Estimation of surface lateral coefficient of friction
A system and method for estimating surface coefficient of friction in a vehicle system. The method includes providing a kinematics relationship between vehicle yaw-rate, vehicle speed, vehicle steering angle and vehicle front and rear axle side-slip angles that is accurate for all surface coefficient of frictions on which the vehicle may be traveling. The method defines a nonlinear function for the front and rear axle side-slip angles relating to front and rear lateral forces and coefficient of friction, and uses the nonlinear function in the kinematics relationship. The method also provides a linear relationship of the front and rear axle side-slip angles and the front and rear lateral forces using the kinematics relationship. The method determines that the vehicle dynamics have become nonlinear using the linear relationship and then estimates the surface coefficient of friction when the vehicle dynamics are nonlinear.
1. A method for estimating a surface coefficient of friction in a vehicle system, said method comprising:
providing a kinematics relationship between vehicle yaw-rate, vehicle speed, vehicle steering angle and vehicle front and rear axle side-slip angles that is accurate for all surface coefficient of frictions on which the vehicle may be traveling;
defining a nonlinear function for the front and rear axle side-slip angles relating to front and rear lateral forces and coefficient of friction;
using the nonlinear function in the kinematics relationship;
providing a linear relationship of the front and rear axle side-slip angles and the front and rear lateral forces using the kinematics relationship;
determining that vehicle dynamics have become nonlinear using the linear relationship; and
estimating the surface coefficient of friction when the vehicle dynamics become nonlinear.
2. The method according to claim 1 wherein estimating the surface coefficient of friction includes estimating the surface coefficient of friction when the tire forces saturate.
3. The method according to claim 1 wherein determining that the vehicle dynamics have become nonlinear includes determining that an equality defined by the linear relationship becomes unequal and the inequality exceeds a predetermined threshold.
4. The method according to claim 3 wherein the linear relationship is defined by the equation:
L
r
v
x
≈
tan
(
δ
+
F
y
F
c
F
)
-
tan
(
F
yR
c
R
)
where L is the vehicle wheel base, r is vehicle yaw-rate, ν x , is vehicle speed, δ is vehicle steering angle, F yF is the front axle force, F yR is the rear axle force, C F is a front vehicle corning stiffness and C R is a rear vehicle cornering stiffness.
5. The method according to claim 1 wherein the estimated surface coefficient of friction is set to one when the vehicle dynamics are linear.
6. The method according to claim 1 wherein the front and rear axle lateral forces are estimated.
7. The method according to claim 1 wherein the front and rear axle lateral forces are measured.
8. The method according to claim 1 wherein the kinematic relationship is:
L
r
v
x
=
tan
(
δ
+
α
F
)
-
tan
α
R
where L is the vehicle wheel base, r is vehicle yaw-rate, ν x is vehicle speed, δ is a vehicle steering wheel angle, α F is a front axle side-slip angle and α R is a rear axle side-slip angle.
9. The method according to claim 1 wherein estimating the surface coefficient of friction includes using the equation:
μ
estimate
=
F
yF
+
F
yR
F
yF
,
MAX
+
F
yR
,
MAX
where μ estimate is the estimate of the coefficient of friction, F yF is the front axle lateral force, F yR is the rear axle lateral force, F yF MAX is the front axle lateral force when the coefficient of friction is one and F yR MAX is the rear axle maximum lateral force when the coefficient of friction is one.
10. The method according to claim 1 wherein the estimated surface coefficient of friction is gradually returned to a predetermined default value when the vehicle dynamics become linear after being nonlinear.
11. A method for estimating a surface coefficient of friction in a vehicle system, said method comprising:
defining a linear function of side-slip angle and lateral force that provides an equality between vehicle wheel base, vehicle yaw-rate and vehicle wheel speed on one side of the equality and vehicle steering angle, vehicle front axle lateral force, vehicle rear axle lateral force, vehicle front cornering stiffness and vehicle rear cornering stiffness on an opposite side of the equality;
determining that the equality in the linear function has exceeded a predetermine threshold indicating that vehicle dynamic are nonlinear; and
estimating the surface coefficient of friction using a predetermined relationship when the equality exceeds the threshold.
12. The method according to claim 11 wherein the linear relationship is defined by the equation:
L
r
v
x
≈
tan
(
δ
+
F
yF
c
F
)
-
tan
(
F
yR
c
R
)
where L is the vehicle wheel base, r is vehicle yaw-rate, ν x is vehicle speed, δ is vehicle steering angle, F yF is the front axle force, F yR is the rear axle force, C F is a front vehicle corning stiffness and C R is a rear vehicle cornering stiffness.
13. The method according to claim 11 wherein the estimated surface coefficient of friction is set to one when the equality is less than the threshold.
14. The method according to claim 11 wherein estimating the surface coefficient of friction includes using the equation:
μ
estimate
=
F
yF
+
F
yR
F
yF
,
MAX
+
F
yR
,
MAX
where μ estimate is the estimate of the coefficient of friction, F yF is the front axle lateral force, F yR is the rear axle lateral force, F yF MAX is the front axle lateral force when the coefficient of friction is one and is the rear axle maximum lateral force when the coefficient of friction is one.
15. The method according to claim 11 wherein the estimated surface coefficient of friction is gradually returned to a predetermined default value when vehicle dynamics become linear after being nonlinear.
16. A system for estimating a surface coefficient of friction in a vehicle, said system includes one or more computing devices coupled to a memory, wherein said computing devices are programmed to execute instructions stored thereon for:
providing a kinematics relationship between vehicle yaw-rate, vehicle speed, vehicle steering angle and vehicle front and rear axle side-slip angles that is accurate for all surface coefficient of frictions on which the vehicle may be traveling;
defining a nonlinear function for the front and rear axle side-slip angles relating to front and rear axle forces and coefficient of friction;
means for using the nonlinear function in the kinematics relationship;
providing a linear relationship of the front and rear axle side-slip angles and the front and rear lateral forces using the kinematics relationship;
determining that the vehicle dynamics have become nonlinear using the linear relationship; and
estimating the surface coefficient of friction when the vehicle dynamics become non-linear.
17. The system according to claim 16 wherein determining that the vehicle dynamics have become nonlinear includes determining that an equality defined by the linear relationship becomes unequal and the inequality exceeds a predetermined threshold.
18. The system according to claim 17 wherein the linear relationship is defined by the equation:
L
r
v
x
≈
tan
(
δ
+
F
yF
c
F
)
-
tan
(
F
yR
c
R
)
where L is the vehicle wheel base, r is vehicle yaw-rate, ν x is vehicle speed, δ is vehicle steering angle, F yF is the front axle force, F yR is the rear axle force, C F is a front vehicle corning stiffness and C R is a rear vehicle cornering stiffness.
19. The system according to claim 16 wherein the kinematic relationship is:
L
r
v
x
=
tan
(
δ
+
α
F
)
-
tan
α
R
where L is the vehicle wheel base, r is vehicle yaw-rate, ν x is vehicle speed, δ is a vehicle steering wheel angle, α F is a front axle side-slip angle and α R is a rear axle side-slip angle.
20. The system according to claim 16 wherein the means for estimating the surface coefficient of friction uses the equation:
μ
estimate
=
F
yF
+
F
yR
F
yF
,
MAX
+
F
yR
,
MAX
where μ estimate is the estimate of the coefficient of friction, F yF is the front axle lateral force, F yR is the rear axle lateral force, F yF MAX is the front axle lateral force when the coefficient of friction is one and F yR MAX is the rear axle maximum lateral force when the coefficient of friction is one.