WO2013141787A1

WO2013141787A1 - Method and arrangement for estimating height of center of gravity for a trailer

Info

Publication number: WO2013141787A1
Application number: PCT/SE2013/050266
Authority: WO
Inventors: Joseph Ah-King; Deleer BARAZANJI
Original assignee: Scania Cv Ab
Priority date: 2012-03-22
Filing date: 2013-03-15
Publication date: 2013-09-26
Also published as: SE1250609A1; EP2828633A1; EP2828633A4; SE536560C2

Abstract

A method in connection with an arrangement for a vehicle, comprising a trailer coupled to a tractor, for estimating the height of the center of gravity HCG for the trailer, wherein the tractor comprises a front wheel axle and a rear wheel axle, wherein at least the rear wheel axle is resiliently suspended by a wheel axle suspension system and the trailer comprises at least one wheel axle and is coupled to the tractor via a fifth wheel, and wherein the arrangement comprises a calculating unit (2) adapted to receive the values related to the acceleration a\ in the longitudinal direction of the vehicle and to the axle load N₂ pertaining to the rear wheel axle of the tractor. The method comprises the steps for - determining the associated values for the axle load N₂for the rear axle of the tractor and the acceleration a; of the vehicle, for a number of different acceleration values, - determining a parameter j related to a relation between the said determined associated values for the axle load N₂ and the acceleration a_i - estimating the height of the center of gravity HCG for the trailer via calculations performed in accordance with a predetermined algorithm in which said parameter j is included.

Description

I

Title

Method and arrangement for estimating height of center of gravity for a trailer Field of the invention

The present invention concerns a method and an arrangement according to the preambles of the independent claims.

The invention concerns in particular a method and an arrangement for estimating the height of the center of gravity for a trailer using an algorithm in which the values regarding the axle load and the vehicle acceleration are included.

Background of the invention

Arrangements for estimating the center of gravity for vehicles often involve load sensors that sense the load values on the vehicle wheels. The center of gravity of the vehicle can be estimated based on the positions of the vehicle wheels and the distribution of the vehicle weight over the various wheels. Such an estimate of the center of gravity of the vehicle is then obtained in a horizontal plane, and can be made with good precision. For goods vehicles, which can have different kinds of loads, the position of the center of gravity must be estimated in height as well. One way of making such an estimate is to determine the height of the center of gravity as a function of the total vehicle mass, i.e. a heavily loaded vehicle here will have a higher estimated center of gravity than a less heavily loaded vehicle. However, such a determination is not always accurate for goods vehicles that are transporting loads of varying composition and weight distribution. For example, a vehicle will have a considerably lower center of gravity if it is loaded with steel plates than if it is loaded with a corresponding weight of lumber.

Many vehicles contain electrically controlled stabilizing systems that are adapted to achieve optimal vehicle stability during operation. For such stabilizing systems to be effective, they must have access to reliable information regarding a plurality of parametric values, which are measured using sensors or estimated in some other way. One parameter that is important to the function of such stabilizing systems is the center of gravity of the vehicle. The position of the center of gravity in a horizontal plan can thus be determined with good precision using load sensors that sense how the weight of the vehicle is distributed over the vehicle wheels. On the other hand, it is difficult to determine the height of the center of gravity for a goods vehicle with correspondingly good precision, as said height can vary considerably depending on the composition of the load in question, and the stabilizing systems currently in use may in many cases fail to achieve optimum stability for a goods vehicle in operation.

It is possible to estimate the center of gravity by studying the roll motion of the vehicle, i.e. when the vehicle sways to the left and right. This is based on the fact that the amplitude at which the vehicle sways is related directly to the height of its center of gravity. When the amplitude reaches a certain point, the vehicle starts to tip over. By determining a characteristic amplitude for the vehicle, it is possible to see how high the center of gravity is, assuming the availability of data such as torsional rigidity, spring rigidity and tire rigidity. Another solution is proposed in SE-525 248, which, in brief, is based on estimating the height of the center of gravity by using moment and force equations. This is achieved, using load-sensing sensors, by sensing the load on at least two of the vehicle axles, the vehicle acceleration, and the angle of grade of the roadway, given already known information about dynamic movements due to accelerations and the road grade that produce different axle loads.

Solutions that are based on roll motion have the disadvantage that the trailer is not a completely rigid body, and that the spring rigidity must be known. Load estimates for at least two of the vehicle axles are required in the arrangement described in SE-525 248.

The object of the present invention is to achieve an improved method and an improved arrangement for estimating the height of the center of gravity (HCG) for a trailer by using essentially only information and measurement results that are available for the tractor, i.e. where as little information as possible is required regarding the trailer. Summary of the invention

The aforementioned objects are achieved with the invention defined in the independent claim. Preferred embodiments are defined in the dependent claims.

According to one embodiment, the axle load is determined for the rear axle of the tractor, preferably based on output signals from the pneumatic suspension. It will be possible to improve the systems that utilize the height of the center of gravity by applying the present invention. A warning and assistance system for issuing warnings and preventing the vehicle from rolling over represents one such system that cannot be used because it does not currently have accurate values for the height of the center of gravity. Rollover occurs when a vehicle tips over precisely because it has a high center of gravity that causes it to tip over at a lower speed in curves than if it had a low center of gravity. Rollovers are one of the most dangerous types of accidents, and there is much evidence that practically all such accidents could be prevented if good height of center of gravity estimation were available, which currently is not the case. Brief description of the drawing

Figure 1 is a flow diagram that illustrates the method according to the present invention.

Figure 2 is a simplified block diagram of the arrangement according to the invention.

Figure 3 illustrates the force ratio for a vehicle as it turns, and clearly illustrates the risk that the vehicle will roll over.

Figure 4 shows a schematic representation of a tractor, the forces that are related to the model, and other parameters.

Figure 5 shows a schematic representation of a trailer, the forces that are related to the model, and other parameters.

Figure 6 schematically depicts a tractor in which attractive forces are indicated.

Figure 7 schematically depicts a tractor in which repulsive forces are indicated.

Figure 8 shows a pneumatic suspension configuration according to a first embodiment. Figure 9 shows a pneumatic suspension configuration according to a second embodiment. Figure 10 schematically depicts a tractor and a trailer to illustrate the forces associated with the calculation of the effect of drag.

Detailed description of preferred embodiments of the invention

The present invention employs a so-called longitudinal model to produce an estimate of the height of the center of gravity of the vehicle. One advantage of this model is that it involves relatively few uncertain parameters. One difficulty with the model is that involves detecting and estimating load changes, which is a difficult task, but they can be estimated through the incorporation of pneumatic suspensions on goods vehicles. New ways of making load estimates using pneumatic suspension systems are being developed constantly, and are becoming better and better at utilizing the properties of the pneumatic suspension.

A description of the longitudinal model for estimating the height of the center of gravity will now be provided.

The transfer of loads between the vehicle axles and coupling points differ for each acceleration value and each situation. The load on the rear axle is given as a function of the acceleration, and this relation is defined differently and uniquely for each height of center of gravity value (HCG value) defined using equations for the torque equilibrium, which will be presented below.

The following designations will be used in the description below, and in the drawings: i = 1, 2, 3, 4 designate the front axle, rear axle and fifth wheel of the tractor, and the axles of the trailer.

X] is the wheelbase of the tractor (m).

x₂ is the distance from the position of the center of gravity (CG) of the tractor to the rear axle of the tractor (m).

x₃ is the distance between the fifth wheel and the rear axle of the tractor (m).

x₄ is the distance between the center of gravity (CG) of the trailer and the rear axle of the trailer (m). x₅ is the distance between the rear axle of the trailer and the fifth wheel (m).

yi is the height of the center of gravity (HCG) for the tractor (m).

y₂ is the height of the fifth wheel (m).

y₃ is the height of the center of gravity (HCG) for the trailer (m).

Nj is the vertical force at the point in (N).

F, is the forward-directed longitudinal force for wheels at the axle in (N).

t is the gauge for the trailer (m).

a_y is the acceleration transverse to the vehicle (m/s²).

a is the longitudinal acceleration of the vehicle (m/s ).

g is the gravitational constant (m/s²).

mj is the mass of the tractor (kg).

m_t is the mass of the trailer (kg).

m is the total mass of the vehicle (kg).

r is the wheel radius (m).

s is the displacement of the center of CG transversely from the line of symmetry of the vehicle RC (m).

F_r is the normal force on the right wheels (N).

F_\ is the normal force on the left wheels (N).

p is the pressure that the brakes apply to the wheels (bars).

pi is the pressure that the brakes apply to the wheels on an axle in (bars).

p_s is the pressure that is required to initiate braking of the wheels (bars).

p_Si is the pressure that is required to initiate braking of the wheels on an axle in (bars).

T i is the braking torque per pressure (Nm/bars).

m_s is the sprung weight of the vehicle (kg).

k is the spring constant (N/m).

F_b is the braking force (N).

T_e is the engine drive torque (Nm).

F_t is the driving force (N).

U_t is the final gear ratio, i.e. from the transmission and the differential.

F_h is the retardation force (N).

T_h is the retardation torque (Nm).

U_d is the gear ratio for the differential. C_d is the coefficient of drag,

v is the vehicle velocity (m/s)

As a first step, the load transfer for the tractor will be assessed for the purpose of estimating the longitudinal and vertical position of the center of gravity of the vehicle. Figure 4 shows a schematic representation of a tractor, and shows the forces that are related to the model, as well as other parameters.

The weight of the empty tractor m_djempty and the normal forces Ni and N₂ are all known. Consequently, the share of the normal forces for the tractor that depends on a given amount of fuel in the fuel tank can be calculated if the longitudinal position Xf of the center of gravity of the fuel tank is known.

N₂,f_ueiXi - m_fuelgx_f cos(0) = 0 Q J ) The same calculation can be performed regarding the normal force on the front axle. Equation (3.1) can be written as:

Which is added to the normal force for the empty tractor, which then yields the kerb weight of the vehicle:

N₂ = N 2, mpty + N- 2, uei (3.3)

In the next step the longitudinal position of the center of gravity obtained from the equation for the torque equilibrium with reference to Figure 4 is calculated. Ν *I - m_d.qx₂ cos(0) = 0 (3.4)

This equation is rewritten as _χ Ni _ m_dg cos(g) - N_{z χ}

² m_dg cos(0) m_dg cos(0) ¹ (3.5)

The equation for the torque equilibrium for the vertical center of gravity of the tractor must then be determined.

-N_A2 x i - m_Ld a _Ai + m_Ad gy_Li sin(0 )+ m_Ld g(xii - ¾2 )cos(0 )=o (3.6) Rewriting equation (3.6) we obtain:

V _ ^Νι^χχ - ^mdS (*i - *;)cos(0)

m_d(5 Sin[(9) - )] (3.7)

By inserting x₂ from equation (3.5) into equation (3.7) and knowing the normal force for at least one of the vehicle axles and information about the acceleration and the road grade, the equation is solved, yielding the height yi of the center of gravity of the tractor.

Corresponding calculations will now be described for the trailer.

Figure 5 shows a schematic representation of a trailer, the forces that are related to the model, and other parameters. In connection with acceleration or retardation and when driving on hilly roads, the loads will be transferred between the trailer axles and fifth wheel in dependence on the acceleration or retardation and the road grade; acceleration transfers load from the front axle to the rear, while retardation transfers the load from the rear axle to the front axle. The position x₄ of the longitudinal equilibrium of the trailer is calculated using the following stationary torque equilibrium equation (on flat terrain), the designations for which are presented in Figure 5.

This equation (3.8) can be written as m_t and N₃ are determined either by weighing at least one of the tractor axles or the trailer axles, as x₃ is known or obtained from the vehicle control unit, which calculates an estimate of the load on the rear axle and for m_t. m_t can also be determined by comparing a determination of the total vehicle weight with the weight of the tractor.

The sought value y₃, i.e. the height of the center of gravity (HCG), is obtained from the torque equation using designations from Figure 6, which schematically depicts a trailer where attractive forces are indicated, as follows: tf₃ s - F₃y₂ - m_tg cos(0)x₄ + m_tg sin(0)>'_s +- m_tay₃ = 0 (3.10)

The forces N₃ and F₃ in relation to the fifth wheel must also be calculated in order to estimate y₃. One way of determining them will now be described. We refer here to the forces that are acting on the coupling point between the tractor and the trailer.

The direction and magnitude of the longitudinal force F₃ on the fifth wheel depend on the relation between the tractor and the trailer, and on the rolling resistance and drag forces, and affect the load transfer measured on the rear axle of the tractor. This force must consequently be taken into account and estimated. If the vehicle accelerates, the relation will be as illustrated in Figure 6, while braking will give rise to different scenarios. If the trailer brakes only a portion f of or all (f = 100%) of the mass of the tractor, or if the tractor brakes only a portion f of or all (f = 100%) of the mass of the trailer, then the forces will be as shown in Figure 7. Figure 7 schematically depicts a trailer where repulsive forces are indicated. The following equation will show how F₃ is estimated in connection with acceleration or braking of the tractor. f-J =™-t^a + pRollandDrag (3 · 1 1 )

The following equation applies if the trailer brakes a part of the tractor: ^F3 = f^md^a + FRollandDrag (3.12)

And the following equation will apply if the trailer brakes a part of itself and the tractor also brakes: ^F3 = f^mt^a + ^FRollandDrag (3.13)

The force F_RoiiandDrag will be determined below using the equations (3.24 - 3.26), and f will be derived based on the relation between the braking forces for the trailer and the tractor. The braking forces will be discussed below, and the following relation applies for f in the case described by equation (3.13).

m_ta (3.14)

N₃ is the vertical force for the fifth wheel, and is the part of the load that is borne by the tractor. Typical values for this are roughly one-third of the mass of the trailer. This force in turn distributed between the axles of the tractor according to the following:

The rear axle of the tractor:

2

(3.15) The front axle of the tractor:

The weight transfer between the tractor axles will be in accordance with the following equation (the force on the rear wheels of the tractor):

*1 (3.17)

The forces on the rear and front axle of the tractor are dependent on acceleration and retardation, and will be as per the following with reference to the designations in Figure 4:

(3.18)

For the sake of simplicity, the road grade will be ignored, i.e. Θ = 0 in both these equations and below, i.e. N₃ is derived from equation (3.18).

The next step is to use the information from the pneumatic suspension that is used for the tractor in order to estimate the load N₂ on the rear axle of the tractor. N₂ is a parameter that is needed to estimate the height of the center of gravity, and the way it is determined will be described below. A number of parameters will now be described with respect to how they are determined. Estimate of the weight of the vehicle m

The weight of the tractor is assumed to be known. The weight of the trailer is estimated, e.g. using signals from the pneumatic suspension, the engine and/or information about changes in the velocity of the vehicle. m = md + m_t (3.20) Detecting and estimating weight transfer

The pneumatic suspension system of the vehicle is preferably used to estimate the transfer of weight between the vehicle axles. It should be noted that the invention is suitable for vehicles having other suspension systems that can emit signals that represent the load on the wheel axle.

Use of the pneumatic suspension system of the vehicle will be exemplified by describing two different types of pneumatic suspension systems for the rear axle of the tractor. One of them is shown in Figure 8 and consists of two pneumatic springs at the rear axle, each of which is disposed between the chassis above and a connected rod below, which are in turn mounted under the drive shaft and connect the pneumatic spring on one side of the drive shaft to a joint that enables rotation around the joint. The joint is connected to the chassis via a rigid arm, and the drive shaft is secured from above on the adjacent rod. This configuration is affected not only by vertical forces on the wheels, but also by longitudinal forces such as braking forces, traction forces and forces that depend on the road grade. The reason for this is the torque on the rod between the pneumatic spring and the frame, which is proportional to the longitudinal forces on the wheel. These longitudinal forces make up a part of the forces on the pneumatic spring, and must consequently be subtracted from the resulting force on the axle that is registered by the pneumatic spring in order to obtain only the load that is transferred between the axles.

The second pneumatic spring configuration is shown in Figure 9 and consists of four pneumatic springs, two of which are arranged on each respective side of the drive shaft, connected via a number of joints. It can be assumed that the bellows in this configuration are not affected by longitudinal forces, but rather only by vertical forces, which are the forces that are of interest here. The force acting on the pneumatic springs depends on the air pressure in the pneumatic spring, and on the length of the spring. As a supplement to the estimation of the weight transfer discussed above, the weight transfer can also be measured using leaf spring systems arranged on the front axle by applying Hook[e]'s Law. The longitudinal forces acting on the wheels will now be discussed.

It was noted above that the air pressure and thus the weight estimate for the pneumatic springs are affected by the longitudinal forces. Different forces come into play in connection with different maneuvers, such as braking and traction forces, and because these forces affect the measurement of the axle loads, they must be estimated so that they can be subtracted from the total force on the pneumatic springs. These forces, their effect and how they are estimated are discussed below.

Traction forces

The traction force is the force that is exerted on the wheels of the vehicle to move the vehicle and counteract natural forces in the direction of vehicle motion, such as road grade forces (Fgra_de), drag (F_drag) and roll resistance (F_ron).

These forces are usually consolidated using the following equation: " = ^mi; + ^Froll + ^Fdrag + Fgrade

The same force must be generated by the vehicle engine, and equals:

T_eU_t

t^_ r (3.22)

Braking forces

Braking is initiated by applying pressure to the brake cylinders, the pressure that is transferred to each of the vehicle axles is measured, and the pressure then creates torque that in turn generates a force that stops the vehicle. The relationship between pressure and torque is normally set so that a pressure of 1 bar corresponds to 5,500 Nm of torque. The pressure that is needed to initiate braking is on the order of 0.4 bars. The values given are approximations that differ between different vehicles and axles depending on many factors, such as temperature and the age and wear status of the brake components. To reduce the uncertainty, a rolling brake test can be performed, so that the following equation can be derived for applied brake torque per unit of brake pressure. T_h =

P - P») (3.23)

Retarding force

The retarder is a system that is intended to brake the vehicle by applying a force that is counter to the traction force. It can be described simply as braking the vehicle by affecting the power train. The retarding force can be calculated in a similar way to the traction force, using the following equation:

T U_d

(3.24)

The drag on the vehicle must also be estimated, and the following general expression for drag is then used:

^F = \^pC*^Av (3.25) where

p is the density of the air,

C_d is the drag coefficient, and

A is the front area of the vehicle.

The following exemplary values have been used: Cd = 0.73, p = 1.225 (kg/m ), and the force on the trailer has been assumed to be equal to the force on the tractor, i.e. F_ai = F_a2 which leads to the following force F_a being present on the fifth wheel:

F_a = F_al - F_a2 (3.26)

The remaining contributions from drag are addressed using the following equation, which is based on the torque equilibrium in Figure 10 at points A and B:

Road grade

The road grade can be estimated in various ways. According to one method, a map database that is updated with data regarding the road grade is used. Another method is to utilize the output signal from an accelerometer in combination with geometric relations. Yet another method is to use a GPS unit that provides information about the road grade.

Acceleration

The acceleration can be determined, for example, by deriving the wheel speed, using an accelerometer, or with a GPS unit.

Derivation (differentiation) of the wheel speed signal is a practical means of determining the acceleration, but it does not work as well during braking, when the wheel slides. The following equations offer examples of how the acceleration can be calculated: g. = - "'-1

ft (3.28)

where:

aj: the acceleration at the point in time in (m/s²).

Vj-. the speed at the point in time in (m/s).

h: tj-tj-i, i.e. the difference between adjacent points in time t is constant.

The height of the fifth wheel

The vertical position of the fifth wheel is a variable that depends on both the distance between the axle and the frame, and the wheel radius.

Ay 2 = Ay_f + AH + r (3.30) Where ΔΗ is the distance between the axle and the frame. yr is the distance between the frame and the coupling point for the fifth wheel. The change in y₂, which is related to the tire pressure and the load, is assumed to be negligible in connection with load transfer, and it is assumed that the variation in the wheel radius is minimal. The distance between the frame and the coupling point is assumed to be constant. Using these assumptions (3.30) can be solved, and a value for y₂ can be estimated.

Complete model

The relation between the axle load on the rear axle of the tractor and the acceleration provides information about the height of the center of gravity, as indicated in the description above.

Equation (3.18) together with equation (3.1 1) in which equation (3.10) is inserted is reduced to equation (3.31).

In equation (3.18) N₂ is determined, i.e. the axle force for the rear axle of the tractor. Equation (3.1 1) is used to determine the force F₃ that is acting on the fifth wheel, and equation (3.10) is the equilibrium equation for the torque, in which the sought parameter y₃ is included.

The relation so determined, equation (3.31), applies during acceleration and only braking of the tractor , or during the use of the retarder after reducing the axle load by the force from drag, as these forces would otherwise give rise to a non-linear relation if they were not subtracted from equation (3.18), i.e. the force N_2a from equation (3.27) is subtracted from N₂ in equation (3.18) prior to insertion.

(3.31) In the formula, j designates the slope of a curve that is obtained through linear regression for a number of associated points for the load on the rear axle of the tractor as a function of the acceleration. Other parameters that are involved are available to a calculating unit in the arrangement according to the invention, in the manners described above.

The greater the difference between the acceleration values, the greater the certainty with which the height of the center of gravity can be determined. For an acceleration value to be acceptable for use in the calculation, the acceleration must be constant for at least a predetermined time on the order of, for example, a few seconds.

A large number of associated values are used to achieve reliable results, i.e. so that the slope of the curve can be determined with the greatest possible certainty.

These calculations are performed continuously during vehicle operation.

A number of different situations can arise when using the estimation process as per equation (3.31).

During acceleration the tractor pulls the trailer with the longitudinal force F₃ via the fifth wheel. This force increases at higher longitudinal acceleration values, and produces a greater transfer of weight from the front axle of the tractor to its rear axle. Furthermore, the vertical force on the fifth wheel decreases with higher HCG, as more load is transferred rearward to the axles of the trailer. Thus, the higher the HCG, the lower the load on the rear axle of the tractor compared to when HCG was lower.

The situation in which each part brakes itself, i.e. the tractor and the trailer respectively brake themselves, entails that the longitudinal force on the fifth wheel remains unchanged, and consequently only the vertical forces are changed, which adds weight to the rear axle of the tractor with decreasing longitudinal acceleration. The increased weight becomes higher with increasing HCG.

During, for example, retarder braking, the tractor brakes itself and the trailer. This increases the longitudinal force on the fifth wheel with decreasing longitudinal acceleration. This means that the weight transferred from the trailer axles to the fifth wheel will be less than in other situations involving similar acceleration values. The same longitudinal force at the fifth wheel will affect the weight transfer of the tractor in such a way that even more weight will be transferred from the rear axle of the tractor to its front axle than in other situations. This will cause the weight on the rear axle of the tractor to be less.

This weight will also be less with decreasing HCG, because the lower the HCG, the less weight transferred from the trailer axles to the fifth wheel, which in turn means that less weight is transferred to the rear axle of the tractor.

The situation in which the trailer brakes the tractor entails that the longitudinal force on the fifth wheel pulls on the tractor, which adds weight from the front axle of the tractor to its rear axle, resulting in increasing weight on the rear axle of the tractor. Moreover, the higher the HCG, the more weight transferred from the trailer axles to the fifth wheel and, finally, to the rear axle of the tractor. There are air pressure sensors in the bellows of the pneumatic suspension that transmit information regarding the air pressure in the bellows, and a system for estimating the axle load based on the air pressure in the bellows is already available today.

The solution according to the present invention differs depending on the type of wheel suspension on the vehicle.

As discussed earlier, Figures 8 and 9 show two examples of suspension types. For the first type, shown in Figure 8, it is necessary to subtract traction forces, braking forces and retarding forces from the axle load obtained from the bellows, as the geometry of the suspension affects the bellows, from which the axle load is in turn measured. The second type, shown in Figure 9, is not affected by this.

The drag must also be subtracted in the same way.

The present invention thus concerns a method in connection with an arrangement for a vehicle that comprises a trailer coupled to a tractor. The method concerns the estimatation the height of the center of gravity HCG for the trailer. The flow diagram in Figure 1 provides a schematic illustration of the method. The tractor comprises a front wheel axle and a rear wheel axle, wherein at least the rear wheel axle is resiliently suspended by means of an axle suspension system. The trailer comprises at least one wheel axle and is coupled to the tractor via a fifth wheel (see for example Figure 10). The arrangement comprises a calculating unit 2 (see Figure 2) adapted to receive the values related to the acceleration a\ in the longitudinal direction of the vehicle, and to the axle load N₂ with regard to the rear wheel axle of the tractor.

The method comprises the steps for

- determining the associated values for the axle load N₂ for the rear axle of the tractor and the acceleration a; of the vehicle, for a number of different acceleration values,

- determining a parameter j related to a relation between said associated values for the axle load N₂ and the acceleration ¾,

- estimating the height of the center of gravity HCG for the trailer via calculations performed in accordance with a predetermined algorithm (equation 3.31) in which said parameter j, acceleration a; and the axle load N₂ are included.

The axle load is preferably determined based on output signals from the wheel axle suspension system for the rear wheel axle of the tractor. According to one embodiment, the wheel axle suspension system consists of a pneumatic suspension.

The parameter j consists of the direction of a line calculated, by the calculating unit 2, via linear regression of the said associated values for N₂ and aj.

For the calculations to be reliable, the acceleration ¾ must be constant over at least a predetermined time in order for the value of j to be included in the calculations. This predetermined time during which the acceleration must be essentially constant is on the order of, e.g., 5 seconds. The acceleration is allowed to vary by a maximum of only, e.g., ±10% during this time.

The gathering of the associated values for N₂ and ¾ preferably occurs continuously, and the more values gathered, the greater the certainty with which j can be determined; for example, at least 10 associated values are needed to calculate j.

According to one embodiment, the estimation of the height of the center of gravity HCG, i.e. y₃, occurs continuously. This can, for example, be initiated when the sensors used to determine the axle load indicate that the vehicle is being loaded or unloaded, which will entail a change in the height of the center of gravity.

The predetermined algorithm thus consists of the following equation (3.31):

The invention also comprises an arrangement for implementing the method. The arrangement comprises a calculating unit 2, which is depicted schematically in Figure 2. The input signals consist of the axle load N₂ for the rear axle of the tractor and the acceleration a,. The calculating unit also utilizes already known parameters, which are indicated in the figure by means of a block arrow. These known parameters comprise, for example, the vehicle-related dimensions i , x₃ and x₅ (see Figures 4 and 5) and the tractor weight m_d.

We refer otherwise to the foregoing review of the method, in which the arrangement is also described.

The present invention is not limited to the foregoing preferred embodiments. Various alternatives, modifications and equivalents may be used. The embodiments above must consequently not be viewed as limiting the protective scope of the invention, which is defined by the accompanying claims.

Claims

1. A method in connection with an arrangement for a vehicle, comprising a trailer coupled to a tractor, for estimating the height of the center of gravity HCG for the trailer, wherein the tractor comprises a front wheel axle and a rear wheel axle, wherein at least the rear wheel axle is resiliently suspended by a wheel axle suspension system and the trailer comprises at least one wheel axle and is coupled to the tractor via a fifth wheel, and wherein the arrangement comprises a calculating unit adapted to receive the values related to the acceleration a_{ in the longitudinal direction of the vehicle and to the axle load N₂ pertaining to the rear wheel axle of the tractor, characterized in that the method comprises the steps for

- determining the associated values for the axle load N₂ for the rear axle of the tractor and the acceleration a, of the vehicle, for a number of different acceleration values,

- determining a parameter j related to a relation between the said determined associated values for the axle load N₂ and the acceleration a„

- estimating the height of the center of gravity HCG for the trailer via calculations performed in accordance with a predetermined algorithm in which said parameter j is included.

2. The method according to claim 1, wherein the axle load N₂ is determined based on output signals from the wheel axle suspension system for the rear wheel axle of the tractor.

3. The method according to claim 1 or 2, wherein said wheel axle suspension system consists of pneumatic suspension.

4. The method according to any of claims 1-3, wherein said parameter j consists of the direction of a line calculated by linear regression of the said associated values for N₂ and a;.

5. The method according to any of claims 1-4, wherein the acceleration a; must be essentially constant for at least a predetermined time in order for the value to be included in the calculations of j.

6. The method according to any of claims 1 -5, wherein the number of associated values for N₂ and ¾ that is needed to calculate j must exceed 10.

7. The method according to any of claims 1-6, wherein the estimation of the height of the center of gravity HCG occurs continuously.

8. The method according to any of claims 1-7, wherein said predetermined algorithm consists of the following equation (3.31):

9. An arrangement for a vehicle, comprising a trailer coupled to a tractor, wherein said arrangement is adapted to estimate the height of the center of gravity HCG for the trailer, and wherein the tractor comprises a front wheel axle and a rear wheel axle, wherein at least the rear wheel axle is resiliently suspended by a wheel axle suspension system and the trailer comprises at least one wheel axle and is coupled to the tractor via a fifth wheel, and wherein the arrangement comprises a calculating unit (2) adapted to receive the values related to the acceleration a; in the longitudinal direction of the vehicle and to the axle load N₂ pertaining to the rear wheel axle of the tractor, characterized in that the calculating unit (2) is adapted to

- determine the associated values for the axle load N₂ for the rear axle of the tractor and the acceleration ¾ of the vehicle, for a number of different acceleration values,

- determine a parameter j related to a relation between the said determined associated values for the axle load N₂ and the acceleration aj,

- estimate the height of the center of gravity HCG for the trailer via calculations performed in accordance with a predetermined algorithm in which said parameter j is included.

10. The arrangement according to claim 9, wherein the axle load is determined based on output signals from the wheel axle suspension system for the rear axle of the tractor.

1 1. The arrangement according to claim 9 or 10, wherein said wheel axle suspension system consists of pneumatic suspension.

12. The arrangement according to any of claims 9-11, wherein said parameter j consists of the direction of a line calculated by linear regression for the said associated values for N₂ and

13. The arrangement according to any of claims 9-12, wherein the acceleration ¾ must be essentially constant for at least a predetermined time in order for the value to be included in the calculation of j.

14. The arrangement according to any of claims 9-13, wherein the number of associated values for N₂ and a; that is needed to calculate j must exceed 10.

15. The arrangement according to any of claims 8-14, wherein the estimation of the height of the center of gravity HCG occurs continuously.