Method and system for determining friction between the ground and a tire of a vehicle
There is provided a method for estimating friction between a tire of a vehicle and a road surface, the method comprising acquiring, a front wheel axle torque, a rear wheel axle torque, a vehicle longitudinal acceleration, a vehicle pitch rate and wheel rotational velocities. The method further comprises determining a front wheel normal force and a rear wheel normal force, based on a center of gravity of the vehicle and the longitudinal acceleration; determining a longitudinal tire stiffness, jointly determining a vehicle longitudinal velocity, based on the wheel rotational velocities and vehicle longitudinal acceleration, and a vehicle pitch angle relative to the horizontal plane based on the vehicle pitch rate; and determining a friction coefficient between tires and ground based on the front and rear wheel axle torque, the front wheel normal force and the joint estimation of pitch angle and vehicle longitudinal velocity. There is also provided a system for performing the described method.
1. A method for estimating friction between a tire of a vehicle and a road surface, the method comprising:
acquiring:
a front wheel axle torque, T f ;
a rear wheel axle torque, T r ;
a vehicle longitudinal acceleration, a x ;
a vehicle pitch rate, Ω y ; and
a plurality of wheel rotational velocities, ω m f/r ;
determining a front wheel normal force, F zf , and a rear wheel normal force, F zr , based on a center of gravity of the vehicle and the longitudinal acceleration;
determining a longitudinal tire stiffness, k i ;
jointly determining a vehicle longitudinal velocity, v x , based on the wheel rotational velocities and vehicle longitudinal acceleration, and a vehicle pitch angle, θ y , relative to a horizontal plane based on the vehicle pitch rate; and
determining a friction coefficient, μ i , between a tire and the road surface based on the front and rear wheel axle torques, the front wheel normal force and the joint determination of the pitch angle and the vehicle longitudinal velocity.
2. The method according to claim 1 wherein the friction coefficient is determined based on a complete state dynamics model according to
J wf {dot over (ω)} f =T f −F zf g ( s f ;θ f ) r f
J wr {dot over (ω)} r =T r −F zr g ( s r ;θ r ) r r
{dot over (θ)} y =Ω y
{dot over (v)} x =a x +g sin θ y
where J f/r is the front and rear wheel inertia, s f/r is the front and rear wheel slip, and θ is a vector containing the model parameters, θ i =[k i μ i ].
3. The method according to claim 2 wherein the function g is described by a brush model.
4. The method according to claim 1 wherein the center of gravity of the vehicle is determined based on a known vehicle geometry.
5. The method according to claim 1 wherein the vehicle longitudinal acceleration and the vehicle pitch rate are acquired from an inertial measurement unit, IMU.
6. The method according to claim 1 wherein determining a wheel axle torque comprises determining a brake torque based on a hydraulic brake pressure and determining an engine torque based on a mass flow and a fuel flow of a combustion engine of the vehicle.
7. A tire-road friction determination system in a vehicle, the system comprising:
a wheel axle torque sensing arrangement configured to detect a front wheel axle torque and a rear wheel axle torque;
an acceleration sensor configured to detect a vehicle longitudinal acceleration;
a pitch rate sensor configured to detect a pitch rate of the vehicle;
at least one rotational velocity sensor configured to detect a wheel rotational velocity of at least one wheel; and
an electronic control unit configured to
acquire:
a front wheel axle torque, T f ;
a rear wheel axle torque, T r ;
a vehicle longitudinal acceleration, a x ;
a vehicle pitch rate, Ω y ; and
at least one wheel rotational velocity, ω m f/r ;
the electrical control unit being further configured to
determine a front wheel normal force, F zf and a rear wheel normal force, F zr , based on a center of gravity of the vehicle and the longitudinal acceleration;
determine a longitudinal tire stiffness, k i ;
jointly determine a vehicle longitudinal velocity, v x , based on the at least one wheel rotational velocity and vehicle longitudinal acceleration, and a vehicle pitch angle relative to the horizontal plane based on the vehicle pitch rate; and
determine a friction coefficient, u i , between a wheel and ground based on the front and rear wheel ale torque, the front wheel normal force and the joint determination of pitch angle and vehicle longitudinal velocity.
8. The system according to claim 7 wherein the electronic control unit is further configured to determine the friction coefficient based on a complete state dynamics model according to
J wf {dot over (ω)} f =T r −F zf g ( s f ;θ f ) r f
J wr {dot over (ω)} r =T r −F zr g ( s r ;θ r ) r r
{dot over (θ)} y =Ω y
{dot over (v)} x =a x +g sin θ y
where J f/r is the front and rear wheel inertia, s f/r is the front and rear wheel slip, and θ is a vector containing the model parameters, θ i =[k i μ i ].
9. The system according to claim 7 wherein the pitch rate sensor comprises an inertial measurement unit, IMU.
10. The system according to claim 7 wherein the wheel axle torque sensing arrangement comprises:
at least one hydraulic brake pressure sensor configured to determine a brake torque of each wheel; and
a mass flow sensor and a fuel flow sensor configured to determine an engine torque provided to each of the wheels based on a mass flow and a fuel flow of a combustion engine of the vehicle.
11. A vehicle comprising a tire-road friction determination system according to any one of claim 7 .