Estimation of surface lateral coefficient of friction

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.

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.