A METHOD FOR DETERMINING A TRACTOR LONGITUDINAL FORCE THRESHOLD VALUE FOR A TRACTOR LONGITUDINAL RETARDATION FORCE

Abstract

The present disclosure relates to a method for determining a tractor longitudinal force threshold

[00001]$\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right)$

for a tractor longitudinal retardation force

[00002]$\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret}}\right)$

that can be imparted on a tractor of a vehicle combination including the tractor and a trailer for retarding the vehicle combination. The trailer has a trailer longitudinal extension in a trailer longitudinal direction (L.sub.TL), a trailer lateral extension in a trailer lateral direction (T.sub.TL) and a trailer vertical extension in a trailer vertical direction (V.sub.TL), and the tractor has a tractor longitudinal extension in a tractor longitudinal direction (L.sub.TR), a tractor lateral extension in a tractor lateral direction (T.sub.TR) and a tractor vertical extension in a tractor vertical direction (V.sub.TR ), wherein the tractor longitudinal retardation force

[00003]$\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret}}\right)$

extends in a direction parallel to a tractor longitudinal direction (T.sub.TR).

Claims

1. A method for determining a tractor longitudinal force threshold value $\left(F_{L_{TR}}^{\mathrm{ret},\mathrm{threshold}}\right)$ for a tractor longitudinal retardation force $\left(F_{L_{TR}}^{\mathrm{ret}}\right)$ that can be imparted on a tractor of a vehicle combination comprising said tractor and a trailer for retarding said vehicle combination, said trailer having a trailer longitudinal extension in a trailer longitudinal direction (L.sub.TL), a trailer lateral extension in a trailer lateral direction (T.sub.TL) and a trailer vertical extension in a trailer vertical direction (V.sub.TL), wherein said trailer longitudinal direction (L.sub.TL) corresponds to an intended direction of travel of said trailer when said vehicle combination is travelling straight ahead, said trailer vertical direction (V.sub.TL) corresponds to a direction of a normal to a planar surface supporting the trailer and said trailer lateral direction (T.sub.TL) being perpendicular to each one of said trailer longitudinal direction (L.sub.TL) and said trailer vertical direction (V.sub.TL), said tractor having a tractor longitudinal extension in a tractor longitudinal direction (L.sub.TR), a tractor lateral extension in a tractor lateral direction (T.sub.TR) and a tractor vertical extension in a tractor vertical direction (V.sub.TR), wherein said tractor longitudinal direction (L.sub.TR) corresponds to an intended direction of travel of said tractor when said vehicle combination is travelling straight ahead, said tractor vertical direction (V.sub.TR) corresponds to a direction of a normal to a planar surface supporting the tractor and said tractor lateral direction (T.sub.TR) being perpendicular to each one of said tractor longitudinal direction (L.sub.TR) and said tractor vertical direction (V.sub.TR), wherein said tractor longitudinal retardation force $\left(F_{L_{TR}}^{\mathrm{ret}}\right)$ extends in a direction parallel to said tractor longitudinal direction (T.sub.TR), said method comprising: determining a trailer lateral force value $\left(F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor}}\right),$ indicative or a trailer lateral force being or predicted to be imparted on said tractor in said tractor lateral direction, using a trailer lateral force value determination procedure comprising: obtaining a trailer mass value (m.sup.trailer) indicative of the current mass of said trailer; obtaining a longitudinal trailer inclination angle value () indicative of the inclination angle, in said trailer longitudinal direction, of the ground supporting said trailer; determining a longitudinal gravity force value $\left(F_{L_{TL}}^{\mathrm{trailer},\mathrm{gravity}}\right)$ indicative of a longitudinal gravity force, in said trailer longitudinal direction (L.sub.TL), imparted on said trailer on the basis of at least said trailer mass value (m.sup.trailer) and said longitudinal trailer inclination angle value (); determining an articulation angle value () indicative of a current articulation angle between said tractor longitudinal direction (L.sub.TR) and said trailer longitudinal direction (L.sub.TL), and determining said trailer lateral force value $\left(F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor}}\right)$ using said longitudinal gravity force value $\left(F_{L_{TL}}^{\mathrm{trailer},\mathrm{gravity}}\right)$ and said articulation angle value (); determining a horizontal friction force value $\left(F_{\mathrm{total}}^{\mathrm{tractor}}\right)$ indicative of a possible total horizontal frictional force obtainable between said ground supporting said tractor and ground engaging members of said tractor, and determining said tractor longitudinal force threshold value $\left(F_{L_{TR}}^{\mathrm{ret},\mathrm{threshold}}\right)$ using said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right)$ and said horizontal friction force value $\left(F_{\mathrm{total}}^{\mathrm{tractor}}\right).$

2. The method according to claim 1, wherein said trailer lateral force value determination procedure further comprises: obtaining a longitudinal trailer retardation value indicative of a longitudinal trailer retardation being or predicted to be imparted on said trailer; determining a longitudinal inertial trailer force value indicative of a longitudinal inertial force, in said trailer lateral direction, imparted on said trailer on the basis of at least said trailer mass value and said longitudinal trailer retardation value, and determining said tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right)$ using also said longitudinal inertial trailer force value.

3. The method according to claim 1, wherein said trailer lateral force value determination procedure further comprises: determining a lateral centrifugal force value indicative of a centrifugal force, in said trailer lateral direction, imparted on said trailer on the basis of at least said trailer mass value, and determining said trailer lateral force value using also said lateral centrifugal force value.

4. The method according to claim 1, wherein said trailer lateral force value determination procedure further comprises: obtaining a lateral inclination angle value indicative of the inclination angle, in said trailer lateral direction, of the ground supporting said trailer; determining a lateral gravity force value indicative of a lateral gravity force, in said trailer lateral direction, imparted on said trailer on the basis of at least said trailer mass value and said lateral inclination angle value, and determining said trailer lateral force value using also said lateral gravity force value.

5. The method according to claim 1, wherein said trailer lateral force value determination procedure further comprises: multiplying each force value indicative of a force, in said trailer longitudinal direction, with the sine of said articulation angle value.

6. The method according to claim 3, wherein said trailer lateral force value determination procedure further comprises: multiplying each force value indicative of a force, in said trailer lateral direction, with the cosine of said articulation angle value.

7. The method according to claim 1, wherein said tractor comprises an inclination sensor, adapted to determine a longitudinal tractor inclination angle value indicative of the inclination angle, in said tractor longitudinal direction, of the ground supporting said tractor; wherein obtaining said longitudinal trailer inclination angle value indicative of the inclination angle, in said trailer longitudinal direction, of the ground supporting said trailer comprises: obtaining a speed value indicative of a current speed of said tractor in said a tractor longitudinal direction; obtaining a distance value indicative of a distance, in said a tractor longitudinal direction, between said inclination sensor and a reference point of said trailer; using said speed value and said distance value for determining an elapsed time from a first time instant at which said inclination sensor is located at a certain global position and a second time instant at which said reference point of said trailer is located at the same global position, and determining said longitudinal trailer inclination angle value using one or more longitudinal tractor inclination angle values determined by said inclination sensor as well as said elapsed time.

8. The method according to claim 1, wherein said tractor comprises a set of ground engaging member axles, wherein said set of ground engaging member axles comprises at least one axle and wherein each ground engaging member axle is connected to individual ground engaging members of said tractor, wherein said method comprises performing the following for each ground engaging member axle in said set of ground engaging member axles: on the basis of said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right),$ determining a trailer axle lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}\right)$ indicative of a trailer lateral force being or predicted to be imparted on said ground engaging member axle; determining a horizontal friction force value $\left(F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{axle}}\right)$ indicative of a possible total horizontal frictional force obtainable between said ground supporting said tractor and said individual ground engaging members of said ground engaging member axle, and determining an axle tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{axle}}\right)$ using said trailer axle lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}\right)$ and said horizontal friction force value $\left(F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{axle}}\right),$ and summarizing the axle tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{axle}}\right)$ for each ground engaging member axle in said set of ground engaging member axles in order to obtain said tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right).$

9. The method according to claim 8, wherein the step of determining a trailer axle lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}\right)$ indicative of a trailer lateral force being or predicted to be imparted on said ground engaging member axle on the on the basis of said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right)$ comprises using a moment equilibrium equation using the following inputs: said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right);$ a distance (I.sub.f, I.sub.r), in the tractor longitudinal direction (L.sub.TR), from each ground engaging member axle to the centre of gravity of said tractor, and a distance (I.sub.c), in the tractor longitudinal direction (L.sub.TR), from the connection point to the centre of gravity of the tractor.

10. The method according to claim 1, wherein said method comprises performing the following for each ground engaging member of said tractor: on the basis of said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right),$ determining a trailer ground engaging member later force value $\left(F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}\right)$ indicative of a trailer lateral force being or predicted to be imparted on said ground engaging member; determining a horizontal friction fore value $\left(F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{gem}}\right)$ indicative of a possible total horizontal frictional force obtainable between said ground supporting said tractor and said ground engaging member, and determining a ground engaging member tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{gem}}\right)$ using said trailer ground engaging member lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}\right)$ and said horizontal friction force value $\left(F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{gem}}\right),$ and summarizing the ground engaging member tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{gem}}\right)$ for each ground engaging member of said tractor in order to obtain said tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right).$

11. The method according to claim 10, wherein the step of determining a determining a trailer ground engaging member lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}\right)$ indicative of a trailer lateral force being or predicted to be imparted on said ground engaging member on the basis of said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right)$ comprises using a moment equilibrium equation using the following inputs: said trailer lateral force value $\left(F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}\right);$ a distance (I.sub.f, I.sub.r), in the tractor longitudinal direction (L.sub.TR), from each ground engaging member to the centre of gravity of said tractor, and a distance (I.sub.c), in the tractor longitudinal direction (L.sub.TR), from the connection point to the centre of gravity of the tractor.

12. A method for braking a vehicle combination comprising a tractor and a trailer, said tractor comprising a tractor brake assembly for regenerative braking of said tractor and said trailer comprising a trailer brake assembly for braking said trailer, said method comprising: determining a tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right)$ using the method according to claim 1: operating said tractor brake assembly so as to provide a braking force being smaller than or equal to said tractor longitudinal force threshold value.

13. The method according to claim 12, wherein said method further comprises: obtaining a retardation request value (r.sub.req) indicative of a requested retardation of said vehicle combination; determining a requested braking force (F.sup.ret,request) to be imparted on said vehicle combination on the basis of said retardation request value (r.sub.req); in response to said requested braking force (F.sup.ret,request) being smaller than or equal to said tractor longitudinal force threshold value $\left(F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}\right),$ operating said tractor brake assembly but not said trailer brake assembly for braking said vehicle combination.

14. The method according to claim 13, wherein determining a requested braking force to be imparted on said vehicle combination on the basis of said retardation request value further comprises obtaining a tractor mass value (m.sup.tractor) indicative of the current mass of said tractor and a trailer mass value (m.sup.trailer) indicative of the current mass of said trailer.

15. The method according to claim 13, wherein determining a requested braking force to be imparted on said vehicle combination on the basis of said retardation request value (r.sub.req) further comprises determining a longitudinal trailer inclination angle value () indicative of the inclination angle, in said trailer longitudinal direction, of the ground supporting said trailer.

16. The method according to claim 12, wherein determining a requested braking force to be imparted on said vehicle combination on the basis of said retardation request value (r.sub.req) further comprises determining a longitudinal tractor inclination angle value indicative of the inclination angle, in said tractor longitudinal direction, of the ground supporting said tractor.

17. A computer program comprising program code means for performing the method of claim 1 when said program is run on a computer.

18. A computer readable medium carrying a computer program comprising program code means for performing the method of claim 1 when said program is run on a computer.

19. A control unit configured to perform the method according to claim 1.

20. A vehicle combination comprising a tractor, a trailer and a control unit according to claim 19.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0081] With reference to the appended drawings, below follows a more detailed description of embodiments of the invention cited as examples.

[0082] In the drawings:

[0083] FIG. 1 is a schematic plan view of a vehicle combination;

[0084] FIG. 2 is a schematic plan view of a vehicle combination;

[0085] FIG. 3 is a schematic side view of a vehicle combination;

[0086] FIG. 4 is a schematic rear view of a vehicle combination, and

[0087] FIG. 5 is a schematic plan view of a vehicle combination.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION

[0088] FIG. 1 is a schematic plan view of a vehicle combination 10 comprising a tractor 12 and a trailer 14. Purely by way of example, and as indicated in FIG. 1, the tractor 12 may comprise a propulsion assembly 16 for propelling the tractor 12 and consequently the vehicle combination 10. As a non-limiting example, the propulsion assembly 16 may comprise an electric motor. In the FIG. 1 embodiment, the propulsion assembly 16 is connected to a set of ground engaging members 18 via an arrangement comprising a shaft 20. In FIG. 1, the ground engaging members 18 are implemented as wheels, but it is also envisaged that the ground engaging members 18 may be implemented as crawlers (not shown) or the like. Moreover, it is also contemplated that the propulsion assembly 16 may comprise one or more electric motors each one of which being arranged at the hub of a ground engaging member, such as a wheel, of the tractor 12.

[0089] As indicated in FIG. 1, the trailer 14 has a trailer longitudinal extension in a trailer longitudinal direction L.sub.TL, a trailer lateral extension in a trailer lateral direction T.sub.TL and a trailer vertical extension in a trailer vertical direction V.sub.TL. The trailer longitudinal direction L.sub.TL corresponds to an intended direction of travel of the trailer 14 when the vehicle combination 10 is travelling straight ahead, the trailer vertical direction V.sub.TL corresponds to a direction of a normal to a planar surface supporting the trailer 14 and the trailer lateral direction T.sub.TL is perpendicular to each one of the trailer longitudinal direction L.sub.TL and the trailer vertical direction V.sub.TL.

[0090] In a similar vein, and as also indicated in FIG. 1, the tractor 12 has a tractor longitudinal extension in a tractor longitudinal direction L.sub.TR, a tractor lateral extension in a tractor lateral direction T.sub.TR and a tractor vertical extension in a tractor vertical direction V.sub.TR. The tractor longitudinal direction L.sub.TR corresponds to an intended direction of travel of the tractor 12 when the vehicle combination 10 is travelling straight ahead, the tractor vertical direction V.sub.TR corresponds to a direction of a normal to a planar surface supporting the tractor 12 and the tractor lateral direction T.sub.TR is perpendicular to each one of the tractor longitudinal direction L.sub.TR and the tractor vertical direction V.sub.TR.

[0091] Moreover, as indicated in FIG. 1, the tractor 12 may comprise a tractor brake assembly for regenerative braking of the tractor 12. As a non-limiting example, the propulsion assembly 16 may be used for regenerative braking of the tractor 12 and may thus form part of, or even constitute, the tractor brake assembly for regenerative braking of the tractor 12. Thus, when the propulsion assembly 16 is implemented as an electric machine for instance, such an electric machine may function as a generator and generate electric energy to be stored in an electric storage assembly (not shown), such as a battery (not shown). However, it is also contemplated that the tractor brake assembly for regenerative braking of the tractor 12 may comprise, or even be constituted by, one or more electric hub machines 22, 24, each one of which may operate as a generator and generate electric energy to be stored in an electric storage assembly (not shown), such as a battery (not shown).

[0092] Moreover, other implementations of the tractor 12 may comprise a tractor brake assembly for braking of the tractor 12 without necessarily having a regeneration capability. For instance, such implementations may comprise one or more service brakes (not shown in FIG. 1).

[0093] Irrespective of the implementation the tractor brake assembly is adapted to generate a tractor longitudinal retardation force

[00004]$F_{L_{\mathrm{TR}}}^{\mathrm{ret}}$

extending in a direction parallel to the tractor longitudinal direction L.sub.TR.

[0094] Moreover, the trailer 14 may comprise a trailer brake assembly 26 for braking the trailer. The trailer brake assembly 26 may comprise one or more service brakes, one or more electric machines for regenerative braking, or any combination thereof.

[0095] Furthermore, as indicated in FIG. 1, the trailer 14 is pivotally connected to the trailer 12 via a connection point 28. Such a connection point 28 may for instance be implemented as a so called fifth wheel. Thus, the trailer 14 is connected to the tractor 12 such that an articulation angle may be formed between the tractor longitudinal direction L.sub.TR and the trailer longitudinal direction L.sub.TL. Moreover, the above-mentioned articulation angle may vary, preferably in a stepless manner, depending on for instance the operating condition of the vehicle combination 10. The articulation angle is indicated with a minus sign in FIG. 1 thereby implying that a negative articulation angle is assumed in the FIG. 1 condition.

[0096] Additionally, FIG. 1 illustrates that the vehicle combination 10 may comprise a control unit 30 configured to perform the method according to the present invention. In the FIG. 1 embodiment, the control unit 30 is located in the tractor 12 although other positions of the control unit 30 are also conceivable.

[0097] FIG. 2 is a schematic plan view of a vehicle combination 10 being similar to the FIG. 1 vehicle combination 10. In FIG. 2, the trailer 12 and the tractor 14 are illustrated at a distance from each other in order to elucidate the forces acting between the tractor 12 and the trailer 14. However, it should be noted that the coupling forces between the tractor 12 and trailer 14 occur when the trailer 14 is connected to the tractor 12 via the connection point 28.

[0098] As may be realized from FIG. 2, during driving of the vehicle combination 10, the trailer will be imparted a trailer longitudinal force

[00005]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}},$

in the trailer longitudinal direction L.sub.TL, and a trailer lateral force

[00006]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer}},$

in the trailer lateral direction T.sub.TL. Further details of these forces will be presented hereinbelow.

[0099] The above-mentioned forces will result in connection forces

[00007]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL and the trailer lateral direction T.sub.TL, respectively, between the tractor 12 and the trailer 14. It should be noted that the connection forces

[00008]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

need not necessarily fully correspond to the trailer longitudinal force

[00009]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}}$

and the trailer lateral force

[00010]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer}},$

respectively. This is since at least a portion of the trailer longitudinal force

[00011]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}}$

and/or the trailer lateral force

[00012]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer}}$

may be accommodated by for instance the ground engaging members, such as the wheels, of the trailer 14.

[0100] In FIG. 2, the above-mentioned connection forces are presented in relation to the tractor 12 as well as to the trailer 14. Moreover, as indicated in FIG. 2, the connection forces

[00013]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

are related to the trailer longitudinal direction L.sub.TL and the trailer lateral direction T.sub.TL, respectively. Consequently, in order to transform the connection forces

[00014]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

to the tractor longitudinal direction L.sub.TR and the trailer lateral direction T.sub.TR, respectively, the current articulation angle may be taken into account.

[0101] Moreover, a tractor longitudinal retardation force

[00015]$F_{L_{\mathrm{TR}}}^{\mathrm{ret}}$

imparted on the tractor 12 is illustrated in FIG. 2. Furthermore, a lateral tractor force

[00016]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{ground}},$

viz a force in the tractor lateral direction T.sub.TR imparted on the tractor 12 via the ground engaging members thereof, is indicated in FIG. 2.

[0102] The total horizontal forces that can be imparted on the tractor 12 via its ground engaging members, i.e. from the contact between the ground engaging members and the ground supporting the tractor 12, is limited by a total horizontal frictional force

[00017]$F_{total}^{tractor}$

obtainable between the ground supporting the tractor and ground engaging members of the tractor 12.

[0103] Purely by way of example, the total horizontal frictional force may be determined using the weight

[00018]$F_{V_{TR}}^{tractor}$

of the tractor 12, viz the sum of the forces in the tractor vertical direction V.sub.TR imparted on the ground engaging members of the tractor from the ground supporting the tractor. The weight

[00019]$F_{V_{TR}}^{tractor}$

may be determined by multiplying the total tractor mass m.sup.tractor by an acceleration value g corresponding to acceleration due to gravity. Moreover, in order to determine the total horizontal frictional force, a friction value , indicative of the friction between the set of ground engaging members of tractor 12 and the ground supporting the tractor 12 may be used.

[0104] Such a friction value may be determined using any known procedure, such as using a sensor (such as a camera) for monitoring the condition of the ground onto which the tractor 12 is travelling and/or by using a brush model or using a slip value associated with the ground engaging members, such as wheels, of the tractor 12.

[0105] As such, the total horizontal frictional force

[00020]$F_{total}^{tractor}$

may be determined in accordance with the following:

[00021]$\begin{array}{cc}{F}_{total}^{tractor}=F_{V_{\mathrm{TR}}}^{tractor}.Math.& \mathrm{Eq}.1\end{array}$

[0106] However, it should be noted that the total horizontal frictional

[00022]$F_{total}^{tractor}$

may be determined in accordance with other procedures as well. Purely by way of example, if the individual friction value , indicative of the friction between the one ground engaging members of tractor 12 and the ground supporting the tractor 12, is taken into account, the total horizontal frictional force

[00023]$F_{total}^{tractor}$

may be determined in accordance with the following:

[00024]$\begin{array}{cc}{F}_{total}^{tractor}={.Math.}_{i=1}^n{F}_{V_{TR}}^{tractor,i}.Math.{}_i& \mathrm{Eq}.2\end{array}$

[0107] where:

[00025]$F_{V_{TR}}^{tractor,i}$

is the force in the tractor vertical direction V.sub.TR; imparted on the i:th ground engaging member of the tractor 12 from the ground supporting the tractor 12, and [0108] .sub.i is a friction value indicative of the friction between the i:th ground engaging member of the tractor 12 and the ground supporting the tractor 12.

[0109] Purely by way of example, the force in the tractor vertical direction V.sub.TR imparted on the i:th ground engaging member of the tractor 12 from the ground supporting the tractor 12 may be determined using information from e.g. a ground engaging suspension arrangement (not shown) of the tractor 12.

[0110] As a further alternative, Eq. 3 hereinabove may also be employed for each ground engaging member axle of the tractor 12.

[0111] Irrespective of how the total horizontal frictional force

[00026]$F_{total}^{tractor}$

is determined, the following condition should be met in order to avoid slipping and/or sliding of the ground engaging members of the tractor 12:

[00027]$\begin{array}{cc}{\left(F_{total}^{tractor}\right)}^2={\left(F_{L_{TR}}^{ret}\right)}^2+{\left(F_{T_{TR}}^{t\mathrm{ractor},\mathrm{ground}}\right)}^2& \mathrm{Eq}.3\end{array}$

[0112] For the sake of simplicity, Eq. 3 hereinabove relates to the total forces of the tractor 12. However, it should be noted that Eq. 3 can be expanded to ground engaging member axles or even each ground engaging members of the tractor 12.

[0113] As such, though purely by way of example, Eq. 3 can be expanded to a tractor 12 comprising a set of ground engaging member axles, wherein the set of ground engaging member axles comprises at least one axle and wherein each ground engaging member axle is connected to individual ground engaging members (such as wheels) of the tractor 12. Assuming that the tractor comprises N axles, Eq. 3 can be expanded in accordance with the following:

[00028]$\begin{array}{cc}{.Math.}_{i=1}^N{\left(F_{total}^{tractor,i}\right)}^2={.Math.}_{i=1}^N{\left(F_{L_{TR}}^{ret,i}\right)}^2+{.Math.}_{i=1}^N{\left(F_{T_{TR}}^{\mathrm{tractor},\mathrm{ground},i}\right)}^2& \mathrm{Eq}.4\end{array}$

[0114] Wherein the index i indicates the i:th ground engaging member axle.

[0115] In a similar vein, though purely by way of example, Eq. 3 can be expanded to a tractor 12 to each ground engaging member (such as wheel) of the tractor 12. Assuming that the tractor comprises M ground engaging members, Eq. 3 can be expanded in accordance with the following:

[00029]$\begin{array}{cc}{.Math.}_{j=1}^M{\left(F_{total}^{\mathrm{tractor},j}\right)}^2={.Math.}_{j=1}^M{\left(F_{L_{TR}}^{ret,j}\right)}^2+{.Math.}_{j=1}^M{\left(F_{T_{TR}}^{t\mathrm{ractor},\mathrm{ground},j}\right)}^2& \mathrm{Eq}.5\end{array}$

[0116] Wherein the index j indicates the j:th ground engaging member.

[0117] For the sake of brevity, the below examples are mainly based on Eq. 3 hereinabove. However, it should be noted that the below examples can be expanded in a straightforward manner to each one of Eq. 4 and Eq. 5, respectively.

[0118] As such, using Eq. 3 as an example, a maximum value of the tractor longitudinal retardation force

[00030]$F_{L_{TR}}^{\mathrm{ret},\mathrm{threshold}},$

which value hereinafter will be referred to as a tractor longitudinal force threshold value, may be determined in accordance with the following:

[00031]$\begin{array}{cc}{F}_{L_{TR}}^{\mathrm{ret},th\mathrm{resold}}=\sqrt{{\left(F_{total}^{\mathrm{tractor}}\right)}^2-{\left(F_{T_{TR}}^{\mathrm{tractor},\mathrm{ground}}\right)}^2}& \mathrm{Eq}.6\end{array}$

[0119] Again, the total horizontal frictional force

[00032]$F_{\mathrm{total}}^{\mathrm{tractor}}$

can for instance pe determined in accordance with any one of the procedures mentioned hereinabove.

[0120] The lateral tractor force

[00033]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{ground}}$

is an aggregate of a force

[00034]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor}}$

imparted on the tractor 12, in the tractor lateral direction T.sub.TR, as such as well as the connection forces

[00035]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

between the tractor 12 and the trailer 14. Purely by way of example, the force

[00036]$F_{T_{\mathrm{TL}}}^{\mathrm{tractor}}$

imparted on the tractor 12 as such may be a centrifugal force as will be explained further hereinbelow.

[0121] In a similar vein, the connection force

[00037]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer lateral direction T.sub.TL may relate to a centrifugal force imparted on the trailer 14. On the other hand, the connection force

[00038]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the longitudinal direction L.sub.TL may be related to the mass m.sup.trailer of the trailer 14 as well as the longitudinal acceleration of the trailer 14. This will also be elaborated on further hereinbelow.

[0122] As has been intimated above, in order to transform the connection forces

[00039]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

to the tractor lateral direction T.sub.TR, information indicative of the current articulation angle can be used in accordance with the following:

[00040]$\begin{array}{cc}{F}_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{ground}}=F_{T_{\mathrm{TR}}}^{\mathrm{tractor}}+F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}.Math.\cos \left(\right)+F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}.Math.\sin \left(\right)& \mathrm{Eq}.7\end{array}$

[0123] As may be realized when studying Eq. 6 and Eq. 7 hereinabove, information indicative of the connection forces

[00041]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

between the tractor 12 and the trailer 14 may be useful information when determining a tractor longitudinal force threshold value

[00042]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}$

for a tractor longitudinal retardation force

[00043]$F_{L_{\mathrm{TR}}}^{\mathrm{ret}}$

that can be imparted on a tractor 12 of a vehicle combination 10 comprising the tractor 12 and the trailer 14 for retarding the vehicle combination 10.

[0124] The connection forces

[00044]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}},F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL and the trailer transversal direction T.sub.TL, respectively, may be transformed to a trailer lateral force value

[00045]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}},$

indicative of the trailer lateral force being or predicted to be imparted on the tractor in the tractor lateral direction T.sub.TR, in accordance with the following:

[00046]$\begin{array}{cc}{F}_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}=F_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}.Math.\cos \left(\right)+F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}.Math.\sin \left(\right)& \mathrm{Eq}.8\end{array}$

[0125] In particular, the inventors of the present invention have realized that the connection force

[00047]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL can be determined with an appropriate level of accuracy which in turn may improve the accuracy of the determination of the above-mentioned tractor longitudinal force threshold value

[00048]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}.$

[0126] To this end, reference is made to FIG. 3 illustrating a vehicle combination 10 travelling on a slope with an inclination angle. As may be realized from FIG. 3, the inclination angle will result in a gravity force imparted on the trailer 14 in the trailer longitudinal direction L.sub.TL and the gravity force will thus form part of the connection force

[00049]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL.

[0127] To this end, a first aspect of the present invention relates to a method for determining a tractor longitudinal force threshold value

[00050]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}$

for a tractor longitudinal retardation force

[00051]$F_{L_{\mathrm{TR}}}^{\mathrm{ret}}$

that can be imparted on a tractor 12 of a vehicle combination 10 comprising the tractor 12 and a trailer 14 for retarding the vehicle combination 10.

[0128] With reference to FIG. 3, the method comprises determining a trailer lateral force value

[00052]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}},$

see Eq. 8 hereinabove, indicative of a trailer lateral force being or predicted to be imparted on the tractor in the tractor lateral direction T.sub.TR. The trailer lateral force value

[00053]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

is determined using a trailer lateral force value determination procedure comprising the features presented hereinbelow.

[0129] The procedure comprises obtaining a trailer mass value mass m.sup.trailer indicative of the current mass of the trailer 14. Purely by way of example, the trailer mass value mass m.sup.trailer may be determined using e.g. information from a ground engaging member suspension system (not shown) of the trailer 14. Instead of, or in addition to using information from a ground engaging member suspension system, information indicative of the dead weight of the trailer as well as the current weight of the cargo carried by the trailer 14 may be used.

[0130] Moreover, the procedure comprises obtaining a longitudinal trailer inclination angle value indicative of the inclination angle, in the trailer longitudinal direction L.sub.TL, of the ground supporting the trailer 14. The inclination angle value may for instance be determined using an inclination sensor 32 of the trailer 14. Alternatively, the inclination angle value may be determined using information from a map system or the like. As such, using information concerning e.g. the topography of the ground using the map system as well as the current location of the trailer 14, which for instance may be determined using a global positioning system (not shown), the inclination angle value may be determined.

[0131] Moreover, the method comprises determining a longitudinal gravity force value

[00054]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

indicative of a longitudinal gravity force, in the trailer longitudinal direction L.sub.TL, imparted on the trailer 14 on the basis of at least the trailer mass value m.sup.trailer and the longitudinal trailer inclination angle value . As a non-limiting example, the longitudinal gravity force value

[00055]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

may be determined in accordance with the following:

[00056]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}=g.Math.m^{\mathrm{trailer}}.Math.\sin \left(\right).$

[0132] Additionally, the procedure comprises determining an articulation angle value indicative of a current articulation angle between the tractor longitudinal direction L.sub.TR and the trailer longitudinal direction L.sub.TL. Purely by way of example, the articulation angle value may be determined using an articulation angle sensor (not shown) of the vehicle combination 10. Purely by way of example, such a sensor may be hosted by the tractor 12. However, it is also envisaged that the articulation angle value Y may be determined without the need of an articulation angle sensor. To this end, reference is made to e.g. Eq. 21 hereinbelow.

[0133] Furthermore, the method comprises determining the trailer lateral force value

[00057]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

using the longitudinal gravity force value

[00058]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

and the articulation angle value . As may be realized from Eq. 8 hereinabove, the longitudinal gravity force value

[00059]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

can form part of the trailer lateral force value

[00060]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

since the longitudinal gravity force value

[00061]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

forms part of the connection force

[00062]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL between the tractor 12 and the trailer 14.

[0134] Furthermore, with reference to e.g. Eq. 1 or Eq. 2 hereinabove, the method also comprises determining a horizontal friction force value

[00063]$F_{\mathrm{total}}^{\mathrm{tractor}}$

indicative of a possible total horizontal frictional force obtainable between the ground supporting the tractor 12 and ground engaging members of the tractor 12.

[0135] Further, with reference to e.g. Eq. 6 hereinabove, the method also comprises determining the tractor longitudinal force threshold value

[00064]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}$

using the trailer lateral force value

[00065]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

and the horizontal friction force value

[00066]$F_{\mathrm{total}}^{\mathrm{tractor}}.$

[0136] Purely by way of example, the trailer lateral force value determination procedure further comprises obtaining a longitudinal trailer retardation value r.sub.L.sub.TL indicative of a longitudinal trailer retardation being or predicted to be imparted on the trailer 14. Generally, the longitudinal trailer retardation value r.sub.L.sub.TL may be negative, thus indicating a requested retardation, i.e. acceleration in a direction opposite to the trailer longitudinal direction L.sub.TL. Purely by way of example, the longitudinal trailer retardation value r.sub.L.sub.TL may be determined using a sensor (not shown) such as an accelerometer (not shown) associated with the trailer 14. However, it is also envisaged that the longitudinal trailer retardation value r.sub.L.sub.TL may be determined in other ways, e.g. using a retardation request signal indicative of a requested retardation of the trailer 14.

[0137] Moreover, the trailer lateral force value determination procedure may comprise determining a longitudinal inertial trailer force value

[00067]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}$

indicative of a longitudinal inertial force, in the trailer lateral direction L.sub.TL, imparted on the trailer 14 on the basis of at least the trailer mass value m.sup.trailer and the longitudinal trailer retardation value r.sub.L.sub.TL. Purely by way of example, the longitudinal inertial trailer force value

[00068]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}$

may be determined in accordance with the following:

[00069]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}=r_{L_{\mathrm{TL}}}.Math.m^{\mathrm{trailer}}.$

[0138] Additionally, the trailer lateral force value determination procedure may comprise determining the tractor longitudinal force threshold value

[00070]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}$

using also the longitudinal inertial trailer force value

[00071]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}.$

[0139] As such, though purely by way of example, the longitudinal inertial trailer force value

[00072]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}$

and the longitudinal gravity force value

[00073]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

may be combined in order to form part of, or even constitute, the connection force

[00074]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer longitudinal direction L.sub.TL in accordance with the following (see e.g. Eq. 8 hereinabove):

[00075]$F_{L_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}=F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}+F_{L_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{inertial}}.$

[0140] Furthermore, though purely by way of example, the trailer lateral force value determination procedure may further comprise: [0141] determining a lateral centrifugal force value

[00076]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

indicative of a centrifugal force, in the trailer lateral direction T.sub.TL, imparted on the trailer 14 on the basis of at least the trailer mass value m.sup.trailer, and [0142] determining the trailer lateral force value

[00077]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

using also lateral centrifugal force value

[00078]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}.$

[0143] Purely by way of example, the lateral centrifugal force value

[00079]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

may be determined on the basis of a longitudinal speed value v.sub.L.sub.TL indicative of a speed of the trailer 14 in the trailer longitudinal direction L.sub.TL and a trailer curvature radius R.sup.trailer, indicative of the radius of the curvature of a path that the centre of gravity of the trailer 14 currently is following (see FIG. 5). As a non-limiting example, the lateral centrifugal force value

[00080]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

may be determined in accordance with the following:

[00081]$\begin{array}{cc}{F}_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}=m^{\mathrm{trailer}}\frac{v_{L_{\mathrm{TL}}}^2}{R^{\mathrm{trailer}}}& \mathrm{Eq}.9\end{array}$

[0144] In a similar vein as for the lateral centrifugal force value

[00082]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

mentioned above, the force

[00083]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor}}$

imparted on the tractor 12, in the tractor lateral direction T.sub.TR, may comprise an addend relating to a lateral centrifugal force value

[00084]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{centrifugal}}$

indicative of a centrifugal force, in the tractor lateral direction T.sub.TR, imparted on the tractor 12 on the basis of at least the tractor mass value m.sup.tractor, a longitudinal speed value v.sub.L.sub.TR indicative of a speed of the tractor 12 in the tractor longitudinal direction L.sub.TR and a tractor curvature radius R.sup.tractor, indicative of the radius of the curvature of a path that the centre of gravity of the tractor 12 currently is following. Thus, in analogy with Eq. 9 hereinabove, the lateral centrifugal force value

[00085]$F_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{centrifugal}}$

for the tractor 12 may be determined in accordance with the following:

[00086]$\begin{array}{cc}{F}_{T_{\mathrm{TR}}}^{\mathrm{tractor},\mathrm{centrifugal}}=m^{\mathrm{tractor}}\frac{v_{L_{\mathrm{TR}}}^2}{R^{\mathrm{tractor}}}& \mathrm{Eq}.10\end{array}$

[0145] In embodiments of the present invention, the longitudinal speed value v.sub.L.sub.TR indicative of a speed of the tractor 12 in the tractor longitudinal direction L.sub.TR may be determined using a speed sensor (not shown) of the tractor 12. Moreover, though purely by way of example, in embodiments of the present invention the longitudinal speed value v.sub.L.sub.TL indicative of a speed of the trailer 14 in the trailer longitudinal direction L.sub.TL may be set so as to equal the longitudinal speed value v.sub.L.sub.TR indicative of a speed of the tractor 12 in the tractor longitudinal direction L.sub.TR.

[0146] Going back to the lateral centrifugal force value of the trailer 14, though purely by way of example, the lateral centrifugal force value

[00087]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

for the trailer 14 may form part of, or even constitute, the connection force

[00088]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

in the trailer transversal direction T.sub.TL in accordance with the following (see e.g. Eq. 8 hereinabove):

[00089]$\begin{array}{cc}{F}_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}=C.Math.F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}.& \mathrm{Eq}.11\end{array}$

[0147] It should be noted that that only a portion of the lateral centrifugal force value

[00090]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}$

may be added to the trailer lateral force value

[00091]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

As such, the factor C in Eq. 11 hereinabove may be within the range of 0 to 1. Here, it should be noted that the ground engaging members of the trailer 14 may accommodate a portion of the lateral centrifugal force imparted on the trailer 14. As such, though purely by way of example, the portion of the lateral centrifugal force that will be imparted on the connection point 28 may be determined by means of a moment equilibrium equation taking the distance, in the trailer longitudinal direction L.sub.TL, between the ground engaging members of the trailer 14 and the centre of gravity of the trailer, as well as the distance, in the trailer longitudinal direction L.sub.TL, between the connection point 28 and the centre of gravity of the trailer 14 into account. To this end, reference is made to Eq. 29 hereinbelow presenting an example of how the above-mentioned distances may be taken into account.

[0148] However, it should also be noted that, though purely by way of example, the trailer lateral force value determination procedure may further comprise obtaining a lateral inclination angle value indicative of the inclination angle, in the trailer lateral direction T.sub.TL, of the ground supporting the trailer 14. To this end, reference is made to FIG. 4 illustrating an implementation of a trailer 14 located on a transversally inclined slope.

[0149] As such, though purely by way of example, the trailer lateral force value determination procedure may comprise determining a lateral gravity force value

[00092]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}$

indicative of a lateral gravity force, in the trailer lateral direction T.sub.TL, imparted on the trailer 14 on the basis of at least the trailer mass value m.sup.trailer and the lateral inclination angle value . Moreover, the procedure may further comprise determining the trailer lateral force value using also the lateral gravity force value

[00093]$F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}.$

As such, though purely by way of example, Eq. 11 hereinabove may be extended in accordance with the following:

[00094]$\begin{array}{cc}{F}_{T_{\mathrm{TL}}}^{\mathrm{trailer}2\mathrm{tractor}}=C.Math.\left(F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{centrifugal}}+F_{T_{\mathrm{TL}}}^{\mathrm{trailer},\mathrm{gravity}}\right).& \mathrm{Eq}.12\end{array}$

[0150] Again, the factor C in Eq. 12 may be within the range of 0 to 1 and may relate to the distances, in the trailer longitudinal direction L.sub.TL, between the ground engaging members of the trailer 14, the centre of gravity of the trailer 14, and the connection point 28. As has been indicated hereinabove with reference to Eq. 7 for example, the trailer lateral force value determination procedure may further comprise multiplying each force value indicative of a force, in the trailer longitudinal direction L.sub.TL, with the sine of the articulation angle value . In a similar vein, again with reference to Eq. 7 for example, the trailer lateral force value determination procedure may further comprise multiplying each force value indicative of a force, in the trailer lateral direction T.sub.TL, with the cosine of the articulation angle value .

[0151] As has been intimated above, the longitudinal trailer inclination angle value may for instance be determined using an inclination sensor 32 of the trailer 14. However, alternatively, the longitudinal trailer inclination angle value may be determined using an inclination sensor 34 hosted by the tractor 12 as will be elaborated on hereinbelow. As such, the tractor 12 may comprise an inclination sensor 34, adapted to determine a longitudinal tractor inclination angle value indicative of the inclination angle, in the tractor longitudinal direction L.sub.TR, of the ground supporting the tractor 12. Moreover, with reference to FIG. 3, obtaining the longitudinal trailer inclination angle value indicative of the inclination angle, in the trailer longitudinal direction L.sub.TL, of the ground supporting the trailer 14 may comprise: [0152] Obtaining a speed value v.sub.L.sub.TR indicative of a current speed of the tractor 12 in the tractor longitudinal direction L.sub.TR. [0153] Obtaining a distance value 36 indicative of a distance, in the tractor longitudinal direction L.sub.TR, between the inclination sensor 34 and a reference point of the trailer 14. Purely by way of example, and as indicated in FIG. 3, the reference point may be the centre of gravity of the trailer 14. [0154] Using the speed value v.sub.L.sub.TR and the distance value 36 for determining an elapsed time t from a first time instant t.sub.1 at which the inclination sensor 34 is located at a certain global position and a second time instant t.sub.2 at which the reference point of the trailer is located at the same global position. [0155] Determining the longitudinal trailer inclination angle value using one or more longitudinal tractor inclination angle values determined by the inclination sensor 34 as well as the elapsed time t.

[0156] As has been intimated hereinabove, the above examples are generally based on Eq. 3 such that the methods are carried on a tractor level. However, as has been intimated above, e.g. with reference to Eq. 4, embodiments may also be performed on a ground engaging member axle level. As such, when a tractor 12 comprises a set of ground engaging member axles, wherein the set of ground engaging member axles comprises at least one axle and wherein each ground engaging member axle is connected to individual ground engaging members of the tractor 12, the method according to the present invention may comprise performing the following for each ground engaging member axle in the set of ground engaging member axles: [0157] on the basis of the trailer lateral force value

[00095]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}},$

determining a trailer axle lateral force value

[00096]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}$

indicative of a trailer lateral force being or predicted to be imparted on the ground engaging member axle; [0158] determining a horizontal friction force value

[00097]$F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{axle}}$

indicative of a possible total horizontal frictional force obtainable between the ground supporting the tractor 12 and the individual ground engaging members of the ground engaging member axle, and [0159] determining an axle tractor longitudinal force threshold value

[00098]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{axle}}$

using the trailer axle lateral force value

[00099]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}$

and the horizontal friction force value

[00100]$F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{axle}}.$

[0160] Moreover, the method may further comprise summarizing the axle tractor longitudinal force threshold value

[00101]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{axle}}$

for each ground engaging member axle in the set of ground engaging member axles in order to obtain the tractor longitudinal force threshold value

[00102]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}.$

[0161] Furthermore, though purely by way of example, the step of determining a trailer axle lateral force value

[00103]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{axle}}$

indicative of a trailer lateral force being or predicted to be imparted on the ground engaging member axle on the on the basis of the trailer lateral force value

[00104]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

may comprise using a moment equilibrium equation using the following inputs: [0162] the trailer lateral force value

[00105]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}};$ [0163] a distance I.sub.f, I.sub.r (see FIG. 5), in the tractor longitudinal direction L.sub.TR, from each ground engaging member axle to the centre of gravity of the tractor 12, and [0164] a distance I.sub.c (see FIG. 5), in the tractor longitudinal direction L.sub.TR, from the connection point 28 to the centre of gravity of the tractor 12.

[0165] An example of the use of a moment equilibrium equation in accordance with the above is presented in Eq. 31 and Eq. 32 hereinbelow. These equations are applicable for a tractor comprising two axles but similar equations can be derived for any number of axles.

[0166] In a similar vein, though purely by way of example, embodiments may also be performed on a ground engaging member level. As such, embodiments of the present invention may comprise performing the following for each ground engaging member of the tractor 12: [0167] on the basis of the trailer lateral force value

[00106]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}},$

determining a trailer ground engaging member lateral force value

[00107]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}$

indicative of a trailer lateral force being or predicted to be imparted on the ground engaging member; [0168] determining a horizontal friction force value

[00108]$F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{gem}}$

indicative of a possible total horizontal frictional force obtainable between the ground supporting the tractor 12 and the ground engaging member, and [0169] determining a ground engaging member tractor longitudinal force threshold value

[00109]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{gem}}$

using the trailer ground engaging member lateral force value

[00110]$F_{T_{\mathrm{TT}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}$

and the horizontal friction force value

[00111]$F_{\mathrm{total}}^{\mathrm{tractor},\mathrm{gem}}.$

[0170] As for the above example for determining the trailer axle lateral force values, the step of determining a trailer ground engaging member lateral force value

[00112]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{gem}}$

indicative of a trailer lateral force being or predicted to be imparted on the ground engaging member on the basis of the trailer lateral force value

[00113]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}}$

may comprise using a moment equilibrium equation using the following inputs: [0171] the trailer lateral force value

[00114]$F_{T_{\mathrm{TR}}}^{\mathrm{trailer}2\mathrm{tractor}};$ [0172] a distance I.sub.f, I.sub.r, in the tractor longitudinal direction L.sub.TR, from each ground engaging member to the centre of gravity of the tractor 12, and [0173] a distance I.sub.c, in the tractor longitudinal direction L.sub.TR, from the connection point 28 to the centre of gravity of the tractor 12.

[0174] An example of the use of a moment equilibrium equation in accordance with the above is presented in Eq. 31 and Eq. 32 hereinbelow. Although, these example equations are used for ground engaging member axles, the equations can be expanded in a straightforward manner to each ground engaging member of a tractor 12.

[0175] Moreover, the method may further comprise summarizing the ground engaging member tractor longitudinal force threshold value

[00115]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold},\mathrm{gem}}$

for each ground engaging member of the tractor 12 in order to obtain the tractor longitudinal force threshold value

[00116]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}.$

[0176] It is also envisaged that embodiments of the present invention may use combination of the above indicated ground engaging member axle level approach and the ground engaging member level approach. Purely by way of example, it is conceived that embodiments of the present invention may use the ground engaging member axle level approach for certain axles of a tractor and the ground engaging member level approach for the remaining ground engaging members of a tractor 12.

[0177] Irrespective of how the of the tractor longitudinal force threshold value

[00117]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}$

has been determined, it is preferably used in a method for braking a vehicle combination 10 comprising a tractor 12 and a trailer 14. The tractor comprises a tractor brake assembly for regenerative braking of the tractor and the trailer comprises a trailer brake assembly for braking the trailer.

[0178] The method comprises: [0179] determining a tractor longitudinal force threshold value

[00118]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},t\mathrm{hreshold}}$

using the method according to the first aspect of the present invention, for instance in accordance with any one of the embodiments presented hereinabove, and [0180] operating the tractor brake assembly so as to provide a braking force being smaller than or equal to the tractor longitudinal force threshold value

[00119]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}}.$

[0181] As a non-limiting example, the method for braking a vehicle combination 10 may further comprise: [0182] Obtaining a retardation request value r.sub.req indicative of a requested retardation of the vehicle combination 10. [0183] Determining a requested braking force F.sup.ret,request to be imparted on the vehicle combination 10 on the basis of the retardation request value r.sub.req. [0184] In response to the requested braking force F.sup.ret,request being smaller than or equal to the force tractor longitudinal force threshold value

[00120]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{threshold}},$

operating the tractor brake assembly but not the trailer brake assembly for braking the vehicle combination 10.

[0185] The requested braking force F.sup.ret,request may be determined in a plurality of different ways. However, as a non-limiting example, determining a requested braking force F.sup.ret,request to be imparted on the vehicle combination 10 on the basis of the retardation request value r.sub.req may comprise obtaining a tractor mass value m.sup.tractor indicative of the current mass of the tractor and a trailer mass value m.sup.trailer indicative of the current mass of the trailer.

[0186] Purely by way of example, the requested braking force

[00121]$F_{L_{\mathrm{TR}}}^{\mathrm{ret},\mathrm{request}}$

may be expressed as a force in the tractor longitudinal direction L.sub.TR and may be determined in accordance with the following:

[00122]$F_{L_{TR}}^{ret,request}=\left(m^{tractor}+m^{trailer}\right).Math.r_{L_{TL}}+F_{L_{TR}}^{resistance}.$

[0187] The force term

[00123]$F_{L_{TR}}^{resistance}$

may relate to resistance from e.g. drag loads imparted on the vehicle combination 10.

[0188] Moreover, determining the requested braking force F.sup.ret,request to be imparted on the vehicle combination 10 on the basis of the retardation request value r.sub.reg may further comprise determining a longitudinal trailer inclination angle value indicative of the inclination angle, in the trailer longitudinal direction, of the ground supporting the trailer.

[0189] Optionally, determining a requested braking force to be imparted on the vehicle combination on the basis of the retardation request value further may comprise determining a longitudinal tractor inclination angle value indicative of the inclination angle, in the tractor longitudinal direction, of the ground supporting the tractor.

[0190] FIG. 5 is a schematic plan view of a vehicle combination 10 comprising a tractor 12 and a trailer 14. In the specific embodiment of the vehicle combination illustrated in FIG. 5, the tractor 12 comprises two sets of wheels, viz a front set of wheels 38 and a rear set of wheels 40. Purely by way of example, the front set of wheels 38 may be steerable, and may thus have a variable steering angle , but the rear set of wheels 40 need not necessarily be steerable.

[0191] The implementation of the trailer 14 illustrated in FIG. 5 comprises a set of wheels 42 and the trailer 14 is pivotally connected to the tractor 12 via a connection point 28. Moreover, FIG. 5 indicates the following distances: [0192] I.sub.f being the distance, in the tractor longitudinal direction L.sub.TR , from the front set of wheels 38 to the centre of gravity of the tractor 12; [0193] I.sub.r being the distance, in the tractor longitudinal direction L.sub.TR, from the rear set of wheels 40 to the centre of gravity of the tractor 12; [0194] I.sub.c being the distance, in the tractor longitudinal direction L.sub.TR, from the connection point 28 to the centre of gravity of the tractor 12; [0195] I.sub.f,t being the distance, in the trailer longitudinal direction L.sub.TL, from the connection point 28 to the centre of gravity of the trailer 14; [0196] I.sub.r,t being the distance, in the trailer longitudinal direction L.sub.TL, from the connection point 28 to the set of wheels 42 of the trailer 14; [0197] R.sub.f being the turning radius of the front set of wheels 38; [0198] R.sub.r being the turning radius of the rear set of wheels 40; [0199] R.sub.f,t being the turning radius of the connection point 28, and [0200] R.sub.r,t being the turning radius of the set of wheels 42 of the trailer 14.

[0201] Purely by way of example, the above distances may be known (for instance furnished by the supplier of the tractor 12 and the trailer 14) and the steering angle may be determined using a steering angle sensor (not shown). Using the above distances I.sub.f, I.sub.r, I.sub.c, I.sub.ft and I.sub.r,t as well as a value indicative of the steering angle , the above-mentioned turning radii as well as the previously mentioned articulation angle can be determined in accordance with the following set of equations:

[00124]$\begin{array}{cc}{R}_f=\frac{\left(l_f+l_r\right)}{\sin .Math..Math.}& \mathrm{Eq}.13\end{array}$$\begin{array}{cc}{R}_r=\frac{\left(l_f+l_r\right)}{\tan .Math..Math.}& \mathrm{Eq}.14\end{array}$$\begin{array}{cc}{R}_{f,t}=\sqrt{R_r^2+{\left(l_r-l_c\right)}^2}& \mathrm{Eq}.15\end{array}$$\begin{array}{cc}{R}_{r,t}=\sqrt{R_{f,t}^2-{\left(l_{f,t}+l_{r,t}\right)}^2}& \mathrm{Eq}.16\end{array}$$\begin{array}{cc}{R}_{CoG}=\sqrt{R_r^2+l_r^2}& \mathrm{Eq}.17\end{array}$$\begin{array}{cc}{R}_{\mathrm{CoG},t}=\sqrt{R_{r,t}^2+l_{r,t}^2}& \mathrm{Eq}.18\end{array}$$\begin{array}{cc}u={\tan }^{-1}\left(\frac{R_{r,t}}{l_{f,t}+l_{r,t}}\right)& \mathrm{Eq}.19\end{array}$$\begin{array}{cc}w={\tan }^{-1}\left(\frac{R_r}{l_r-l_c}\right)& \mathrm{Eq}.20\end{array}$$\begin{array}{cc}=-\mathrm{sign}\left(\right)\left(w-u\right)& \mathrm{Eq}.21\end{array}$

[0202] When the tractor 12 has a certain speed v.sub.L.sub.TR in the tractor longitudinal direction L.sub.TR, the trailer 14 has a certain speed v.sub.L.sub.TL, in the trailer longitudinal direction L.sub.TL, the previously mentioned longitudinal trailer retardation value r.sub.T.sub.TL indicative of a longitudinal trailer 5 retardation being or predicted to be imparted on the trailer 14 has been obtained and the trailer 14 is travelling on a slope with an inclination angle , the tractor longitudinal force threshold value,

[00125]$F_{L_{TR}}^{ret,thr\mathrm{eshold}}$

can be determined in accordance with the following of the FIG. 5 embodiment:

[00126]$\begin{array}{cc}{F}_{L_{TR}}^{req\mathrm{uested}}=\left(m^{\mathrm{tractor}}+m^{\mathrm{trailer}}\right).Math.r_{L_{TL}}+F_{L_{TR}}^{\mathrm{resistance}}& \mathrm{Eq}.22\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{tractor},\mathrm{centrifugal}}=m^{\mathrm{tractor}}\frac{v_{L_{TR}}^2}{R_{\mathrm{CoG}}}& \mathrm{Eq}.23\end{array}$$\begin{array}{cc}{F}_{T_{TL}}^{\mathrm{trailer},\mathrm{centrifugal}}=m^{\mathrm{trailer}}\frac{v_{L_{TL}}^2}{R_{\mathrm{CoG},t}}& \mathrm{Eq}.24\end{array}$$\begin{array}{cc}{F}_{L_{TL}}^{\mathrm{trailer},\mathrm{inertial}}=m^{\mathrm{trailer}}.Math.r_{L_{TL}}& \mathrm{Eq}.25\end{array}$$\begin{array}{cc}{F}_{L_{TL}}^{\mathrm{trailer},\mathrm{gravity}}=m^{\mathrm{trailer}}.Math.g.Math.\sin \left(\right)& \mathrm{Eq}.26\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{trac\mathrm{tor},\mathrm{centrifugal},\mathrm{front}}=F_{T_{TR}}^{trac\mathrm{tor},\mathrm{centrtfugal}}\frac{l_r}{l_r+{\mathrm{.Math.}}_f}& \mathrm{Eq}.27\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{trac\mathrm{tor},\mathrm{centrifugal},\mathrm{rear}}=F_{T_{TR}}^{trac\mathrm{tor},\mathrm{centrifugal}}\frac{l_f}{l_r+l_f}& \mathrm{Eq}.28\end{array}$$\begin{array}{cc}{F}_{T_{TL}}^{\mathrm{trailer},\mathrm{centrifugal},\mathrm{cp}}=F_{T_{TL}}^{trat\mathrm{ler},\mathrm{centrifugal}}\frac{l_{r,t}}{l_{f,t}+{\mathrm{.Math.}}_{r,t}}& \mathrm{Eq}.29\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total}}=F_{T_{TL}}^{\mathrm{trailer},\mathrm{centrifugal},\mathrm{cp}}\cos +\left(F_{L_{TL}}^{\mathrm{trailer},\mathrm{inertial}}+F_{L_{TL}}^{\mathrm{trailer},\mathrm{gravity}}\right)\sin & \mathrm{Eq}.30\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total},\mathrm{front}}=F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total}}\frac{l_r-{\mathrm{.Math.}}_c}{l_f+l_r}& \mathrm{Eq}.31\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total},\mathrm{rear}}=F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total}}\frac{l_f+l_c}{l_f+l_r}& \mathrm{Eq}.32\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{front}}=F_{T_{TR}}^{\mathrm{tractor},\mathrm{centrifugal},\mathrm{front}}+F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total},\mathrm{front}}& \mathrm{Eq}.33\end{array}$$\begin{array}{cc}{F}_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{rear}}=F_{T_{TR}}^{\mathrm{tractor},\mathrm{centrifugal},\mathrm{rear}}+F_{T_{TR}}^{\mathrm{trailer}2\mathrm{tractor},\mathrm{total},\mathrm{rear}}& \mathrm{Eq}.34\end{array}$$\begin{array}{cc}{F}_{L_{TR}}^{\mathrm{ret},\mathrm{threshold}}=\sqrt{{\left(F_z\right)}^2-{\left(F_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{front}}+F_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{rear}}\right)}^2}& \mathrm{Eq}.35\end{array}$

[0203] In the above equations, the superscript front indicates forces associated with the front set of wheels 38, the superscript rear indicates forces associated with the rear set of wheels 40 of the tractor 12 and the superscript cp indicates forces associated with the connection point 28.

[0204] It should be noted that Eq. 35 hereinabove could alternatively be reformulated to a sum of the thresholds over the front and rear set of wheels in accordance with the following:

[00127]$\begin{array}{cc}{F}_{L_{TR}}^{\mathrm{ret},\mathrm{threshold}}=\sqrt{{\left(F_z^{\mathrm{front}}\right)}^2-{\left(F_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{front}}\right)}^2}+\sqrt{{\left(F_z^{rear}\right)}^2-{\left(F_{T_{TR}}^{\mathrm{tractor},\mathrm{total},\mathrm{rear}}\right)}^2}& \mathrm{Eq}.36\end{array}$

[0205] The above equations and FIG. 5 are related to a vehicle combination 10 comprising a tractor 12 having two set of wheels 38, 40 and a trailer 14 having one set of wheels 42. However, the above equations Eq. 13 to Eq. 35 can of course be expanded to any number of set of wheels of each one of the tractor 12 and the trailer 14.

[0206] Although the present invention has been presented in relation to methods, it should be noted that the above disclosure is equally applicable to each one of the following: [0207] a computer program comprising program code means for performing the method of the first or second aspects of the invention when the program is run on a computer; [0208] a computer readable medium carrying a computer program comprising program code means for performing the method of the first or second aspects of the invention when the program product is run on a computer; [0209] a control unit 30 configured to perform the method according to the first or second aspects of the invention; [0210] a vehicle combination comprising a tractor 12, a trailer 14 and a control unit 30 according to the above.

[0211] It is to be understood that the present invention is not limited to the embodiments described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the appended claims.