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0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Slip
Friction
coefficient
Asphalt
Wet asphalt
Snow
Ice
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7/29/2019 Slip Based Estimation of Tire-Road friction
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x
y
B
L
R rr
R fr
Rfl
R rl
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x
Mg
zg
za
bxf
Nf
Ff
Fa
Fx
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7/29/2019 Slip Based Estimation of Tire-Road friction
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0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. File: asf2l_3
xxxxx
xxx xxxxx x
x
x xxxx
xxx
x xxx xx
xx
xx
x
x
xx
x
x
x
x
x
x
x
x
x
xx xx
x
x x
x
x
x
x
x
x
xx
xxx x
xx
x
xxxx
xxxxx
x
x
xxxx
xxx
xx
x
x
xxx x
x
x
xx
x
x
xx x
x
x
x
xxx
xx
xxx
xx
x
x
x
xx
xx x
x
x
x
xxx
xx xxxxx
xxx
x
xx
x
x
x
x
xxx
x
x
x
x
x x
x
x
x
x
x
xx xx
x
x
ooooo
o oo oo ooo oo
o oo oo
oooo o
ooo
o
oo
oo
o
o
ooooo
o
o
o
o
o
o
oooo
o
o o
o
o
o
o
o
o
oo
o
ooo o
oo
o
oo ooooo
ooo
o
o
ooo
o oo
oo
o
o
ooo o
o
o
oo
o
o
oo
o
o
o
oo
o
oo
oo
oo
o
o
o
o
oo
oo o
o
o
oo
oo o
ooo
oo
ooo
o
o
o
o
o
o
o
o oo
o
o
o
o
oo
o
o
o
o
o
oo o
o
o
o
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. File: asf5c_1
xx xxxx x xxx x x
x x xx x xxxxx xxxxxxxx xx xxxxxxx xxxxx xxxxxx xx xx
xxxx xx
x
x
x
xx
x
xx
x xxx
x
x
xx
x x
x
xx x
xx
xxx
xxxx
x
xx
x
x
x
x
xx
x
x
xx
xx
xx
x
x
xx
x
xx xxxxx
xxxxx
xxx
x
xx
xxxx
xx
xx xxx x
xxx
xx
xx
xx xx x
x
xxxxx
x
xx xx xx xxxx x x xx xx xx xx
xxxx xx xxxx
xoo o oooo ooo o oo o oo oo ooo o ooo oo ooo oo oo ooo
oo ooooo ooo ooo oo o oo ooo oo o
o
o
o
o
o
o
o
oooooo o
oo
o
oo
oo
o
o
oo
ooo o
o
ooo
o oooooo
ooooo
o ooo o
o o
oo oooo oo
o oooooo o
o oo o
o ooo
o oooo
o
o
oo oo oo ooooo o oo oo oo oo
oooo oo oooo
o
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. File: grus2l_5
xx
x
x x
x
x
xx
x
x
xx x xxxx xxxx
xx
x
x x
xx
x
xx x
x xx
xx x x
x
x x x
xx xx
x
x
x
x
xx
x
xx
x
xx xx
xx xx
x
xxxx x
x
xx
x x
x
x
x
x xx
x
x
x
x
x
xx xxx
x
x
xxx
xxx x
xx
x
x
x xx x
xx
x
oo
o
o o
o
o
o
o
o
o
o
ooo ooo o oooo
oo
o
oo
o
o
o
oo o
o o
o
oo oo
o
o oo
ooo o o
o
o
oo
o
oo
ooo o o
ooo o
o
oo ooo
o
oo
o o
o
o
o
o o
oo
oo
o
o
oo oo
o
o
o
oooooo
ooo o
oo ooo
oo
o
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. File: grus5l_2
xx x
xx
x x
x
xx x
x
x
x
xx
xx
x
x
xx
x
x
xx
x
x
x
x xx
x
xx
x
xx
x xx xxx
x
x x
x
x
xx
x
x
x
x
x x
x
x
x
xx
x
x
x xx xx
x
x
x
x
x
x
x
x
x
x
x
x
xx
x xxx xxx
x x
x
x
x
xx
xx
x x
x
xx
x xx
xxx xx xxx
xxxxxx x
x x xxx
xx
x
xxx
x
x x
x
x
xx
xxx
x x
x
x
x
xx
x x
x x
x
xx
x
xx x
xx
xxx xx x
x
x
x
x
xx
x
x
x
x
x
xx
xx
o oo
oo
o o
o
o
oo
o
o
o
oo o o
o
o
o o
o
o
ooo
o
o
oo
o
o
oo
o
oo
oo oooo
o
o
o
o
o
o
o
o
o
o o
o
o
o
oo
o
oo
oo ooo
o
o
o
o
o
o
o
o
o
o
oo
o o ooooo
o o
o
o
o
o
oo
oo
o
o
o
o
o oo
oo oo
ooo
ooo
o
oo oo
ooo ooo o
o
ooo
o
o o
o
o o
o
o
o
o o
o
o
oooo
oo
o
o
oo
oo
ooo
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o
o
o o
oo
oo
o
o
o
oo
oo
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. Fil e: is2c_1
x
x
x
x
x
x
x
x
x xx
x xxx
xxxx
x xxx xx
xxx
x xxx
xx xxx x
x
x
xx
xx
x
x
xx
x
x x
xx
xxx
x
xxxx xx
x xxxxx xxxx xx
xxxx
xxx xxxxxx
x
xx
x
xxx
x
o
o
o
o
o
o
o ooo
oo
o ooo o oo
oooo
ooo
oo oo
oo ooo o
o
o
oo
oo
o
o
o o
o
o o
oo
o oo
o
oo oo o
ooo ooooo
oo o
ooooo
o oooo
ooooo
o
oo
o
oo
o
o
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8 10 12 14 16 18 20
Friction force/ normal force versus slip. File: is5c_a
x
x
x x
x
x
xx
x
xx
x
x
xx
xx
x xx xxx
xx xx x
x
x
xxx x
x
x
x
x
x
x
x
x
xxx x
xx
xx
x
xx
x xx
x
xx xx x xxx xxxx xxx xx xx
xx
x xx
xxxx xxxxx xx
xxx xxxxxx
xxx x
x
x xxxx
x xxxxx
x
x
x
xxx
x
xx
xx
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
x
xx
xx
x
xxxx
x
x
xxx xx
xxx
xxx
o
o
o
o o
o
ooo
o
oo
o
o
ooooo
oo oo
oo
oooo
o
o
oo
oo
o
o
o
o
o
o
o
o
o
oo ooo oo
o
oo
oo
o
o
oo ooo o oooo oo oo o
oooo
ooo oo o
o ooo oo
o o oo oo oo
oooo
oooo o
o
o
o
ooo
oo o
ooo
o
o
o
o
oo
oo
o
oo
o oo
o
o
o
oo
o
o
oo
o
o
o
o
o
o
oo
o
o
o
oooo
o
o
ooooo o
oo
ooo
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7/29/2019 Slip Based Estimation of Tire-Road friction
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7/29/2019 Slip Based Estimation of Tire-Road friction
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7/29/2019 Slip Based Estimation of Tire-Road friction
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0
0.1
0.2
0.3
0.4
0.5
0.6
0 2 4 6 8 10 12 14 16 18 20
x
x
xxxxx xxx
xxxxxx xx xxxxx
x
xxxx
xx x x
x
xxxxxxxxxx xxx
xx xx xxxxxx xxxxx xxx xxx
x
xxxxx
x
xxxxxxxxx xxxxxxxxxxx
xxx
Friction force/ normal force versus slip. File: slatvas5
o
o
o ooooo ooooooo
o oooooooo
ooooo
o o o
o
ooooooo
ooo o
oo
oo oo oo oo
oo ooo oo ooo ooo
o
oo ooo
o
ooo ooooooooo oooo oo oo
ooo
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2 4 6 8 10 12 14 16 18 20
xxx xxxxx xxxxxx
x
x xx xxxx xxx
x
x
xx xxxxx xxxx
xx
x x
xx
xx
xx xxx
xxx
x x
x
x
xxx xx xxx
xxxxx
xxxxxxxxxx xxxx xxx xxxx
xx
xx
xxxxxxxx xxxx
x
x xx x
x x xxxxxxxxxx
xxx xxxxxxxx
xxxxxxxxx
Friction force/ normal force versus slip. File: grovas5
oo o oo ooo ooooooo
ooo oooo o
oo
o
o
oo ooo oo o
oooo
oo o
oooo
ooo
ooooo
oo
o
o
ooo oo oo
oooo
oooo ooo
ooo oo
oooo ooo ooo
oo
o
o
o
o
ooooo oo o oo
o
o
oo
ooo o
ooooooooooo oo ooooooo o
oo ooooooo
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7/29/2019 Slip Based Estimation of Tire-Road friction
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