Method and system for determining friction between the ground and a tire of a vehicle

Abstract

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.

Claims

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.sub.f; a rear wheel axle torque, T.sub.r; a vehicle longitudinal acceleration, a.sub.x; a vehicle pitch rate, .sub.y; and a plurality of wheel rotational velocities, .sup.m.sub.f/r; determining a front wheel normal force, F.sub.zf, and a rear wheel normal force, F.sub.zr, based on a center of gravity of the vehicle and the longitudinal acceleration; determining a longitudinal tire stiffness, k.sub.i; jointly determining a vehicle longitudinal velocity, v.sub.x, based on the wheel rotational velocities and vehicle longitudinal acceleration, and a vehicle pitch angle, .sub.y, relative to a horizontal plane based on the vehicle pitch rate; and determining a friction coefficient, .sub.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.sub.wf{dot over ()}.sub.f=T.sub.fF.sub.zfg(s.sub.f;.sub.f)r.sub.f
J.sub.wr{dot over ()}.sub.r=T.sub.rF.sub.zrg(s.sub.r;.sub.r)r.sub.r
{dot over ()}.sub.y=.sub.y
{dot over (v)}.sub.x=a.sub.x+g sin .sub.y where J.sub.f/r is the front and rear wheel inertia, s.sub.f/r is the front and rear wheel slip, and is a vector containing the model parameters, .sub.i=[k.sub.i .sub.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.sub.f; a rear wheel axle torque, T.sub.r; a vehicle longitudinal acceleration, a.sub.x; a vehicle pitch rate, .sub.y; and at least one wheel rotational velocity, .sup.m.sub.f/r; the electrical control unit being further configured to determine a front wheel normal force, F.sub.zf and a rear wheel normal force, F.sub.zr, based on a center of gravity of the vehicle and the longitudinal acceleration; determine a longitudinal tire stiffness, k.sub.i; jointly determine a vehicle longitudinal velocity, v.sub.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.sub.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.sub.wf{dot over ()}.sub.f=T.sub.rF.sub.zfg(s.sub.f;.sub.f)r.sub.f
J.sub.wr{dot over ()}.sub.r=T.sub.rF.sub.zrg(s.sub.r;.sub.r)r.sub.r
{dot over ()}.sub.y=.sub.y
{dot over (v)}.sub.x=a.sub.x+g sin .sub.y where J.sub.f/r is the front and rear wheel inertia, s.sub.f/r is the front and rear wheel slip, and is a vector containing the model parameters, .sub.i=[k.sub.i .sub.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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects of the present disclosure will now be described in more detail, with reference to the appended drawings showing an example embodiment of the disclosure, wherein:

(2) FIG. 1 is a flow chart outlining the general steps of a method according to an embodiment of the disclosure;

(3) FIG. 2 is a block chart outlining general features of the present disclosure; and

(4) FIG. 3 is a schematic illustration of a vehicle comprising a system according to an embodiment of the disclosure.

DETAILED DESCRIPTION

(5) As required, detailed embodiments are disclosed herein. However, it is to be understood that the disclosed embodiments are merely exemplary and that various and alternative forms may be employed. The figures are not necessarily to scale. Some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art.

(6) In the present detailed description, various embodiments of the method and according to the present disclosure will be described.

(7) FIG. 1 is a flow chart outlining the general steps of a method for estimating friction between a tire of a vehicle and a road surface according to an embodiment of the disclosure.

(8) The method comprises acquiring: a front wheel axle torque, T.sub.f 102; a rear wheel axle torque, T.sub.r 104; a vehicle longitudinal acceleration, a.sub.x 106; a vehicle pitch rate, .sub.y 108; and wheel rotational velocities, .sup.m.sub.f/r 110.

(9) The method further comprises determining 112 a front wheel normal force, F.sub.zf and a rear wheel normal force, F.sub.zr, based on a center of gravity of the vehicle and the longitudinal acceleration; determining 114 a longitudinal tire stiffness, k.sub.i; jointly determining 116 a vehicle longitudinal velocity, v.sub.x, based on the wheel rotational velocities and vehicle longitudinal acceleration, and a vehicle pitch angle, .sub.y, relative to the horizontal plane based on the vehicle pitch rate; and determining 118 a friction coefficient, .sub.i, 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.

(10) The described method for determining tire/road friction is based on an analytical model which models the physics between the slip and the force. In particular, a model is provided which determines vehicle velocity taking the vehicle pitch into account.

(11) The model assumes access to standard vehicle dynamics sensors such as wheel speed signals from an ABS system and the longitudinal acceleration from an Inertial Measurement Unit (IMU) as well as access to measurements of the vehicle pitch rate from a pitch rate sensor such as the IMU.

(12) In the following, signal processing algorithms for estimation of the tire/road friction coefficient will be described in further detail. First, information related to wheel velocities is derived. The vehicle geometry is as follows: l.sub.f: Longitudinal distance from center of gravity to the front axle. l.sub.r: Longitudinal distance from center of gravity to the rear axle. w.sub.f: Half front track width. w.sub.r: Half rear track width.

(13) It is assumed that the vehicle is moving in the plane and that the longitudinal and lateral vehicle velocity expressed in the center-of-gravity coordinate system is v.sub.x and v.sub.y, respectively. It is further assumed that the vehicle yaw-rate is .sub.z. The basic relation used next is that the velocity vector v.sup.P at a point P which is rotating with rate .sub.z relative the center-of-gravity coordinate system is:

(14) $v^{P} = v + [\begin{matrix} 0 \\ 0 \\ _{z} \end{matrix}] P$
Here v=[v.sub.x v.sub.y 0].sup.T is the velocity vector at the center of gravity, and v.sup.P=[v.sub.x.sup.P v.sub.y.sup.P 0].sup.T. Note that all velocity components are expressed using the vehicle attached center-of-gravity coordinate system. In the following the short hand notation FL==1, FR==2, RL==3, and RR==4 is used.

(15) Assume further that the front and rear wheels have steering angles ,.sub.f and ,.sub.r, respectively. The longitudinal component of the wheel velocity in the local tire coordinate system P.sub.i is thus related to the vehicle center of gravity velocities as:

(16) $[\begin{matrix} v_{x}^{P_{1}} \\ v_{x}^{P_{2}} \\ v_{x}^{P_{3}} \\ v_{x}^{P_{4}} \end{matrix}] = [\begin{matrix} (v_{x} - w_{f}_{z}) \cos_{f} + (v_{y} + I_{f}_{z}) \sin_{f} \\ (v_{x} + w_{f}_{z}) \cos_{f} + (v_{y} + I_{f}_{z}) \sin_{f} \\ (v_{x} - w_{r}_{z}) \cos_{r} + (v_{y} - I_{r}_{z}) \sin_{r} \\ (v_{x} + w_{r}_{z}) \cos_{r} + (v_{y} - I_{r}_{z}) \sin_{r} \end{matrix}]$

(17) Here it is assumed that the left and right front/rear wheel angles are identical. In the following it is assumed assume for simplicity that the rear wheel angle is zero.

(18) The longitudinal wheel slip is defined as:

(19) $s_{i} = \frac{_{i} r_{i} - v_{x}^{P_{i}}}{v_{x}^{P_{i}}}$
where r.sub.i is the effective wheel radius of the i.sup.th tire.

(20) Next the relation between longitudinal tire slip and the applied normalized longitudinal tire force is considered. Although it is theoretically possible to extend the results to the case with so-called combined slip, this will not be described herein. In the literature an abundance of models relating the wheel slip s.sub.i and the applied normalized traction force f.sub.i can be found. In the current analysis only static models are considered.

(21) A tire-force model common in the field of vehicle dynamics is the brush-model with parabolic normal load distribution, which states:

(22) $f_{i} = {\begin{matrix} k_{i} s_{i} - \frac{s_{i} .Math. s_{i} .Math. k_{i}^{2}}{3_{i}} + \frac{s_{i}^{3} k_{i}^{3}}{27_{i}^{2}}, .Math. s_{i} .Math. < \frac{3_{i}}{k_{i}} \\ _{i} sgn (s_{i}), otherwise \end{matrix}$

(23) Here k.sub.i is the longitudinal tire stiffness parameter and .sub.i is the friction coefficient, and f.sub.i is the normalized (with respect to the wheel normal force) force. Tire stiffness varies for different tires and the stiffness can change, for example through tire wear. However, tire wear is a slowly changing process and in the current context the tire stiffness k.sub.i can be considered to be constant. However, since car users may change tires to unknowns types, the stiffness need to be estimated onboard the vehicle. This is done by estimating the linear relationship between tire force and slip for small forces. The good thing is that stiffness not is dependent on friction for low forces, which makes the estimation of stiffness straightforward. Low forces can here be estimated as forces of up to 30% of the maximum force.

(24) The brush-model is derived from physical considerations. An example among many candidates of a curve-fitting-like non-physical tire-force model is

(25) $f_{i} =_{i} \tanh (\frac{k_{i}}{_{i}} s_{i}) .$

(26) The exact form of the tire-force model is not critical for the development below. Hence, in the following it is simply assumed that the following static tire-force models are available:
f.sub.i=g(s.sub.i;.sub.i)
where .sub.i is a vector containing the parameters of the model; e.g. .sub.i=[k.sub.i .sub.i].

(27) The basic relation utilized here is that the dynamics of the wheel speed signals are given by:
J.sub.wf{dot over ()}.sub.f=T.sub.fF.sub.zfg(s.sub.f;.sub.f)r.sub.f
J.sub.wr{dot over ()}.sub.r=T.sub.rF.sub.zrg(s.sub.r;.sub.r)r.sub.r
for the front and rear wheels, respectively.

(28) For simplicity only one side of the vehicle is studied. Here, the following parameters are assumed to be known with sufficient precision: J.sub.wf=front wheel inertia J.sub.wr=rear wheel inertia tire parameters such as longitudinal stiffness in the brush model r.sub.f/r: front and rear effective wheel radius.

(29) Note that the longitudinal stiffness is considered known in the sense that it can be adapted from data using data where force utilization is low. In particular, at low forces the tire force is dependent on slip but not on the friction. Thereby, the longitudinal stiffness can be determined for low forces and once the longitudinal stiffness is known the friction can be determined when the wheel forces are higher, e.g. higher than 30% of a maximum force.

(30) The front and rear effective wheel radius can be considered known in the sense that it can be adapted from known data.

(31) The state vector (quantities that are to be estimated) for the problem at hand is defined as:
x=[.sub.f .sub.r .sub.y].sup.T

(32) The embodiment described presented herein is focused on the case where the vehicle is travelling in a more or less straight line. This assumption is made to simplify the analysis to a suitable extent.

(33) The sensor data that feeds the proposed algorithm is: T.sub.f front wheel axle torque T.sub.r rear wheel axle torque a.sub.x: longitudinal acceleration acquired from the IMU .sub.y: pitch rate acquired from the IMU F.sub.zf: front wheel normal force F.sub.zr: rear wheel normal force .sup.m.sub.f/r: measured wheel rotational velocities.

(34) It can be noted that there is no sensor available that directly measures the tire normal forces. Instead it is assumed that wheel normal forces can be estimated using standard assumptions on static torque equilibrium around a pitch axis through center of gravity known by the skilled person.

(35) $F_{zf} = \frac{- {mha}_{x} + {mgl}_{r}}{l_{f} + l_{r}}$ $F_{zr} = \frac{{mha}_{x} + {mgl}_{f}}{l_{f} + l_{r}}$

(36) Here h is the height of the center of gravity of the vehicle, which can be assumed to be known with sufficient precision, g is the gravitational constant, and m is the nominal mass of the vehicle, also assumed known with sufficient precision. The above expression can easily be modified to include also the air-resistance by a person skilled in the art.

(37) One problem related to the current analysis is as follows. Assume that the vehicle applies torques T.sub.f/r on the front and/or rear axle and as a result, the wheel rotational velocity changes. However, the change rate will depend on at least the friction. While driving on ice, a small change in applied torque results in a large change in wheel rotational speed. If all wheel rotational velocities are affected by slip then the estimation of the vehicle's longitudinal velocity is difficult. In an attempt to mitigate the problem one can consider to integrate the longitudinal acceleration for estimation of v.sub.x. As long as the vehicle is on flat ground this could work; but in general the problem is that the gravity vector affects the reading of the longitudinal acceleration (valid as long as the vehicle is travelling straight ahead):
a.sub.x={dot over (v)}.sub.xg sin .sub.y.

(38) Thus, for estimation of the longitudinal velocity using integration, also pitch angle has to be estimated, which leads to the conclusion that pitch-rate sensing is essential for accurate estimation of the longitudinal velocity. As long as the vehicle is travelling straight ahead, the model for the pitch-rate sensor signal is:
{dot over ()}.sub.y.sub.y.

(39) In conclusion, the non-linear complete state dynamics model for the problem at hand is:
J.sub.wf{dot over ()}.sub.f=T.sub.fF.sub.zfg(s.sub.f;.sub.f)r.sub.f
J.sub.wr{dot over ()}.sub.r=T.sub.rF.sub.zrg(s.sub.r;.sub.r)r.sub.r
{dot over ()}.sub.y=.sub.y
{dot over (v)}.sub.x=a.sub.x+g sin .sub.y

(40) Based on the above described modelling, the friction coefficient can be estimated based on a torque estimation, a force estimation and a stiffness estimation as illustrated schematically in FIG. 2 where the general flow of calculations can be described as pitch rate.fwdarw.pitch angle.fwdarw.vehicle velocity.fwdarw.tire longitudinal slip.fwdarw.friction.

(41) The modelling described above has defined the equations that govern the state dynamics, and it has been specified which sensor data that is assumed available. The exact choice of non-linear filtering algorithm used can be considered to be less important since this a standard topic for the person skilled in the art.

(42) FIG. 3 schematically illustrate a vehicle 300 comprising a system configured to determine tire-to-road friction. The system comprises a wheel axle torque sensing arrangement 302a-b configured to detect a front and rear wheel axle torque, an acceleration sensor 304 configured to detect a vehicle longitudinal acceleration and a pitch rate sensor 304 configured to detect a pitch rate of the vehicle. Here the acceleration sensor and pitch rate sensor are illustrated as one inertial measurement unit, IMU. The system also comprises a plurality of rotational velocity sensors 306a-d configured to detect a wheel rotational velocity of a respective one of each of the four wheels. The above mentioned sensors are connected to an a electronic control unit (ECU) 308 which in turn is configured to acquire a front wheel axle torque, a rear wheel axle torque, a vehicle longitudinal acceleration, a vehicle pitch rate and wheel rotational velocities from the sensors.

(43) Based on the acquired information, the electrical control unit 308 is further configured to: determine a front and rear wheel normal force based on a center of gravity of the vehicle and the longitudinal acceleration, determine a longitudinal tire stiffness, jointly determine 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. Thereby a friction coefficient, .sub.i, between a wheel and ground can be determined 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.

(44) It should be noted that the ECU 308, as well as any other system, device, unit, arrangement or the like described herein may comprise and/or be implemented in or by one or more appropriately programmed processors (e.g., one or more microprocessors including central processing units (CPU)) and associated memory and/or storage, which may include operating system software, application software and/or any other suitable program, code or instructions executable by the processor(s) for controlling operation thereof, for providing and/or controlling interaction and/or cooperation between the various features and/or components described herein, and/or for performing the particular algorithms represented by the various functions and/or operations described herein.

(45) Even though the disclosure has been described with reference to specific exemplifying embodiments thereof, many different alterations, modifications and the like will become apparent for those skilled in the art. Also, it should be noted that parts of the method and system may be omitted, interchanged or arranged in various ways, the method and system yet being able to perform the functionality of the present disclosure.

(46) Additionally, variations to the disclosed embodiments can be understood and effected by the skilled person in practicing the claimed disclosure, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

(47) While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms of the disclosure. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the disclosure. Additionally, the features of various implementing embodiments may be combined to form further embodiments of the disclosure.

Method and system for determining friction between the ground and a tire of a vehicle

Assignee

Inventors

Cpc classification

Classification Explorer

B60T2250/042

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60W40/068

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T8/172

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T2210/12

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T8/175

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T2240/00

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T2250/00

PERFORMING OPERATIONS; TRANSPORTING

International classification

Classification Explorer

B60T8/172

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60W40/068

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B60T8/175

PERFORMING OPERATIONS; TRANSPORTING

Abstract

Claims

Description