Method for estimating in real time the force on the tie-rods within a power steering mechanism

A method determines a link force within a power-steering mechanism of a vehicle, the method including a step (a) of determining an actuation force, which involves determining the actuation force that results from the assistance force exerted by the assistance motor and the driver force exerted by the driver of the vehicle on the steering mechanism; a step (b) of assessing dry friction; and a step (c) of calculating the link force, which has a summation sub-step which involves calculating an expression representing the link force, which uses the algebraic sum of the actuation force and the dry friction force, and a filtering sub-step which involves applying a low-pass filter in order to smooth the result of the expression when the expression is calculated upon a steering reversal of the steering mechanism.

The present invention relates to the general field of power steering equipping vehicles, and in particular motor vehicles, as well as to the methods for managing such power steering.

In a known manner, a power steering has the main function of helping the driver to turn the steered wheels of the vehicle, by combining an assistance force, provided by an assistance motor, to the driver force, which is manually exerted by the driver on the direction, generally by means of a steering wheel.

The combination of the driver force and of the assistance force forms an actuating force which allows countering the resistant force exerted by the environment of the vehicle on the steering mechanism, wherein said resistant force is essentially caused by the contact between the tyres and the road.

This resistant force, brought to the endpoints of the steering system, that is to say to the endpoints of the system formed by the steering mechanism, constitutes the force called «tie-rod force» (or «force on the tie-rods»).

In practice, within a usual directional running gear, said tie-rod force corresponds in fact to the algebraic sum of the forces exerted on the steering mechanism, and more particularly on the steering rack, on the one hand, by the left steering tie-rod, which connects the rack to the left steered wheel and, on the other hand, by the right steering tie-rod, which connects the rack to the right steered wheel (one of said tie-rods is working, at a considered instant, in traction, while the other is working in compression).

It so happens that the value of the tie-rod force constitutes a particularly useful or even fundamental data, to characterize and manage the power steering, because many problems directly depend on this value. By way of example, the problem of dimensioning of the assistance motor can be in particular cited.

However, it is in practice difficult to estimate accurately this tie-rod force.

Admittedly, force sensors can be provided for this purpose and placed for example at the junctions between the rack and the tie-rods, but such a solution tends to increase the overall dimension, the weight and complexity of the power steering system, as well as the cost thereof.

According to another approach, it can be possible to proceed, in a first approximation, to an estimation of the tie-rod force by summing, on the one hand, the driver force, which can be measured, for example, by means of a torque sensor disposed between the steering wheel and the steering column and, on the other hand, the assistance force, which can be measured, for example, by means of the set point applied to the assistance motor, and by assimilating the tie-rod force to the sum obtained accordingly, that is to say, by considering that the tie-rod force is equal to the actuating force exerted on the steering mechanism.

However, the inventors found that such an approximation was relatively coarse and could have significant differences with the true value of the tie-rod force.

In particular, the inventors have discovered that these differences appear as soon as one begins to apply an actuating force, and tend to accentuate when said actuating force increases, so that, in practice, the aforementioned approximation is only really valid in the vicinity of the straight line, when the steering system is little, or even not operated.

Conversely, the difference between the actuating force and the real tie-rod force is particularly high, and therefore the approximation is particularly inaccurate, during the steering reversals, that is to say when the driver of the vehicle changes (intentionally) the direction in which he actuates the steering wheel, this change having the aim and the effect of changing from a steering situation of turning left, in which the driver exerts a force which pulls the steering wheel to the left, to a steering situation of turning right, in which the driver exerts a force which pulls the steering wheel to the right, or vice versa, from a steering situation of turning right to a steering situation of turning left.

Furthermore, the inventors found that the difference between the actuating force and the real tie-rod force could be particularly sensitive to the operating conditions of the steering mechanism, in particular to the temperature conditions, as well as to the wear status of said mechanism.

In practice, all these limitations can thus considerably reduce the effective availability of the function of assessing the tie-rod force, or even make assessing the tie-rod force relatively uncertain.

The objects assigned to the invention therefore aim to overcome the aforementioned disadvantages and to propose a new method for determining the tie-rod force which allows determining reliably and accurately, at any time, in every situation of life of the vehicle, the tie-rod force which is exerted on a steering mechanism.

The objects assigned to the invention are achieved by means of a method for determining a force called «tie-rod force» which is representative of the force exerted, at a considered instant, by the environment of a vehicle on a power steering mechanism which equips said vehicle and which is maneuvered at least by an assistance motor, said method comprising:

a step (a) of determining an actuating force during which the actuating force exerted at the considered instant on the steering mechanism is determined, such that said actuating force results from the assistance force exerted by the assistance motor on the steering mechanism and/or from the driver force exerted by the driver of the vehicle on said steering mechanism,a step (b) of assessing a dry friction, during which the dry friction force exerted on the steering mechanism at the considered instant is assessed,a step (c) of calculating the tie-rod force which comprises a summing sub-step (c1) during which an expression representative of the tie-rod force is calculated, which involves the algebraic sum of the actuating force and the dry friction force, and a filtering sub-step (c2) during which a low-pass filter is applied, in order to be able to smooth the result of said expression when said expression is calculated at the moment of a steering reversal of the steering mechanism.

Advantageously, taking the dry friction into consideration when assessing the tie-rod force, makes it possible to determine said tie-rod force in a much more accurate manner than before.

Indeed, the inventors have discovered that the dry friction could generally explain a significant part, if not the totality, of the difference observed between the actuating force and the real tie-rod force.

Consequently, by correcting the assessment of the tie-rod force so as not to neglect (anymore) the force component connected to the phenomenon of dry friction, component which can be the cause of a significant difference between the actuating force and the tie-rod force, the precision and the reliability of said assessment is improved in most, and possibly the totality, of the vehicle life situations, in particular in all maneuver situations, whatever the nature and intensity of the concerned maneuver, and in particular during the steering reversals.

Advantageously, it will be noted that this gain in accuracy occurs while still having a calculation formula (expression) which is particularly simple and fast to implement.

Furthermore, the inventors have discovered that the sensitivity to the operating temperature and wear conditions of the known methods for determining the tie-rod force was significantly attributable to the sensitivity of the dry friction to said temperature and wear conditions.

Consequently, again, considering the dry friction allows gaining in accuracy.

More particularly, the fact of assessing this dry friction at the instant chosen to calculate the tie-rod force, for example by carrying out a friction measurement or by using a model which is updated over time from empirical data acquired within the steering mechanism, makes it possible to take account, substantially in real time, of the evolutions of the dry friction due to the temperature factors and wear factors, and thus to assess at any time, reliably, an estimated tie-rod force which is faithfully representative of the effective tie-rod force which is actually exerted on the steering mechanism.

Then, implementing a low-pass filtering makes it possible to take account of the physical dynamics of the steering system, and more particularly the dynamics connected to the duration (even if said is possibly very small) which is necessary for achieving switching of the dry friction value (that is to say the duration required to perform the reversal of sign of said friction value) at the moment of the steering reversals, when the speed of movement of the steering mechanism (and in particular of the steering wheel) is reversed.

Indeed, if the switching of the dry friction value was perceived in a “binary” manner, that is to say as an apparent discontinuity, due in particular to the fact that the calculator which manages the method in accordance with the invention proceeds by sampling, then this switching might punctually cause a divergence during the instantaneous execution of the calculation of the expression representative of the tie-rod force.

In the absence of a filter, such a divergence could then make a peak-type artifact appear, which would totally distort the assessment of the tie-rod force.

That is why using a low-pass filter, whose time constant is of the same order of magnitude as the real switching duration of the dry friction, advantageously allows to soften the effects of the steering reversals on the calculation of the tie-rod force, by a smoothing which allows to maintain, in all circumstances, the result of the expression, that is to say the calculated tie-rod force, as closely as possible to the effective value of the real tie-rod force.

Thanks to the low-pass filter which improves the stability of the calculation of the tie-rod force, the method according to the invention is therefore particularly reliable in all the vehicle life situations, including during the steering reversals and in the vicinity thereof.

The invention concerns a method for determining a force called «tie-rod force» Ftie-rodwhich is exerted within a power steering mechanism1equipping a vehicle, in particular a motor vehicle.

As illustrated inFIG. 4, said steering mechanism1is maneuvered by at least one assistance motor2, capable of delivering for this purpose an assistance force Fassistwhich is applied on said steering mechanism1.

It can be considered indifferently any type of assistance motor2, and more particularly any type of assistance motor which can be operated in either one of the other of two opposite directions.

In particular, the invention can be applied to a rotary assistance motor2intended to exert an assistance force Fassistof the torque type, as well as to a linear assistance motor2, intended to exert an assistance force Fassistof the traction or compression type.

Moreover, said assistance motor2can for example be hydraulic, or preferably electric (the use of an electric motor makes in particular easier implanting and implementing said motor, as well as generating and managing the useful signals).

Particularly preferably, the assistance motor2will be a rotary electric motor, for example of the «brushless» type

Moreover, as illustrated inFIG. 4, the power steering mechanism1preferably comprises, in a manner known per se, a steering wheel3by which the driver of the vehicle can rotatably drive a steering column4which meshes, by means of a pinion5, on a steering rack6that is slidably mounted in a steering casing which is secured to the chassis frame of the vehicle.

The ends of the steering rack6are preferably each connected, by means of a steering tie-rod7,8, to an yaw-orientable knuckle, on which is mounted a steered wheel9,10(which is preferably also a drive wheel) of the vehicle, in such way that the movement of the rack6in translation in the steering casing causes a change in the steering angle (i.e. a change of the yaw orientation) of said steered wheels9,10.

The assistance motor2can engage the steering column4, for example by means of a worm wheel and worm screw reducer, or engage directly the steering rack6, by a driving mechanism of the ball screw type or via a motor pinion11distinct from the pinion5of the steering column (so as to form, for example, a steering mechanism called «dual-pinion» mechanism, as schematized inFIG. 4).

The force setpoint (or, more preferably, the torque setpoint, noted FassistinFIG. 4) which is applied to the assistance motor2so that said motor assists the driver in the maneuvering of the steering mechanism1depends on predetermined assistance laws, stored in a non-volatile memory of a calculator (herein a module for applying assistance laws12), said assistance laws being able to adjust said force setpoint as a function of various parameters such as the steering wheel force (torque) Fcondexerted by the driver on the steering wheel3, the (longitudinal) speed vvehlcof the vehicle, the angular position θsteeringwheelof the steering wheel3, etc.

For the mere sake of description, it will be considered that the force setpoint applied to the assistance motor2faithfully reflects the assistance force Fassistdelivered by said assistance motor, so that the two quantities can be assimilated one to the other.

According to the invention, the tie-rod force Ftie-rodcorresponds to the force exerted, at a considered instantt, by the environment20of the vehicle (that is to say typically the road20on which said vehicle is traveling) on the power steering mechanism1which equips said vehicle.

In practice, with reference to the example ofFIG. 4, said tie-rod force Ftie-rodcorresponds in fact to the algebraic sum of the forces F7/6and F8/6which are exerted on the steering mechanism, herein at the endpoints of the rack6, on the one hand, by the left steering tie-rod7, which in fact transmits to the rack6(such as schematized by the force F7/6) the resistant force that is exerted by the road20on the left steered wheel9and, on the other hand, by the right steering tie-rod8, which transmits to the same rack6(as schematized by the force F8/6) the resistant force that is exerted by the road20on the right steered wheel10(wherein one of said tie-rods7,8is working, at a considered instant, in traction, while the other is working in compression).

It will be noted that the method in accordance with the invention advantageously allows to estimate substantially in real time the tie-rod force Ftie-rod, and therefore to accurately quantify at any moment the action of the road20on the directional running gear, wherein said directional running gear moreover preferably corresponds to the front axle of the vehicle.

According to the invention, the method comprises a step (a) of determining an actuating force Factionduring which the (total) actuating force Factionwhich is exerted at the considered instant on the steering mechanism1is determined, such that said actuating force results from the assistance force Fassistexerted by the assistance motor2on the steering mechanism1, and/or from the driver force Fcond(manually) exerted by the driver of the vehicle on said steering mechanism1(herein via the steering wheel3).

It will be noted that, in practice, the actuating force Factioncan be equal to the (only) driver force Fcord, in case of inaction of the assistance motor2.

Conversely, the actuating force Factioncan be equal to the only assistance force Fassistassist if the driver force Fcondis zero, either because the driver has released the steering wheel3, for example during an automatic maneuver of the direction performed by the assistance motor, such as a parking assistance maneuver, or because the steering wheel3merely serves as a heading indicator and is not mechanically connected to the rack6, so that the forces necessary to the steering maneuvers are ensured exclusively by the assistance motor2.

However, for the sake of description, and with regard to the example of the steering mechanism1illustrated inFIG. 4, it will be considered in what follows that the actuating force Faction, which corresponds to the resultant of the different maneuvering forces which are intentionally applied on the steering mechanism1to change the steering angle of said steering mechanism or to maintain the steering angle of said mechanism to a selected value, is equal to the (algebraic) sum of the respective contributions of the driver force Fcondand of the assistance force Fassist.

Of course, the driver force Fcondand the assistance force Fassistcan be assessed by any appropriate means.

Preferably, the assistance force Fassistcan be assessed by measuring (for example as output of the application module of the assistance laws12) the torque setpoint applied to the assistance motor2, or by measuring, by means of a motor torque sensor placed on the shaft13of the assistance motor2, the assistance force actually delivered by said assistance motor.

The driver force Fcond, or «steering wheel torque», exerted by the driver on the steering wheel3can in turn be measured by an appropriate steering wheel torque sensor14, such as a magnetic torque sensor that measures the elastic deformations of a torsion bar placed between the steering wheel3and the steering column4.

According to the invention, the method also comprises a step (b) of assessing dry friction, during which the dry friction force Fdry, Rdryexerted on the steering mechanism1at the considered instanttis assessed.

It is meant by «dry friction», as opposed to the viscous friction which is dependent on (proportional to) the speed of movement of the mechanism, the friction, not dependent on the sliding speed, which is due to the surface contact (lubricated or not) between two solids, as described by the Coulomb law, and which can be expressed in the form: Fdry=−Rdry·sign({dot over (X)}), where Rdryis the value of said dry friction and where sign({dot over (X)}) represents the sign of the speed of movement of the steering mechanism1.

Preferably, the dry friction force Fdry, Rdryis assessed from the dropHof the actuating force Faction, action such that this dropHis observed during steering reversals15of the steering mechanism1, as illustrated in particular inFIGS. 1 and 2.

Said drop heightHcorresponds substantially to the difference between, on the one hand, the extremum (maximum, called «high value») reached by the actuating force Factionjust before the steering reversal15, wherein said steering reversal15causes in particular the mechanism1(and therefore of the steering wheel3) pass by a zero speed {dot over (X)}, and, on the other hand, the value (called «low value») taken by this same actuating force Factionimmediately after the steering reversal15.

More particularly, the value of the dry friction Rdrywill advantageously correspond to the drop half-height H/2.

In practice, the successive steering reversals15can be detected for example by calculating the first time derivative of the signal representative of the actuating force Faction(or, in a substantially equivalent manner, the signal representative of the assistance force Fassist), and by detecting the passage of this derivative by a peak, characterized by the crossing of a predetermined threshold (of derivative amplitude).

The high value and the low value of the signal of the actuating force Factionwhich delimit (as the ordinate inFIGS. 1 and 2) and characterize the drop heightH, can be calculated at time limits (located on the abscissa in saidFIGS. 1 and 2) which are located on either side of the steering reversal, and which correspond respectively to a first reference instant, which precedes, by a predetermined duration, the instant called «peak start instant» which characterizes the passage of the derivative above the threshold, and to a second reference instant which follows, by a predetermined duration, the instant called «peak end instant» which characterizes the instant where the derivative drops below said threshold. In an alternative and substantially equivalent manner, the first reference instant and the second reference instant can correspond to instants which respectively precede and follow, each by a predetermined duration, the average instant at which the steering reversal takes place, that is to say the instant corresponding to the (time) center of the derivative peak.

Moreover, the step (b) of assessing the dry friction Fdry, Rdryis preferably carried out from an empirical friction model21which is constructed and refreshed over time by measurements of dry friction force Rmes_1, Rmes_2. . . Rmes_nwhich are operated successively as and when using the steering mechanism1, for example (and preferably) at each steering reversal15.

Advantageously, the model21which serves to assess the friction is thus automatically updated in the course of the use of the steering mechanism1, and more globally in the course of the (current) use of the vehicle, so that said model21is permanently re-adapted to the evolution of the conditions in which the steering mechanism1operates, and in particular to the evolution of the temperature or aging (wear) conditions.

By thus using an evolving friction model21which is periodically updated, rather than a constant or an invariant abacus which would be obtained by a single original calibration performed in the factory, the invention allows the estimation of dry friction to faithfully reflect the real (intrinsically non-constant) state of the friction in the steering mechanism1, at any given instantt, whatever the said friction state is.

The accuracy of the method is thus increased.

Preferably, the step (b) of assessing the dry friction comprises a sub-step (b1) of acquiring a series of characterization points, during which the corresponding friction values are measured for several different values taken successively by the actuating force Factionduring the operation of the steering mechanism, in order to obtain empirically a series of distinct characterization points P1, P2, . . . Pnwhich associate each, to a measured value representative of the actuating force Faction_1, Faction_2, . . . Faction_na measured value of dry friction Rmes_1, Rmes_2. . . Rmes_n, then a sub-step (b2) of constructing an empirical friction model21, during which a correlation lawLis established between the characterization points P1, P2, . . . Pnconstituting the series of characterization points, from the scatter chart formed by said series of said characterization points.

As indicated above, the characterization points can advantageously be acquired during the steering reversals15.

Advantageously, by creating a friction model21from a scatter chart of points taken at different (distinct) values of actuating forces, rather than on the basis of a single calibration point, a model21is obtained that covers empirically an operating wide range, and which can thus faithfully give information about the level of dry friction Fdrywhich corresponds to every considered actuating force (every actuating torque) Faction(t) at a given instantt, whatever the intensity of said considered actuating force is.

In particular, in the assessment of the dry friction, it will thus be possible to take account of the fact that the value of the dry friction Rdryis in practice an increasing function of the actuating force (actuating torque) Faction.

Here again, the invention therefore makes it possible to gain in accuracy when determining the dry friction, and therefore, consequently, when determining the tie-rod force.

Advantageously, the step (b1) of acquiring characterization points and the step (b2) of constructing model21can be refreshed iteratively during the operation of the steering mechanism1, in such a way that the learning process that enables constructing the model is an ongoing process, which makes it therefore possible to have said model evolve in a rolling manner over time (wherein the newly acquired characterization points progressively replace the oldest characterization points, and the corresponding correlation lawLis adapted consequently).

By way of indication, the size of the series of characterization points P1, P2, . . . Pncan be comprised between, on the one hand, at least 5 characterization points, or even at least 10 characterization points P1, P2, . . . Pnon the other hand, 50 or even 100 characterization points.

The sample of the characterization points will thus be of sufficiently significant size to create a reliable and representative model21, even in case of punctual occurrence of an erroneous measurement.

As detailed above, the characterization points P1, P2, . . . Pnwill be preferably acquired during the steering reversals15, the measurement of the friction value Rmes_1, Rmes_2. . . Rmes_nat the characterization points P1, P2, . . . Pnbeing obtained from the drop heightH(and more particularly from the drop half-height H/2) of the signal representative of the actuating force Faction.

Preferably, the correlation lawLis established in the form of an interpolation (for example polynomial) curve or of a regression curve relative to the series of characterization points P1, P2, . . . Pn.

Particularly preferably, as illustrated inFIG. 3, the correlation lawLis obtained by linear regression on the series of characterization points P1, P2, . . . Pn, for example by the least squares method.

It is thus possible to obtain quickly, and by mobilizing only a modest power of calculation, a model21which is particularly representative of the real behavior of dry friction.

Furthermore, it will be noted that using a continuous correlation lawLwhose range of definition and validity extends, by extrapolation, beyond the sole characterization points used in the construction of the model21, advantageously makes it possible to associate an estimation of the dry friction value Rdrywith any value of the actuating force Faction(t)measured (or calculated) at the instantt, and this including when said value of the actuating force is situated beyond the range covered by said sole characterization points.

According to the invention, the method comprises a step (c) of calculating the tie-rod force Ftie-rod, which comprises a summing sub-step (c1) during which an expression 22 representative of the tie-rod is calculated, wherein said expression involves the algebraic sum of the actuating force Factionand of the dry friction force Fdry: Faction+Fdry=Fcond+Fassist+Fdry, and a sub-step (c2) of filtering during which a low-pass filter23is applied, in order to be able to smooth the result of said expression 22 (at least) when said expression is calculated at the moment of a steering reversal15of the steering mechanism.

Indeed, since it exists, at the contacts between real solids, a bonding stiffness which is not infinite, then the actual dry friction does not evolve discontinuously during the steering reversals15, that is to say that said actual dry friction does not change instantaneously from a positive value to an opposite negative value (or vice versa), but obeys, on the contrary, to a dynamics of admittedly fast, but nonetheless continuous, transition.

Now, said dry friction Fdryis modeled herein by an expression Fdry=−Rdry·sign({dot over (X)}) which is proportional to the sign sign({dot over (X)}) of the speed of movement {dot over (X)} of the steering mechanism1.

In practice, the speed of the assistance motor2, that is to say the angular speed of rotation of the shaft13of said assistance motor2, which is known very accurately can consider as a value representative of the speed of movement {dot over (X)}.

The signal sign({dot over (X)}) which measures the sign of the speed of movement of the steering mechanism (and thus practically reflects the direction of rotation of the shaft13of the assistance motor) is, by nature, binary (the sign of the speed being either positive or negative).

As a result, if said signal sign({dot over (X)}) is obtained or treated roughly, in numerical form, by a discrete sampling, a change in sign of the speed of movement of the steering mechanism1will be perceived in the form of an instantaneous switching of the binary value of said signal sign({dot over (X)}), wherein said switching will thus occur instantaneously, at the moment of refreshing the signal immediately after the instant where the speed passes through zero.

Accordingly, such an instantaneous switching would have the effect of introducing a discontinuity (a peak) in the assessment of the friction, and therefore, consequently, in the calculation of the tie-rod force.

Here, advantageously, adding the low-pass filter23makes it possible to artificially introduce a dynamic limitation in the signal sign({dot over (X)}) which measures the sign of the speed of movement of the steering mechanism, wherein said dynamic limitation acts on (and as a complement to) the binary perception of the change in sign so as to create, when the sign changes, a continuous transition in said signal sign({dot over (X)}) which is thus filtered, wherein said continuous transition reproduces the real physical dynamics of the reversal phenomenon.

In other words, the low-pass filtering23allows to restore the progressivity of the reversal of the friction, such that this reversal is perceived by the calculator which manages the method according to the invention, thus avoiding that the processing method generates from its own a discontinuity which would be reflected, falsely, in a peak of friction (and thus in a peak of tie-rod force) without any real material cause.

Concretely, as can be clearly seen inFIG. 2despite the low pass filtering23is not absolutely perfect as said filtering may leave a slight residual perturbation24(a damped peak) in the calculated tie-rod force Ftie-rod, at the moment of the steering reversal15, the said low-pass filtering23nevertheless enables keeping the amplitude of said residual perturbation24well below the observed difference between the real tie-rod force and the actuating force Faction, that is to say that said low-pass filtering enables, graphically, to permanently keep the calculated tie-rod force curve (appearing in dotted lines inFIG. 2) much closer to the real tie-rod force curve (appearing in continuous line on this sameFIG. 2) than the curve representative of the actuating force Faction(shown in mixed line in saidFIG. 2).

Conversely, it will be noted that in the absence of filtering, the calculated tie-rod force curve could, at the moment of the steering reversals15, have a peak which would move said curve away from the real tie-rod force curve, farther than the curve representative of the actuating force, which means, in this case, that the calculated tie-rod force value Ftie-rodwould be (temporarily) even less reliable than if said tie-rod force value had been simply considered equal to the actuating force value Faction.

It can therefore be observed that using the low-pass filter23according to the invention allows determining in all circumstances the calculated tie-rod force Ftie-rodwith a much higher accuracy than the previously known methods could achieve, and this including at the critical moment of the steering reversal15.

More globally, it is remarkable that the fact of combining, according to the invention, on the one hand, a consideration of the dry friction and, on the other hand, the use of a low-pass (peaks dampening) filter23makes it possible to have the tie-rod force estimated by the calculation be as close as possible to the real tie-rod force, and keeping this proximity (this cohesion between the curves) in all circumstances, including (in particular) in the vicinity of the steering reversal areas15(in which the filter allows attenuating significantly the effects of the discontinuity of the raw signal reflecting the sign of the speed of movement).

Preferably, as illustrated inFIG. 4, the low-pass filtering will intervene on the signal sign({dot over (X)}) that is representative of the sign of the speed of movement of the steering mechanism1, upstream of the calculation (c1) of the expression 22, and even upstream of the calculation of the dry friction Fdry(which consists in multiplying the sign of the speed sign({dot over (X)}) by the dry friction value Rdry), thus allowing in particular to restore the dynamics of continuous transition “at the source”, directly in the concerned signal (sign of speed), as «input» of the expression 22.

However, it can be also possible to operate this low-pass filtering23further downstream, for example on the dry friction signal Fdryderived from the product Fdry=−Rdry.*sign({dot over (X)}), or even possibly on the expression 22, after calculation (c1) of the latter, that is to say as «output» of said expression 22.

Preferably, the time constant of the low-pass filter23is comprised between 0.05 s and 0.5 s, and preferably between 0.1 s (100 milliseconds) and 0.3 s (300 milliseconds), for example substantially equal to 0.15 s (150 milliseconds).

Advantageously, these orders of magnitude correspond substantially to the characteristic duration of the real switching dynamics of the dry friction, that is to say the characteristic duration of the continuous transition of said dry friction, as it is observed during the steering reversals15.

The low pass filter23will thus be able to reproduce a realistic artificial dynamics, close to the real transition dynamics.

Moreover, during the step (c) of calculating the tie-rod force, it is preferably also possible to take in consideration the viscous friction force Fvisqwhich affects the movement of the steering mechanism1, and which is proportional to the speed of movement {dot over (X)} of said steering mechanism.

Although the contribution of this term of viscous friction Fvisqis not predominant, but on the contrary rather ancillary, with regard to the contributions of the actuating force Factionand of the dry friction Fdry, consideration thereof nevertheless allows to further improve the calculation accuracy of the tie-rod force Ftie-rod.

Concretely, this viscous friction can be expressed in the form Fvisq=−Rvis. {dot over (X)} where Rvisqis the viscous friction coefficient and where {dot over (X)} represents the speed of movement of the steering mechanism.

The viscous friction coefficient Rvisqcan be predetermined by a test campaign and stored in the form of a chart in a non-volatile memory of the calculator that manages the method.

For example, the speed of movement can be calculated, by a time-derivative calculation, from a position sensor capable of measuring the angular position of the steering wheel3, the linear position of the rack6, or the angular position of the shaft13of the assistance motor.

In an analogous manner, during step (c) of calculating the tie-rod force, it will be also possible to take in consideration the inertial force M·Ü which is exerted on the steering mechanism1.

Here again, although it is a term whose contribution is generally rather ancillary with regard to the contributions of the actuating force Factionand of the dry friction Fdry, consideration thereof will nevertheless allow to further improve the calculation accuracy of the tie-rod force Ftie-rod.

Concretely, said inertial force can be calculated by making the product of the—known-(movable) massMof the steering mechanism by the instantaneous acceleration {umlaut over (X)} of said steering mechanism, wherein said acceleration can be obtained, for example, by calculating the derivative of the speed {dot over (X)}.

In practice, since the inertia of the assistance motor2is very much greater than the inertia of the other movable members of the steering mechanism1(such as the rack6), it will be possible, as a first (realistic) approximation to consider only the mass and the acceleration of the shaft13of the assistance motor2in order to assess the inertial force M·{umlaut over (X)}.

Ultimately, the expression 22 representative of the tie-rod force will be preferably given by: Ftie-rod=Fcond+Fassist+Fdry+Fvisq−M·{umlaut over (X)}, with:

Fdrythe dry friction, with Fdry=−Rdry·sign({dot over (X)}) where Rdryis the value of the dry friction and where sign({dot over (X)}) represents the sign of the speed of movement of the steering mechanism,

Fvisqthe viscous friction, with Fvisq=−Rvisq. {dot over (X)}, where Rvisqis the viscous friction coefficient and where {dot over (X)} represents the speed of movement of the steering mechanism.

M·{umlaut over (X)} the inertial force which depends on the movable massMof the steering mechanism and the instantaneous acceleration {umlaut over (X)} of said steering mechanism.

As indicated above, the dry friction value Rdryis preferably obtained from a model21, and is preferably an increasing function (which typically follows the regression lineLmentioned above) of the actuating force: Rdry=ƒ (Fassist+Fcond).

It will be noted that the expression representative of the tie-rod force above corresponds to the application of the fundamental principle of the dynamics to the endpoints of the steering mechanism1.

It should also be noted that the predominant terms (which are therefore sufficient on their own to obtain a result representative of the real tie-rod force) of this expression 22 are, as a first approximation, the actuating force (Fassist+Fcond) and the dry friction force Fdry.

Of course, the functions assigned to the method according to the invention can be carried out by appropriate calculation modules, and more particularly by an assistance law12application module, an acquisition module (of characterization points)16, a model construction module (calculation module of the correlation lawL)17, and a friction assessment module18(applying the correlation lawLdefined accordingly to estimate, at any moment and for any value of the actuating force Caction(t), the corresponding friction value Rdry(t)), a tie-rod force Ftie-rodcalculation module19, and a low-pass filtering (or «filter») module23.

Each of the aforementioned modules can be formed by an electronic circuit, an electronic card, a calculator (computer), a programmable logic controller, or any other equivalent device, preferably arranged to process in (discrete) digital form the signals that are necessary to the method.

Each of the aforementioned modules can present a physical control structure, defined by the wiring arrangement of its electronic components, and/or, preferably, a virtual control structure, defined by computer programming.

Of course, the invention also concerns as such any data medium readable by a computer and containing computer program code elements allowing to execute the method in accordance with the invention when said medium is read by a computer.

It also concerns a power steering system comprising a power steering mechanism1controlled by a management module including all or part of the aforementioned modules, and therefore able to implement the method according to the invention.

It also concerns a motor vehicle, in particular with steered wheels9,10, which may be possibly also drive wheels, equipped with such a power steering system.

Finally, it should be noted that the method in accordance with the invention, that makes use of signals which are generally already available within power steering systems, can be easily generalized to any power steering systems, including by retrofitting many already existing power steering systems, by a mere reprogramming of the calculator thereof.

Of course, the invention is in no way limited to the only embodiments described above, the person skilled in the art being in particular capable of isolating or freely combining together either of the abovementioned characteristics, or of substituting equivalents thereto.