10.0 12.0

fric

tio

n v

alu

es

Vsa

fe (

km

/h)

s (%)

Vsafe vs Grade (fmax=0.35, Vd=70km/h, R=184m)

Vsafe

fTfi

fRfi

fR point mass

Grade Impact during Vsafe Determination

• Impending skid

fR demand :critical on mild grades

fT demand :critical on steep grades

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

HP Utilization Rates during Vsafe Determination

• Impending skid

vehicle skids when driven above suggested HP utilization values

92.4

90.4

87.9

84.7

81.0

76.3

70.224

31

37

42

4649

51

0

10

20

30

40

50

60

60

65

70

75

80

85

90

95

0.0 2.0 4.0 6.0 8.0 10.0 12.0

n (

%)

Vsa

fe (

km

/h)

s (%)

HP Utilization vs Grade (fmax=0.35, Vd=70km/h, R=184m)

Vsafe

n (%)

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Friction Safety Margins for V < Vsafe

• Comfortable driving

0.310.29

0.28 0.270.26

0.16

0.13

0.10

0.07

0.050.050.04 0.03 0.03 0.02

0.16

0.12

0.10

0.07

0.05

0.35

0.32

0.300.28

0.26

0.16

0.13

0.10

0.08

0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

70 65 60 55 50

fric

tio

n v

alu

es

V (km/h)

Friction vs Comfortable Speed (fmax=0.35, Vd=70km/h, R=184m)

fTfi (s=12%)

fRfi (s=12%)

fTfi (s=0%)

fRfi (s=0%)

fdemanded (s=12%)

fdemanded (s=0%)

fR point mass

fT : grade dependent

fR ≈ fR point mass model

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Vsafe Variation for Control Design Values (fmax = 0.35)

• Impending skid

critical cases (fmax = 0.35):

• Vd = 50km/h, s>11%

• Vd = 60km/h, s>11%

4446

56

49

59

70

51

62

73

52

64

76

87

97

40

50

60

70

80

90

100

79(Vd=50km/h)

123(Vd=60km/h)

184(Vd=70km/h)

252(Vd=80km/h)

336(Vd=90km/h)

V (

km/h

)

Rmin (m)

Vsafe Calculation, fmax=0.35

VAASHTO

s=14%

s=13%

s=12%

s=11%

s=10%

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Vsafe Variation for Control Design Values (Vd = 50km/h)

• Impending skid

critical cases (Vd = 50km/h):

• fmax < 0.40

• s > 11%

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Conclusions (1/3)

• Investigation of the ability a C-class passenger car

on steep grades to maintain Vd

• AASHTO 2011 design guidelines (Vd =50km/h – Vd =90km/h)

• 3 pavement friction values (0.35, 0.50, 0.65)

• 2 cases examined for assessing safety margins

• comfortable curve negotiation (V<Vsafe)

• Vsafe impending skid conditions

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Conclusions (2/3)

Comfortable curve negotiation (V<Vsafe)

• fR demand independent to grade

• fT demand increases with grade

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Conclusions (3/3)

Vsafe impending skid conditions

• fR demand critical on mild grades

• fT demand critical on steep grades

• Steady state cornering not always feasible• Vd = 50km/h, s>11%, fmax = 0.35

• Vd = 60km/h, s>11%, fmax = 0.35

• Point mass model model somehow underrates

lateral friction requirements

• Vehicles equipped with excessive HP rates

must be driven very conservatively

in road with poor friction pavement

S. Mavromatis, «Safety Assessment of Control Design Parameters through Vehicle Dynamics Model»

Recommendations - Further Research

• Identified critical cases

to be treated cautiously through actions• adoption of acceptable parameter arrangements

(new alignments)

• posted speed management

(existing alignments)

• scheduling friction improvement

programmes more accurately (both cases)

• Assessment on entire vehicle fleet

• Further analysis of interaction between

driver – vehicle

Stergios Mavromatis1, Alexandra Laiou2

1Technological Educational Institute of Athens, Greece

School of Civil Eng. and Surveying & Geoinformatics Eng.2National Technical University of Athens, Greece

Department of Transportation Planning and Engineering

email: stemavro@teiath.gr

The Hague, October 2017

Safety Assessment

of Control Design Parameters

through Vehicle Dynamics Model