阅读说明：本技术 用于对轮胎的扭转弹性释放建模以确定横拉杆力从而管理驻车和驾驶之间的过渡的方法 (Method for modeling torsional elastic release of a tire to determine tie-rod force to manage transitions between parking and driving ) 是由 塞巴斯蒂安·布尔德勒泽 皮埃尔·杜普拉斯 塞尔日·高登 帕斯卡尔·穆莱尔 山本和纱 于 2018-05-15 设计创作，主要内容包括：本发明涉及一种用于估计在车辆(2)装备有的动力转向系统(1)中施加在横拉杆(3)上的横拉杆力(Fb)的方法,所述横拉杆属于将比如转向盘(5)或动力转向马达(6)等致动器连接至转向轮(7)的转向机构(4),该转向轮能在偏转方向上定向并且支承轮胎(8),轮胎的胎面(8BR)与地面(9)接触,通过对轮胎(8)的弹性扭转的释放进行建模的力分量(F2)根据车辆的纵向速度(V_vehic)来校正估计的横拉杆力(Fb)的值,以便当车辆从车辆的纵向速度(V_vehic)为零的驻车状况过渡到车辆的纵向速度(V_vehic)非零的驾驶状况时就绝对值而言根据车辆的纵向速度(V_vehic)降低估计的横拉杆力(Fb)。(The invention relates to a method for estimating a tie rod force (Fb) exerted on a tie rod (3) in a power steering system (1) with which a vehicle (2) is equipped, belonging to a steering mechanism (4) connecting an actuator, such as a steering wheel (5) or a power steering motor (6), to a steered wheel (7), the steering wheel being capable of orienting and supporting a tyre (8) in a yaw direction, the tread (8BR) of the tyre being in contact with the ground (9), correcting the value of the estimated tie-rod force (Fb) as a function of the longitudinal speed (V _ vehic) of the vehicle by means of a force component (F2) which models the release of the elastic torsion of the tyre (8), so as to reduce, in absolute terms, the estimated tie-rod force (Fb) as a function of the longitudinal speed (V _ vehic) of the vehicle when the vehicle transitions from a parking condition in which the longitudinal speed (V _ vehic) of the vehicle is zero to a driving condition in which the longitudinal speed (V _ vehic) of the vehicle is non-zero.)

1. A force estimation method for estimating a value of an actuation force, referred to as "force at tie rod" (Fb), exerted on a transmission member, such as a tie rod (3), belonging to a steering mechanism (4) connecting an actuator, such as a steering wheel (5) or a power-assisted motor (6), to a steering wheel (7) which is deflectably oriented and carries a tyre (8) the tread (8BR of which is in contact with the ground (9), in a power steering system (1) equipping a vehicle (2), characterized in that the value of the estimated force (Fb) at the tie rod is corrected as a function of the longitudinal speed (V _ vehic) of the vehicle in order to lower the estimated force at the tie rod in absolute value as a function of the longitudinal speed (V _ vehic) of the vehicle when the vehicle transitions from a parking condition in which the longitudinal speed (V _ vehic) of the vehicle is zero to a driving condition in which the longitudinal speed (V _ vehic) of the vehicle is non-zero Force (Fb).

2. The force estimation method according to claim 1, in which method the force at the tie rod is evaluated by a model (15) using:

a first force component (F)₁) Representing a deflection elastic torsion of said tyre (8) corresponding to a position (X) imparted to said transmission member (3) by said power steering system (1) on the one hand_CR) And on the other hand the position (X) of the tread (8BR) of said tyre_BR) A position of the tread exerted by the ground (9) on the tread (8BR) of a tyre_c) Is retained against displacement of the transmission member;

and a second force component (F2) which, as soon as the vehicle (2) assumes a non-zero longitudinal speed, causes the first force component (F) to be dependent on the longitudinal speed (V _ vehic) of the vehicle₁) -damping in order to take into account the gradual release of the deflecting elastic torsion of the tyre (8) during the transition between a parking condition in which the longitudinal speed of the vehicle is zero and a running condition in which the longitudinal speed of the vehicle is non-zero.

3. Method for estimating a force according to claim 2, characterised in that said first force component (F)₁) By means of a first stiffness coefficient (k) representing the torsional stiffness of the tyre (8)_t) Modeling, the first stiffness coefficient being multiplied by a position deviation (Δ x) between a tread (8BR) of the tyre and a transmission member (3): f₁＝k_t*Δx。

4. The force estimation method according to claim 2 or 3, characterized in that the second force component (F)₂) By a second coefficient (k)_d) Multiplying the longitudinal speed (V _ vehic) of the vehicle and the position deviation (Δ x) between the tread (8BR) of the tyre and the transmission member (3) to model: f₂＝k_d*V_vehic*Δx。

5. The force estimation method according to any of the claims 2 to 4, characterized in that the second force component (F)₂) Is calculated from the longitudinal speed (V _ vehic) of the vehicle and the static friction value (Frot) which represents the tread (8B) within the sliding limitsR) and the ground (9), which must be overcome by the action of the transmission member (3) to cause a deflection displacement of the tread (8BR) of the tyre on the ground (9) when the vehicle (2) is stopped.

6. Method for estimating forces according to claims 3, 4 and 5, characterized in that the force (Fb) at the track rod is calculated from a first order term with respect to the speed (V _ vehic) of the vehicle and is equal to

7. The force estimation method according to claims 4 and 5 or claim 6, characterized in that the second coefficient (k) is adjusted according to the static friction value (Frot)_d)。

8. The force estimation method according to any one of claims 4, 6 or 7, characterized in that the second coefficient (k) is adjusted in dependence of the longitudinal speed (V vehic) of the vehicle_d)。

9. Force estimation method according to any one of claims 5 to 7, characterized in that the static friction value (Frot) is adjusted according to parameters specific to the vehicle or the environment of the vehicle and which may alter the adherence of the tyre (8) on the ground (9).

10. The force estimation method according to any one of claims 2 to 9, characterized in that a model (15) allowing to evaluate the force (Fb) at the tie rod additionally uses a position (X) depending on the transmission member (3)_CR) Of (d) is a third force component (F)₃) In order to model the lifting effect of the vehicle (2) during yaw steering of the wheels (7).

11. Method for force estimation according to claim 10, characterized in that the third force component (k)_d) Is calculated from a quadratic polynomial comprising the position (X) relative to the transmission member (3)_CR) Linear and quadratic terms of (c): f₃＝kf1*X_CR+kf2*X_CR ²。

12. The force estimation method according to claim 11, characterized in that the coefficients (kf1, kf2) of the quadratic polynomial are adjusted according to the longitudinal speed (V vehic) of the vehicle.

13. The force estimation method according to any of the preceding claims, characterized in that the force estimation method is used for estimating the force from the longitudinal speed (V vehic) of the vehicle and the position (X) of the rack, which is considered as a representative position of the transmission member (3)_CR) To determine an actuation force, referred to as "force at tie rod" (Fb), which represents the force exerted by a transmission member formed by a tie rod (3) on one end of a rack (12) mounted movably relative to the frame (14) of the vehicle, and the tie rod (3) being connected to the steered wheels (7).

Technical Field

The present invention relates to power steering systems, and more particularly to a method that allows for the evaluation of a force, referred to as "force at tie rod", which represents the force transmitted by a running gear to a steering rack via the tie rod.

Background

In fact, the driver and the steering power assist system must overcome this "force at the tie rod" to change the yaw orientation of the steered wheels.

There are methods that allow estimating the force at the tie rod by a magnitude characteristic of the lateral dynamics of the vehicle, for example, from the lateral acceleration or yaw rate of the vehicle.

However, this method relies on a model that is valid only under driving conditions and starts from a significant longitudinal speed of the vehicle, typically from 50 km/h.

Otherwise when the vehicle is stationary, the force at the tie rod in the park condition may be estimated.

However, once the vehicle starts moving, the model for estimating the force at the tie rod at rest is no longer applicable.

However, with the increasing complexity of power steering systems, and in particular with the declaration of an extension of the steering system known as "steer-by-wire" (which no longer comprises a mechanical transmission between the steering wheel and the steering mechanism actuating the wheels), it is necessary to reliably evaluate the force at the tie-rod in all cases, in particular in the low speed range, typically between 0km/h and 30km/h, in order to return to the driver a reliable perception of the road and vehicle behaviour through the steering wheel.

Disclosure of Invention

The objects allocated to the invention are therefore: the disadvantages of the known methods are overcome and a new method for evaluating the force at the track rod is proposed, which allows to reliably evaluate the force at the track rod in low speeds and more particularly during transitions between parking conditions and driving conditions (or vice versa).

The object assigned to the invention is achieved by a force estimation method for estimating the value of an actuating force, called "force at tie rod", exerted on a transmission member, such as a tie rod, belonging to a steering mechanism connecting an actuator, such as a steering wheel or a power assist motor, to a steered wheel, which is deflectably oriented and carries a tire, the tread of which is in contact with the ground, in a power steering system equipping a vehicle, characterized in that an estimated value of the force at the tie rod is corrected as a function of the longitudinal speed of the vehicle, so as to reduce the estimated force at the tie rod in absolute value as a function of the longitudinal speed of the vehicle when the vehicle changes from a parking condition, in which the longitudinal speed of the vehicle is zero, to a driving condition, in which the longitudinal speed of the vehicle is non-zero.

Advantageously, using the longitudinal speed of the vehicle as a parameter attenuating the estimated value of the force at the tie-rod according to the invention allows to model the deflection torsion force exerted by the tyre on the wheel and the tie-rod and therefore to take into account this deflection torsion force (which is generated due to the friction of the tread of the tyre on the ground against the directional movement of the wheel), and in particular allows to model and take into account the gradual relaxation of said torsion force, which occurs during the transition from a parking condition of zero speed to a driving condition of non-zero speed.

In fact the inventors have found that: when stopped, the displacement of the rack and therefore of the tie rods connected to said rack and the rigid rim of the wheel causes an elastic torsional deformation of the tyre when deflected, due to the presence of static friction between the ground and the tyre tread (which tends to keep said tread against the deflection displacement of the rim).

Due to the elastic deformation of the tire side wall connecting the rim to the tread, an angular offset occurs upon deflection, i.e. a positional deviation between the rim on the one hand and the tire tread in contact with the ground on the other hand.

More specifically, when stopped, when the steering wheel is turned to increase the steering angle of the steering system, the steering angle (yaw angle) of the tread is smaller than the steering angle (yaw angle) of the rim, which is determined by the position of the rack.

Once the vehicle starts to run, however, the rotation of the wheel has the effect of causing the tyre to progressively recover elastically, that is to say to deflect torsionally, elastically relaxing, so that the tread of the tyre tends to align with the rim, substantially "capturing" the deflection angle of said rim.

Advantageously, the invention allows taking into account such transient relaxation phenomena by means of a model comprising the rack position (considered to represent the deflection position of the rim in view of the relatively rigid nature of the connection that connects them to each other) and the longitudinal speed of the vehicle, and therefore allows simulating in a very complete way the variations of the elastic torsional stresses exerted by the tyre on the steering mechanism, and more particularly on the tie-rods and the rack.

The method according to the invention thus allows a particularly accurate and reliable estimation of the force at the track rod, in particular during the transition between parking conditions and driving conditions (or vice versa), and when the vehicle is travelling at low speeds, typically between 0km/h and 20km/h or even 30 km/h.

Drawings

Other objects, features and advantages of the present invention will appear in more detail on reading the following description and on using the accompanying drawings, which are provided for illustrative purposes only and are not limiting, wherein:

fig. 1 shows an example of a power steering system to which the method according to the invention can be applied, according to a schematic diagram.

Fig. 2 shows a physical model for determining the force at the tie rod according to the method of the invention.

Fig. 3 shows a functional conversion of the model of fig. 2 according to a block diagram.

Fig. 4, 5 and 6 correspond to comparative graphs representing hysteresis cycles of the measured forces at the active track rod estimated by the method according to the invention for different vehicle speeds, i.e. 0km/h, 3km/h, 7km/h and 15km/h, as a function of the rack position, which varies periodically in alternating manoeuvres from left to right and vice versa.

Detailed Description

The present invention relates to a force estimation method for estimating the value of an actuation force Fb, referred to as "force at tie rod", which is exerted on a transmission member 3, such as a tie rod 3, in a power steering system 1 of a equipped vehicle 2.

The transmission member 3 belongs to a steering mechanism 4 which connects an actuator 5, 6, such as a driving wheel 5 or a power-assisted motor 6, preferably an electric power-assisted motor 6, to a steering wheel 7 which can be oriented upon deflection.

The wheel 7 carries a tyre 8, the tread 8BR of which is in contact with the ground 9.

The ground 9 may be of any type and correspond to any surface or coating over which the vehicle 2 may travel, including but not limited to asphalt (road), gravel, dirt, sand. The floor 9 may be dry or wet.

For ease of description, the concept of the wheel 7 will be herein equated with a rigid portion of the wheel 7, typically formed by a rim, preferably formed by metal).

According to a first variant, the steering mechanism 4 will comprise a mechanical connection 10, such as a steering column 10, allowing the transmission of motion (and force) between the steering wheel 5 and the steered wheels 7, for example via a pinion 11 mounted on said steering column 10 and meshing on a rack 12.

According to a second variant of the invention, it is particularly preferred that the connection between the steering wheel 5 and the wheels 7 will be performed virtually by the electric controller 13, so that the power steering system will form a system known as a "steer-by-wire" system.

The mechanical connection 10 between the steering wheel 5 and the wheels 7 may be disengageable so as to be able to switch alternately from the first variant (mechanical connection between steering wheel and wheels) to the second variant (steer-by-wire).

Preferably, regardless of the considered variant and as shown in fig. 1, the steering mechanism comprises a rack 12, which rack 12 is movably mounted with respect to a frame 14 of the vehicle 2 and more particularly is guided in translation according to its longitudinal axis with respect to the vehicle frame 14.

As indicated above, the transmission member 3 is preferably formed by a tie rod 3.

Preferably, here the tie rod 3 connects one end of the rack 12 to the steered wheel 7 and more particularly to a stub axle which, when deflected, can be oriented and carries the steered wheel 7.

In practice, the force Fb at the track rod will thus correspond to a longitudinal tensile or compressive force of the rack 12, which force is exerted by the running gear, here the wheel 7, and via the track rod 3 on each end of the rack 12.

Therefore, this method is preferably used in practice for determining an actuation force, referred to as "force at tie rod" Fb, which represents the force exerted by the transmission member formed by the tie rod 3 on one end of the rack 12, which rack 12 is movably mounted with respect to the frame 14 of the vehicle, and which tie rod 3 is connected to the steered wheel 7.

For convenience of description, hereinafter, the transmission member may be identical to the tie rod 3.

In addition, regardless of its shape, the transmission member 3 is of course rigid and in particular has a greater rigidity than the sidewall 8L of the tyre 8.

The sidewall 8L of the tire here refers to the lateral portion of the tire 8 that connects the wheel 7 and more specifically the rim to the tread 8 BR.

More generally, the steering mechanism 4, and more particularly the kinematic chain extending from the rack 12 to the wheel 7 and more particularly from the rack 12 to the rigid rim of said wheel 7 through the tie rods 3, is rigid and has a rigid behaviour compared to the sidewalls 8L of the tyre, being almost insensitive to elastic deformations.

It can therefore be considered that, at least in the first solution, the position of the rim and therefore of the wheel 7 can be equivalent to the position of the tie-rods 3 and therefore to the position of the rack 12, while most or even all of the positional offset between the tread 8BR of the tyre and the rack 12 will be due to the elastic torsion of the tyre 8 with respect to the wheel 7 (rim).

Nevertheless, according to another alternative, a more complete modeling considering the elasticity of the kinematic chain extending from the rack 12 to the wheel 7 can be used for the purposes of the present invention.

Such a modelling can take into account, for example, possible position shifts between the wheel 7 and the rack 12 due to the intrinsic elasticity of the mechanical members corresponding to the mechanical parts generally considered to be rigid, such as the tie rod 3 or the stub shaft, or due to the elasticity of the kinematic connection between said mechanical members (generally a ball-joint connection) and in particular of the connection between the rack 12 and the tie rod 3.

Also for ease of description, the positions of the different elements, in particular the yaw orientation of the wheel 7 and the tread 8BR of the tyre, will be indicated in linear position and back to the same frame of reference as the rack 12.

Thus, X_CRWill denote a position called "central position of the wheel 7" corresponding to the deflected orientation of the rigid rim of said wheel 7.

For ease of description and for the reasons previously mentioned, this position X of the wheel centre_CRIt will be known that the position of the actuating member 3 (position of the tie rod 3) and the position of the rack 12 are preferably identical: said position X of the wheel centre_CRCan be determined by the position of the track rod 3 and/or the position of the rack 12 by taking into account the geometry of the kinematic connection between these components and, where appropriate, the elasticity.

Similarly, X_BRA position corresponding to the deflected orientation of the tread 8BR of the tyre 8 in contact with the ground 9 will be indicated.

In any case, according to the method of the invention, the value of the estimated force Fb at the tie rod is corrected in accordance with the longitudinal speed V _ vehic of the vehicle 2, in particular as shown in fig. 3, so that the estimated force Fb at the tie rod is reduced in absolute value in accordance with the longitudinal speed V _ vehic | >0 of the vehicle when the vehicle transitions from a parking condition in which the longitudinal speed V _ vehic of the vehicle is zero (V _ vehic ═ 0) to a driving condition in which the longitudinal speed V _ vehic of the vehicle is non-zero.

As indicated above, taking into account the effect of the speed V vehic of the vehicle on the residual elastic torsion between the tread 8BR of the tyre and the wheel 7, allows to extend the effective range of the model proposed by the invention to parking conditions and low speed driving conditions, in particular between 0km/h and 20km/h or up to 30km/h and to manage the transition between parking conditions and driving conditions.

The fact of providing a correction with a reduced effect of the estimated force Fb at the tie-rod, when moving the vehicle, advantageously allows to include in the estimation of the force Fb at the tie-rod according to the invention a progressive release effect of the deflection torsion of the tyre 8, and therefore a progressive alignment effect of the tread 8BR on the deflection position of the wheel 7, caused by the rotation of said wheel 7 and tyre 8 (about the horizontal axis of the wheel).

As will be described in greater detail below, the invention allows the force Fb at the tie-rod to be evaluated by a model 15 which provides, on the one hand, the elastic deflection torsion of the tyre 8 under the combined action of the actuators (more specifically, under the action of the tie-rod 3 driven by a rack 12 moved by the steering wheel 5 and/or the power-assisted motor 6) and, on the other hand, under the friction of the ground 9, and which comprises a correction assembly which simulates the release of the elastic deflection force of the tyre 8 during the transition from the parking condition to the driving condition.

In this respect, it is possible, according to what alone may constitute preferred features of the invention, that: from the longitudinal speed V vehic of the vehicle on the one hand and from the position X of the rack 12, which is regarded as a representative position of the transmission member 3 (track rod 3) on the other hand_CROr more generally from a deflected orientation representing the rim of the wheel 7, i.e. a position X representing the centre of the wheel 7_CROr allowing determination of said position X of the centre of the wheel 7_CRTo determine the force Fb at the track rod.

It should therefore be noted that: according to the invention and according to a feature which can be separately embodied, only two input parameters (measured parameters), namely the longitudinal speed V vehic of the vehicle and the position X of the toothed rack 12, are acquired in real time_CR(or any other equivalent position of the rigid member of the mechanism 4, representing or allowing a yaw orientation X close to the wheel centre_CR) It is sufficient to calculate the force Fb at the track rod.

According to a preferred feature which may constitute the invention alone and as shown in fig. 2, the force Fb at the track rod is evaluated by a model 15 using:

first force component F₁Which represents the elastic deflection torsion of the tyre 8 corresponding to the position X imparted to the transmission member 3 (more specifically to the wheel 7) by the power steering system 1 on the one hand_CR(i.e., the position X of the center of the wheel which is actually equivalent to the position of the rack 12)_CR) And on the other hand the position X of the tread 8BR of the tyre_BR(this position is exerted by the ground 9 on said tread 8BR of the tyre, here by the term "Frot, k in FIG. 2_cThe frictional resistance indicated by "is maintained against the displacement of the transmission member) is determined as a position deviation Δ X ═ X)_CR-X_BR；

And a second force component F₂Once the vehicle 2 assumes a non-zero longitudinal speed, this second force component causes the first force component F to be dependent on the longitudinal speed V _ vehic of the vehicle₁Damping in order to take into account the gradual release of the elastic deflection torsion of the tyre 8 during the transition between a parking condition in which the longitudinal speed of the vehicle is zero and a running condition in which the longitudinal speed of the vehicle is non-zero.

Position deviation Δ X ═ X_CR-X_BRHere corresponding to the yaw orientation X of the wheel 7 (rim) defined by the action of the rack 12 and the tie rod 3_CRAnd by friction Frot, k on the ground 9_cMaintained deflection orientation X of tread 8BR of tire 8_BRDue to the elastic deformation of the sidewall 8L of the tyre 8 under torsional deflection stress.

When the vehicle starts moving, this position deviation Δ X tends to decrease (that is to say to approach zero) and the rotation of wheel 7 and tyre 8 (that is to say the running movement of tyre 8 on ground 9) tends to align tread 8BR in the deflection on wheel 7, that is to say with the rotation of wheel 7 (of the tread on ground 9) tends to align position X of tread 8BR_BRConverging to the position X of the wheel 7_CR。

It should also be noted that: in addition to the first force component F₁And a second force component F₂In addition, the model 15 allowing to evaluate the force Fb at the tie rod preferably uses the third force component F₃The third force component depends on the position X of the transmission member 3 relative to the frame 14_CR(and more specifically, the yaw orientation X of the wheel 7_CR) In order to model the lifting effect of the vehicle 2 during yaw steering of the wheels 7 (in this case, the lifting of the front of the vehicle when the steered wheels 7 belong to the front axle).

The third force component F₃(the calculation of which will be described in detail below) and the first force component F₁And a second force component F₂Differently and independently, and advantageously allows the model 15 to be completed by taking into account the stresses induced by the rolling and pitching of the vehicle 2 caused by the change in the steering angle of the wheels 7 (change in the yaw orientation).

Diagrammatically shown in fig. 4, 5 and 6, this third force component F₃It is in fact possible to impart their waveform (S-shape) to a hysteresis curve which is expressed as a function of the displacement of the rack 12, i.e. as a function of the deflection position X of the wheel 7_CRForce F at the tie rod as a function of_b。

Preferably, the first force component F₁By a first stiffness coefficient k representing the torsional stiffness of the tyre 8_tTo model, the first stiffness coefficient k_tMultiplied by the position deviation Δ X between the transmission member 3 (and more specifically the rim of the wheel 7) and the tread 8BR of the tyre:

F₁＝k_t*ΔX

a particularly simple modelling is therefore carried out which well represents the elastic deformation of the tyre's side wall 8L connecting the rim, i.e. the rigid part of the wheel 7 and thus the rack 12, to the ground 9.

Further according to a feature which alone may constitute the invention, the second force component F₂Preferably by a second coefficient k_dTo model, this second coefficient is multiplied on the one hand by the longitudinal speed V _ vehic of the vehicle and on the other hand by the position deviation Δ x between the transmission member 3 (and more specifically the rim of the wheel 7) and the tread 8BR of the tyre:

F₂＝k_d*V_vehic*Δx

so here again a relatively simple modeling can be used to reflect the effect of moving the vehicle and thus the transition from zero velocity V vehic to non-zero velocity on the force at the track rod.

It should be noted that: in practice the second coefficient k_dBy N s/m²Expressed and therefore expressed in pa.s, and thus the dynamic viscosity is uniform.

Preferably, the second force component F₂Is calculated from the longitudinal speed V vehic of the vehicle and a static friction value denoted "Frot" which represents the friction between the tread 8BR and the ground 9 within the sliding limits which must be overcome by the action of the transmission member 3 to cause a deflecting displacement of the tread 8BR of the tyre on the ground 9 when the vehicle 2 is stopped.

The static friction value Frot may be determined empirically through testing by operating the power steering system 1 when the vehicle is stationary on the ground 9, preferably on dry ground (i.e. at zero speed V _ vehic).

According to the diagram, the static friction value Frot corresponds to the ordinate at the origin of the hysteresis cycle carried out when the vehicle 2 is stationary, i.e. to the position that must be taken from the neutral centre of the steering mechanism 4 (the wheels 7 are on a straight line, hence X_CR0) to cause tread 8BR to begin yaw sliding on ground surface 9 in a desired steering direction.

More specifically, said static friction value Frot corresponds to a friction value due to the yaw sliding friction of the tread 8BR of the tyre 8 on the ground 9 when the vehicle is stationary (V _ vehic ═ 0), thus maneuvering from left to right (or vice versa)During and when the steering mechanism 4, in particular the rack 12, is non-zero

Passing through the center position (X) at a predetermined speed_CR0) against a given movement of the steering mechanism 4, more specifically against a given movement of the rack 12.

As an indication, the static friction value Frot used at the origin of the curves of fig. 4 to 6 on the vehicle 2 is 3400N.

In addition, according to a feature which may constitute an entirely independent invention, the static friction value Frot may be adjusted according to parameters specific to the vehicle and/or to the environment of said vehicle, for example on the basis of criteria related to meteorological conditions (rain, frost) which may alter the adherence of the tyre 8 on the ground 9.

For example, a model or a numerical table may be provided for this purpose, which allows the static friction value Frot to be adjusted dynamically over time, if necessary, as a function of parameters specific to the vehicle conditions and influencing the adhesion conditions (number of vehicle occupants and/or more generally vehicle load, tire inflation level, vehicle dynamic parameters, such as lateral acceleration or yaw speed with respect to the steering conditions and vehicle speed, etc.) and/or as a function of external parameters specific to the vehicle environment also influencing the adhesion conditions, such as meteorological conditions (temperature, humidity determination, presence of rain, etc.).

In fact, the instantaneous friction values effectively exerted on the tread 8BR of the tyre may vary and take any value comprised between + Frot and-Frot.

The model 15 for evaluating the force Fb at the tie-rods can be done, if necessary, by adding an auxiliary friction model, such as a LuGre model, in order to improve its accuracy, in particular in order to take into account the evolution of the instantaneous friction exerted on the tread 8BR during the transition phase.

These transition phases correspond to the phenomena observed when the tread 8BR starts to slide on the ground 9 and therefore passes from no steering movement to an effective steering movement of the steady state type, which effectively causes a deflection displacement of the tread 8BR in the wake of the wheel 7.

In practice, the transition phase may correspond to the beginning of a steering maneuver, i.e. the beginning of each of the hysteresis cycles in fig. 4 to 6 when the driver starts to turn the steering wheel 5 away from the central home position, or the reversal of the steering direction of the steering wheel 5 when the driver reverses the direction of rotation of the steering wheel 5, for example when the steering wheel 5 is turned to the right and then returned to the left (or vice versa), as is the case with the end of travel of the rack 12 in the hysteresis cycle shown in fig. 4, 5 and 6.

In fact, it is this auxiliary friction model that imparts a curvilinear circular shape to the steering cycle during said transition phase, i.e. when the tread 8BR starts to slide on the ground 9 and therefore in particular at the start of the hysteresis cycle and at the end of the travel of the rack 12, the reversal of the steering.

Possibility of adopting an auxiliary friction model is referred to as "bond stiffness" k by reference on the model 15 of fig. 2_cIs used, which is particularly applicable to the LuGre-type model.

In the block diagram of fig. 3, the different elements mentioned above and presented on the model 15 of fig. 2 can be found mathematically.

The block diagram represents a model 15 that is converted to a laplacian transfer function, where "s" is the laplacian variable.

The diagram particularly illustrates the basic dynamics applied to the wheel 7 and more particularly to the rim (centre).

In this respect it should be noted that if the basic principle of dynamics is written in general form:

here we consider that the computer does not really know how to "derive" the expression, but it is quite clear how to "integrate", which leads to a trend towards the following form:

once converted to the laplace transfer function, it gives:

by convention and for convenience, we will consider the integration constant to be zero, i.e. a model 15 where all state variables are zero at the origin.

However, it is entirely possible to consider using a non-zero integration constant in order to start the simulation at any operating point without departing from the scope of the invention.

To the extent that the basic principle of dynamics is applied here to the yaw rotation of the wheel 7 and the tread 8BR, instead of the mass "m", a quantity is used here which represents the moments of inertia Jcr, Jbr of the wheel 7 (the wheel center) and of the tread 8BR of the tire 8.

Similarly, the block diagram takes into account the type of force component represented in stiffness

F＝k.Δx

Also for reasons of ease of integration, it is converted into:

thus, it is:

in addition, the model of fig. 2 and its transformation in the block diagram of fig. 3 show the force value Fsys, which, for the sake of completeness, represents the force transmitted by the steering mechanism 4 to the wheels 7, which force generally corresponds to the action of the power-assist motor 6 possibly in combination with the manual action of the driver.

However, the force Fsys itself does not interfere with the problem of solving, i.e., determining, the force Fb at the tie rod by the model 15.

In any case, the output of the model 15, i.e. the force Fb at the tie rod that we are trying to estimate, is:

Fb＝-F₁-F₃

it should also be noted that: in the above expression, the symbol "minus" is used by a simple convention to indicate that the force Fb at the tie rod is the reaction force of the tie rod 3 and the rack 12 under the stress condition generated by the yaw displacement of the wheels 7 (i.e., under the stress condition generated by the steering manipulation).

It should also be noted that: in the block diagram proposed in fig. 3, the block "Frot" outputs the estimated instantaneous friction value between the tread 8BR of the tyre 8 and the ground 9, i.e. the instantaneous friction value which, at the moment considered, is rotating against the deflection of the wheel 7 and of said tread 8BR with respect to the ground 9.

Strictly speaking and as described above, the estimated instantaneous friction value returned by the frame "Frot" can be based, for example, on a friction model of the LuGre type according to the yaw displacement speed of the wheel 7

(and more generally according to the displacement speed of the steering mechanism 4

) Any value comprised between-Frot (the value of static friction or "sliding friction" in a first steering direction) and + Frot (the value of static friction or "sliding friction" in a second steering direction opposite to the first steering direction) is used.

However, as a first approximation it can be considered that, in practice, the instantaneous friction value corresponds to a steady state, i.e. when the steering mechanism 4 and more specifically the wheels 7 are at a non-zero speed

When moving with a substantially constant motion, crossing at the centre position (X)_CR0) the value of +/-Frot of the static friction considered.

In fact, this condition does represent an evaluation of the friction during a hysteresis cycle (fig. 4 to 6) corresponding to a series of stable states (a first stable state allowing a steering maneuver to be performed from left to right, then another rapidly stable state allowing a reverse maneuver to be performed from right to left, etc.).

In any case, by simplifying the mathematical expression derived from the block diagram of fig. 3, we obtain:

if the speed of displacement of the wheel 7 (when deflected) and therefore of the rack 12 and more generally of the steering mechanism 4, is positive, i.e. if

Or similarly:

if the displacement speed of the wheels 7 (when deflecting) (and more generally of the steering mechanism 4) is negative, i.e. if

Preferably, therefore, and irrespective of the sign of the yaw displacement speed of the wheel 7, the force Fb at the track rod is (at least) calculated from a first order term relative to the speed V _ vehic of the vehicle, said term being (absolute):

advantageously, this term introduces a variability and more specifically a reduction of the force Fb at the tie-rods, depending on the speed V _ vehic of the vehicle, so as to take account of the elastic release of the tyre 8, while being attached to the second force component F₂Second coefficient k of_dAnd by attaching to the first force component F₁First coefficient k of_tKeeping two force components F modeling the torsional condition of the tyre 8₁、F₂The influence of (c).

It should be noted that when the rack 12 is in its central position, i.e. when X_CRWhen equal to 0, the third force component F₃Is zero (since the vehicle does not rise without steering), so thatWe have:

thus, the first order term above allows the ordinate at the origin of the hysteresis curve (as shown in fig. 4 to 6) to be defined for any vehicle speed V vehic.

It should be noted that the absolute value of the ordinate at the origin decreases with vehicle speed, which explains the "dip" observed between the hysteresis curves as the longitudinal speed V vehic of the vehicle increases.

When the vehicle is at zero speed, i.e. when the vehicle is stationary, we find again that

Fb(V_vehic＝0)＝Frot。

It should also be noted that: as indicated above, the first order term above actually corresponds to a stable steering state, i.e. to the central position X when the position under consideration is crossed, here_CR0 (from left to right, or vice versa) rack 12 and therefore wheel 7 at a given non-zero speed

The condition of exercise.

In addition, the second coefficient k_dPreferably according to the static friction value Frot.

To this end, the model 15 may comprise a representation of said second coefficient k as a function of the static friction Frot_dTo (3) is performed.

In addition, according to one possible embodiment of the present invention, the second coefficient k may be maintained to be the same regardless of the speed V _ vehic of the vehicle_d。

According to the inventors' experiments, this approximation is indeed universally valid.

This is particularly true on the curves of fig. 4 to 6.

Preferably, according to a further implementation possibility and alternatively or additionally to the aforementioned adjustment of the static friction value Frot, the second coefficient k_dIt can be adjusted according to the longitudinal speed V vehic of the vehicle.

Advantageously, when necessaryChanging the second coefficient k according to the speed V _ vehic of the vehicle_dThis possibility of (2) allows in particular to reliably extend the effective range of the model 15 for calculating the force Fb at the tie rod over a low and medium speed range (typically at least up to V _ vehic ═ 30km/h), in order to refine the correlation between said model 15 and the actual behavior of the vehicle.

Adjusting the second coefficient k_dThis possibility of (a) will thus allow to guarantee, if necessary, a reliable overlap between said "low speed" model 15 and the other model for calculating the force Fb at the tie-rod verified for high vehicle speeds V vehic (over 30km/h or even 50 km/h).

For example, the inventors indeed found that it is possible: as a first approximation, a constant second coefficient k between 0km/h and 15km/h is successfully used_dHowever, it may be desirable to modify this coefficient for higher vehicle speeds V vehic, in particular between 15km/h and 30 km/h.

Here again, it is possible to provide a suitable mapping or any suitable evolution law.

Further as shown in fig. 3, the third force component F3 is preferably calculated from a second order polynomial comprising the position X relative to the transmission member 3_CRLinear and quadratic terms of (position of rim of wheel 7):

F₃＝kf1*X_CR+kf2*X_CR2。

strictly speaking, by considering the symbolic convention used previously, we will have:

F₃＝(k_f1.X_CR+k_f2.X_CR2).sgn(X_CR) Wherein "sgn (X)_CR) "is the position value X of the wheel 7 or the rack 12 with respect to the center position_CRThe symbol of (2).

Advantageously, such a quadratic polynomial faithfully takes into account the forces in the steering mechanism 4 caused by the lifting of the vehicle when the wheels 7 are turned in yaw.

As indicated above, when the rack 12 is in the central position, the value of the polynomial expression is zero, i.e. the wheel 7 is oriented in a straight line, so that X_CR0, and thus vehicle 2No lifting occurs.

Preferably, the coefficients kf1, kf2 of the quadratic polynomial are adjusted in dependence on the longitudinal speed V _ vehic of the vehicle.

Here again, this adjustment allows the accuracy and reliability of the refined model 15.

For the purpose of illustration, figures 4, 5 and 6 show some hysteresis curves as a function of the displacement of the rack 12 on the abscissa (i.e. according to the corresponding position X of the rim of the wheel 7) for different values of the speed V _ vehic of the vehicle_CR) The value of the force Fb at the transverse tie is shown on the ordinate.

Here, the rack moves in a back and forth cycle, first to the right of the wheel 7, then to the left, and so on.

On each graph, the smooth curve in the dashed line corresponds to a modeled cycle, i.e., in a parking condition where the vehicle is stopped (V _ vehic ═ 0), corresponds to the value of the force Fb at the tie rod estimated from the model 15.

The smooth curve in the dotted line corresponds to a modeled loop, i.e. to the value of the force Fb at the tie-rod estimated from the model 15 under driving conditions at the indicated speed (in this case 3km/h, 7km/h and 15km/h, respectively).

The noisy curve corresponds to the force Fb at the track rod measured by the extensometer, for example, according to these same cycles of alternating displacement of the rack 12.

We note that there is a very strong correlation, almost overlapping, between the model curve and the measured curve, which indicates a high reliability of the model 15, and this is for different vehicle speed V _ vehic values.

Thus, experimental results demonstrate that the present invention allows to extend the effective range of the model for estimating the force at the track rod from parking conditions to a wide driving range at low speeds, at least to 20km/h, 30km/h or even further.

Strictly speaking, in the graphs shown in fig. 4, 5 and 6, it should be noted that there is a slight deviation of the ordinate between the model force value Fb and the measured force value Fb.

This slight deviation is due to the fact that the gear 7 being tested simply lacks symmetry. Therefore, by appropriately adjusting the gear 7 (and the steering mechanism 4) to restore symmetry with respect to the original center position, mechanical correction can be easily obtained.

The invention is of course not limited to the variants described above, but the person skilled in the art is particularly free to separate or combine any of the features described above, or to replace them with equivalents.

In particular, the invention relates equally to the use of a model 15 for force estimation in a power steering system, which model comprises a correction component F simulating the release of the yaw torsion force of the tyre 8 (gradually with the longitudinal speed V _ vehic of the vehicle) when the vehicle 2 transitions from a parking condition to a driving condition₂。

The invention also relates to a power steering system 1 equipped with a model 15 according to the invention and on a computer-readable data medium and allowing, when the medium is read by a computer, the implementation of a method for estimating the force at the tie rod.