measurement and modeling of tire forces on a low
TRANSCRIPT
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Measurement and Modeling Measurement and Modeling of Tire Forces on a Low of Tire Forces on a Low
Coefficient SurfaceCoefficient Surface
April 4, 2006April 4, 2006by:by:
Dr. Paul A. GrygierDr. Paul A. GrygierAuthors:Authors: M. Kamel Salaani, Gary J. Heydinger, & Paul A. GrygierM. Kamel Salaani, Gary J. Heydinger, & Paul A. Grygier
SAE Paper: 2006SAE Paper: 2006--0101--05590559
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OverviewOverviewIntroductionIntroductionObjectivesObjectivesTire ModelTire ModelTire PropertiesTire PropertiesResultsResultsConclusionsConclusions
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National Advanced Driving National Advanced Driving Simulator (NADS)Simulator (NADS)
Dome with Vehicle and Image Projectors
Yaw Ring (1 DOF)
Hexapod (6 DOF)
20 meter ‘X’ Travel (1 DOF)
20 meter ‘Y’ Travel (1 DOF)
20 m x 20 m X20 m x 20 m X--Y Y platformplatform330330--degree yaw ringdegree yaw ringHexapod mounted on 6 Hexapod mounted on 6 actuatorsactuators360360--degree field of viewdegree field of viewFour fullFour full--size vehicle size vehicle cabscabsFour actuators at cab Four actuators at cab ““suspensionssuspensions””Driver feels feedback on Driver feels feedback on all controlsall controls
44
Testing Objectives:Testing Objectives:
0
0.2
0.4
0.6
0.8
1
1.2
20 40 60 80Speed (mph)
Nor
mal
ized
Lon
gitu
dina
l Pea
k Fo
rce
0.05" Water8/32" Tread0.05" Water6/32" Tread0.05" Water4/32" Tread0.10" Water8/32" Tread0.10" Water6/32" Tread0.10" Water4/32" Tread
From SAE Paper 2002-01-0553
To develop a tire model for a slippery To develop a tire model for a slippery road to test ESC and other advanced road to test ESC and other advanced vehicle technology studiesvehicle technology studies
Peak Coefficient of friction <0.6 to Peak Coefficient of friction <0.6 to ensure ESC activationensure ESC activation
Speed dependent model Speed dependent model –– all other tire all other tire properties are fixedproperties are fixed
Testing on laboratory surface (3M Testing on laboratory surface (3M surface); variations in roadway micro surface); variations in roadway micro and macro textures not accounted forand macro textures not accounted for
Selected 4/32Selected 4/32”” tread depth and 0.05tread depth and 0.05””of water depth, to get a peak about of water depth, to get a peak about 0.6 at 50 mph0.6 at 50 mph
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Testing Facility and Tires:Testing Facility and Tires:TIRF at CALSPAN (General Dynamics )TIRF at CALSPAN (General Dynamics )
Surface Used: 3M 80Surface Used: 3M 80--gritgrit--polycat sandpaperpolycat sandpaper
Goodyear Eagle RSA Goodyear Eagle RSA P225/60R16P225/60R16
All Tires ShavedAll Tires Shavedto 4/32to 4/32”” Tread DepthTread Depth
All Tire Pressures at 34 psiAll Tire Pressures at 34 psi
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Testing MatrixTesting MatrixDiscrete Cambering At Zero Slip AngleDiscrete Cambering At Zero Slip Angle–– Normal loads: 40, 80, 120, 160 and 200% of reference load.Normal loads: 40, 80, 120, 160 and 200% of reference load.–– Wet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speWet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speed: 30 mph (1 test)ed: 30 mph (1 test)–– Inclination angles: Inclination angles: --10, 10, --8, 8, --6, 6, --4, 4, --2, 0, 2, 4, 6, 8 and 102, 0, 2, 4, 6, 8 and 10°°
QuasiQuasi--Static Steering / CorneringStatic Steering / Cornering–– Inclination angle: 0Inclination angle: 0°°–– Slip angle sweep: 0 to Slip angle sweep: 0 to --20 to +20 to 020 to +20 to 0°° at a rate of 3 deg/secat a rate of 3 deg/sec–– Normal loads: 40, 80, 120, 160 and 200% of reference load.Normal loads: 40, 80, 120, 160 and 200% of reference load.–– Wet test speeds: 30, 45, 60 and 75 mph (4 tests)Wet test speeds: 30, 45, 60 and 75 mph (4 tests)
QuasiQuasi--Static Braking / DrivingStatic Braking / Driving–– Inclination angle: 0Inclination angle: 0°°–– Slip ratio sweep: 0 to Slip ratio sweep: 0 to --50% to +50% to 0 || Ramp time (0 to 50%) of 1.5 sec50% to +50% to 0 || Ramp time (0 to 50%) of 1.5 sec–– Normal loads: 40, 80, 120, 160 and 200% of reference load.Normal loads: 40, 80, 120, 160 and 200% of reference load.–– Wet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speWet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speed: 30 mph (1 test)ed: 30 mph (1 test)
QuasiQuasi--Static Combined Steering / Braking / DrivingStatic Combined Steering / Braking / Driving–– Inclination angle: 0Inclination angle: 0°°–– Normal loads: 100% of reference load.Normal loads: 100% of reference load.–– Steady state slip angles: Steady state slip angles: --6, 6, --4, 4, --2, 0, 2, 4, and 62, 0, 2, 4, and 6°°–– Slip ratio sweep:Slip ratio sweep: 0 to 0 to --50% to +50% to 050% to +50% to 0
Ramp time (0 to 50%) of 1.5 secRamp time (0 to 50%) of 1.5 sec–– Wet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speWet test speeds: 30, 45, 60 and 75 mph (4 tests) & Dry test speed: 30 mph (1 test)ed: 30 mph (1 test)
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• At low speed• Water affects boundary conditions, lowering friction• Difference between dry and wet surface not high
• At higher speed• Viscosity induces retardation of water displacement making a wedge of water •Difference between dry and wet forces is higher
• At a particular speed, the film covers all the contact surface: Hydroplaning fluids do not sustain shear forces comparable to direct tire contact
Tire Wet Contact PhenomenaTire Wet Contact Phenomena
Testing Goal
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Tire ModelTire ModelSemiSemi--empirical based on the brush modelempirical based on the brush model
Friction peak values are fitted to polynomials in function of loFriction peak values are fitted to polynomials in function of loadsads
Lateral and longitudinal frictions are differentLateral and longitudinal frictions are different
Stiffnesses are polynomial functions of vertical loadsStiffnesses are polynomial functions of vertical loads
Good predictions for combined slips (lateral and longitudinal)Good predictions for combined slips (lateral and longitudinal)
All parameters are physical parametersAll parameters are physical parameters
Linear interpolation between measured data at different speeds iLinear interpolation between measured data at different speeds is s used to model speed dependencyused to model speed dependency
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Tire Fundamental Physical Tire Fundamental Physical PropertiesProperties
1010
Lateral Peak Coefficient of Lateral Peak Coefficient of FrictionFriction
0 500 1000 1500 2000 25000
0.5
1
1.5
Pea
k (F
y/Fz
)
Fz (lbs)
30 mph Dry
30 mph Wet
45 mph Wet
60 mph Wet
75 mph Wet
Speed Increases
1111
Longitudinal Peak Coefficient of Longitudinal Peak Coefficient of FrictionFriction
0 500 1000 1500 2000 2500 30000
0.5
1
1.5
Pea
k ab
s(Fx
/Fz)
Fz (lbs)
30 mph Dry
30 mph W et
60 mph W et
75 mph W et
Speed Increases
1212
Effective Lateral StiffnessEffective Lateral Stiffness
0 500 1000 1500 2000 25000
50
100
150
200
250
300
350
400
Fz (lbs)
Cor
nerin
g S
tiffn
ess
(lbs/
deg)
30 mph Dry
30 mph Wet
45 mph Wet
60 mph Wet75 mph Wet
30 mph Dry30 mph Wet45 mph Wet60 mph Wet75 mph Wet
1313
Inclination Angle StiffnessInclination Angle Stiffness
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400-10
-5
0
5
10
15
20
25
30
35
Fz (lbs)
Cγ
(lbs/
deg)
30 mph Dry30 mph Wet45 mph Wet60 mph Wet75 mph Wet
Speed Increases
1414
Overturning Moment InclinationOverturning Moment InclinationAngle StiffnessAngle Stiffness
400 600 800 1000 1200 1400 1600 1800 2000 2200 24000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Fz (lbs)
KLT
G (f
t/lbs
)
30 mph Dry30 mph W et45 mph W et60 mph W et75 mph W et
Mx=-KLTG*Fy*Fz
1515
Overturning Moment Overturning Moment StiffnessStiffness
300 400 500 600 700 800 900 1000 1100 1200
0
1
2
3x 10-4
KLT
(lin
ear)
(ft/lb
)
Fz (lbs)
30 mph Dry30 mph Wet45 mph Wet60 mph Wet75 mph Wet
400 600 800 1000 1200 1400 1600 1800 2000 2200
-4
-2
0
x 10-4
KLT
(hig
h FY
) (ft/
lb)
Fz (lbs)
Mx=(KLT0+KLT1*Fz+KLT2*Fz2)*Fy
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Results (Fy)Results (Fy)
-25 -20 -15 -10 -5 0 5 10 15 20 25-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Fz = 457.9 lbs
Fz = 919.8 lbs
Fz = 1380 lbs
Fz = 1842 lbs
Fz = 2306 lbs
Slip Angle (deg)
Late
ral F
orce
(lbs
)
30 MPH DRY
-25 -20 -15 -10 -5 0 5 10 15 20 25-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Fz = 456.1 lbs
Fz = 919.3 lbs
Fz = 1380 lbs
Fz = 1844 lbs
Fz = 2304 lbs
Slip Angle (deg)
Late
ral F
orce
(lbs
)
30 MPH WET
-25 -20 -15 -10 -5 0 5 10 15 20 25-800
-600
-400
-200
0
200
400
600
Fz = 454.4 lbs
Fz = 917.3 lbs
Fz = 1376 lbs
Fz = 1838 lbs
Slip Angle (deg)
Late
ral F
orce
(lbs
)
60 MPH WET
-25 -20 -15 -10 -5 0 5 10 15 20 25-1000
-800
-600
-400
-200
0
200
400
600
800
1000
Fz = 454.4 lbs
Fz = 917.3 lbs
Fz = 1376 lbs
Fz = 1838 lbs
Fz = 2303 lbs
Slip Angle (deg)
Late
ral F
orce
(lbs
)
75 MPH WET
1717
CombinedCombined
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip RatioFx
(lbs
)
Lateral Slip Angle = +- 2 degrees @ 30 mph Wet
Fz = 1147 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fx (l
bs)
Lateral Slip Angle = +- 2 degrees @ 30 mph Dry
Fz = 1147 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
1818
CombinedCombined-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fx (l
bs)
Lateral Slip Angle = +- 4 degrees @ 30 mph Dry
Fz = 1147 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fx (l
bs)
Lateral Slip Angle = +- 4 degrees @ 30 mph Wet
Fz = 1147 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
1919
CombinedCombined-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fx (l
bs)
Lateral Slip Angle = +- 6 degrees @ 30 mph Dry
Fz = 1155 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip RatioFx
(lbs
)
Lateral Slip Angle = +- 6 degrees @ 30 mph Wet
Fz = 1147 lbs
TestModel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1000
0
1000
Slip Ratio
Fy (l
bs)
-1000 -500 0 500 1000
-1000
0
1000
Fx (lbs)
Fy (l
bs)
2020
Important Differences withImportant Differences withOnOn--thethe--Road Tires/SurfacesRoad Tires/Surfaces
Tires were shaved, aging effects is ignored (tire properties chaTires were shaved, aging effects is ignored (tire properties change nge with age and environment)with age and environment)
NHTSA studies indicated the average tread depth for inNHTSA studies indicated the average tread depth for in--service tires service tires is about 7/32is about 7/32””, yet we used 4/32, yet we used 4/32”” to meet peak coefficient of to meet peak coefficient of friction target valuefriction target value
Variations of tread depth, water depth, tire pressure, tire Variations of tread depth, water depth, tire pressure, tire construction, surface texture, and tread patterns are not addresconstruction, surface texture, and tread patterns are not addressedsed
Speed is the only variable affecting the modelSpeed is the only variable affecting the model
The results from the model is physically sound The results from the model is physically sound –– compares well with compares well with experimental results and can be used to validate ESC systemsexperimental results and can be used to validate ESC systems
2121
ConclusionsConclusions
Longitudinal and lateral force and Longitudinal and lateral force and moment data were collectedmoment data were collected
Test conditions were created such Test conditions were created such that a high coefficient of friction was that a high coefficient of friction was generated at low speeds and a lower generated at low speeds and a lower coefficient was generated at high coefficient was generated at high speedsspeeds
2222
Conclusions (cont.)Conclusions (cont.)
Tire parameters were calculated from Tire parameters were calculated from the test datathe test data
Parameters were verified by Parameters were verified by comparing calculated forces to comparing calculated forces to measured forcesmeasured forces
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Questions ?Questions ?
Contact: Contact: [email protected]@[email protected]@nhtsa.dot.gov.dot.gov