DE102008046259A1 - Driving stability determining method for use during braking of e.g. passenger car, involves determining position of center of gravity of vehicle and side coefficients of wheels, and determining value for driving stability of vehicle - Google Patents

Abstract

The method involves determining a position of center of gravity of a vehicle. Side force coefficients of wheels of the vehicle are determined using tangential force of the wheels, slip of the wheels and wheel-specific constants. A value for driving stability of the vehicle is determined from the speed of the vehicle, the determined position of center of gravity of the vehicle, the determined side force coefficients of wheels, a vehicle mass and a vehicle moment of inertia around a vehicle vertical axis. An independent claim is also included for a driving stability determining device comprising two processing units.

Description

The The present invention relates to a method and an apparatus for determining a driving stability a vehicle when braking and a device and a method for adjusting a brake pressure for a vehicle.

The main criteria when braking vehicles, such. B. passenger cars or truck, are the braking distance, the steerability and the Stability. Steerability and stability comes here because of the higher Safety a greater importance to. If a vehicle loses its stability, it is practical for a normal driver not possible, to recapture a rotational movement of the vehicle.

brake systems Today's vehicles are mostly with automatic anti-lock brakes (ABV), so-called anti-lock braking systems (ABS) equipped. The ABS acts on the braking of the vehicle, the tendency of the wheels to lock Control of the brake pressure against the side guide of the Wheels too guarantee and in most cases also to achieve a short braking distance.

The steerability of the vehicle is usually due to the blockage avoidance of steerable wheels, in General of the front wheels, ensured. The prevention of the blocking of rear wheels sets in Generally a necessary but not sufficient condition a driving stability dar. Especially at higher Speeds can make the vehicle uncontrollable rotations To run, although the rear wheels do not block. About that In addition, due to the concept some vehicles, such as vehicles with a higher one Focus, in certain braking maneuvers, for example, from high Speeds in a curve or on a one-sided smooth Roadway, difficult to stabilize. The reason is unfavorable Radlastverlagerung between the wheels during the braking process. A Such displacement affects the lateral guidance of the wheels and results in certain conditions to instability of the vehicle.

task The present invention is therefore the driving stability of a To ensure vehicle braking to ensure a stable braking process.

According to the invention this Task by a method for determining a driving stability of a vehicle when braking according to claim 1, a method for adjusting a Brake pressure for a vehicle according to claim 11, an apparatus for determining a driving stability of a vehicle when braking according to claim 16 and a device for adjusting a brake pressure for a vehicle according to claim 18 solved. The dependent ones claims define preferred and advantageous embodiments of the invention.

in the Within the scope of the present invention, a method for determining a driving stability of a vehicle when braking provided. The method comprises determining a speed of the vehicle, for example with the help of a detection of speeds of wheels of the Vehicle, determining a center of gravity of the vehicle and determining lateral force coefficients of wheels of the vehicle. From the Speed of the vehicle, the center of gravity of the vehicle, the lateral force coefficients of the wheels of the vehicle and a vehicle mass and a vehicle moment of inertia a vehicle's vertical axis then becomes the driving stability of the vehicle certainly.

The Center of gravity of the vehicle, for example, a distance a center of gravity of the vehicle from the front axle and a distance the center of gravity of the vehicle from the rear axle. The Side force coefficients can for each single wheel of the vehicle, d. H. the front left wheel, the front wheel right, the wheel at the left rear and the wheel at the rear right, individually be determined. The for the driving stability value determined by the vehicle can have a range of values, which indicates a stable driving condition of the vehicle, and a have another range of values, which is an unstable driving condition of the vehicle. For example, a negative value for the driving stability of the vehicle indicate a stable driving condition of the vehicle and a positive value an unstable driving condition of the vehicle Show.

According to one embodiment is the lateral force coefficient for a wheel of the vehicle by determining a peripheral force of the wheel, Determining a slip of the wheel, for example from the angular velocity of the wheel and the vehicle speed, and determining the lateral force coefficient of the wheel from the circumferential force, the slip and a wheel-specific Constant determined.

According to a further embodiment, the peripheral force of the wheel is determined by a Brake pressure of a wheel brake cylinder of a brake of the wheel is detected, an angular acceleration of the wheel is determined and the circumferential force of the brake pressure, the angular acceleration and vehicle-specific variables is determined. The vehicle-specific variables may include a piston area of the wheel brake cylinder, an average friction radius of a brake pad of the brake, a brake characteristic of the brake, an inertia of the wheel and all the masses connected thereto, and a dynamic tire diameter.

Furthermore can additionally determine a drag torque of the Motors, which acts on the wheel, captured and in the determination the peripheral force become.

According to one embodiment can be the center of gravity of the vehicle, for example, the distance the center of gravity of the vehicle from the front axle and the distance the center of gravity of the vehicle from the rear axle, from the peripheral forces of the Wheels and the wheelbase of the vehicle.

With Help of the method described above can be a value for the driving stability of the vehicle reliable be determined from measured values and vehicle-specific sizes. The measured values are already available for many modern vehicles anyway or can be detected in a simple manner with suitable sensors.

According to the present The invention further provides a method for adjusting a brake pressure for a Vehicle provided. The method includes determining Slip angles the wheels of the vehicle and determining a value for driving stability of the vehicle when braking. The brake pressure on the wheels of the vehicle then becomes dependent on the determined slip angle and the certain driving stability set such that a predetermined slip angle is not exceeded is and that a predetermined range of values for the driving stability met becomes. The driving stability can be determined as previously described. The predetermined range of values for the Driving stability, in which a vehicle condition is considered stable, for example range from -∞ to -0.5.

With Help of the method according to the invention to adjust the brake pressure, the driving stability when braking ensured and thus prevents the vehicle from breaking out.

According to one embodiment of the method, a yaw rate of the vehicle is detected, and from it and from other sizes Slip angle of a wheel of the vehicle. The other sizes can the Speed of the vehicle, the lateral force coefficients of the wheels of the Vehicle, the circumferential forces the wheels of the vehicle, the center of gravity of the vehicle and the vehicle mass and the vehicle inertia to include a vehicle vertical axis.

As previously described the slip angle with the help of the front axle and the rear axle of the vehicle easy-to-grasp sizes of the Vehicle to be determined. The predetermined slip angle, which in the Setting the brake pressure of the vehicle should not be exceeded, may be, for example, a maximum slip angle of 6 °. To to such a slip angle is a stabilization of the vehicle by a steering intervention of the Driver in a simple way possible, allowing stabilization of the vehicle when braking on, for example, very different grippy surfaces on the right and left wheels of the vehicle allows becomes.

According to the present The invention further relates to a device for determining a driving stability of a Vehicle provided during braking. The device comprises a Processing unit which coupled with sensors of the vehicle is. The sensors provide measured values for an angular velocity of a each wheel of the vehicle and a brake pressure on each wheel of the vehicle Vehicle ready. The processing unit is configured, a Speed of the vehicle from, for example, the angular velocity the wheels, a value for the driving stability of the vehicle from the speed of the vehicle, the angular velocities the wheels of the vehicle, the brake pressures on each wheel of the vehicle and vehicle-specific information to determine. The value for the driving stability may be from the processing unit, as previously related to the method for determining a driving stability of a vehicle when braking be determined.

Finally, in accordance with the present invention, an apparatus for adjusting a brake pressure for a vehicle is provided. The device comprises a processing unit which is coupled to sensors and an actuator of the vehicle. The sensors provide measured values of an angular velocity of each wheel of the vehicle, a yaw rate of the vehicle, and a brake pressure for each wheel of the vehicle. The actuator is used to set a brake pressure for the vehicle determined by the processing unit. The processing unit is configured such that it determines slip angles of the wheels of the vehicle and a value for driving stability of the vehicle during braking from the measured values of the sensors and further vehicle-specific information. Depending on the particular slip angle and the particular driving stability, the brake pressure at the wheels is then adjusted such that a predetermined slip angle is not exceeded at any of the wheels and that a predetermined value range for driving stability is maintained. To determine the driving stability, for example, the device described above for determining a driving stability of a vehicle during braking can be used. The brake pressure adjusting device may determine the slip angles of the wheels and the running stability of the vehicle, for example, as described in connection with the method for adjusting a brake pressure for a vehicle and adjust the brake pressure for the vehicle accordingly.

The The present invention will be described below with reference to FIGS Drawings explained with reference to preferred embodiments.

1 shows a schematic block diagram of a device for adjusting a brake pressure for a vehicle according to an embodiment of the present invention.

2 shows a schematic representation of a view of a vehicle from above with forces and moments acting on the vehicle.

3 shows a schematic representation of a vehicle with forces acting on the vehicle to determine the wheel loads.

4 shows a diagram showing the wheel loads of the wheels of a vehicle over time when braking.

5 Figure 11 is a graph showing the lateral force coefficients of the wheels of a vehicle over time during braking.

6 shows in four diagrams for each wheel of the vehicle respectively simulated lateral forces and according to one embodiment, certain lateral forces over time in a braking operation.

7 represents a relevant for the driving stability size according to the present invention during a braking operation over time.

8th represents a characteristic quantity according to the present invention for a stability of the vehicle during a braking operation over time.

9 Figure 12 illustrates further characteristic quantities according to the present invention for the driving stability during a braking operation over time.

10 FIG. 12 illustrates a schematic top view of a vehicle with forces acting on the vehicle with the right wheels of the vehicle on a ground having a different coefficient of friction than the ground on which the left wheels of the vehicle are located. FIG.

11 FIG. 12 is a graph showing the progress of a value characteristic of the running stability of the vehicle according to the present invention during a braking operation over time. FIG.

12 FIG. 10 is a diagram illustrating the braking pressures on four wheels of a vehicle over time during a braking operation regulated in accordance with the present invention. FIG.

13 shows a slip angle of the rear wheels during a braking operation over time.

14 shows a course of a steering wheel angle during a braking operation over time.

1 shows a device 1 for adjusting a brake pressure for a vehicle. The device 1 includes a device 2 for determining a running stability of a vehicle during braking and a processing unit 3 , The device 2 for determining the driving stability comprises a processing unit 5 , which with sensors 4 of the vehicle is coupled. With the help of the sensors 4 become the processing unit 5 Angular velocities ν _VL , ν _VL , ν _HL , ν _HR for a front left wheel, a front right wheel, a rear left wheel and a rear right wheel of the vehicle and brake pressures p _B, V L, p _{B, VR} , p _{B, HL} , p _{B, HR} for the front left wheel, the front right wheel, the rear left wheel, and the rear right wheel of the vehicle. The processing unit 5 determined from those of the sensors 4 provided values and other vehicle-specific information, a speed of the vehicle and Seitenkraftbeiwerte c _{α, VL} , c _{α, VR} , c _{α, HL} , c _{α, HR} for the front left wheel, the front right wheel, the rear left wheel and the rear right Rad. Another processing unit 6 the device 2 for determining the driving stability, from the lateral force coefficients, a stability value θ and slip angles α _VL , α _VR , α _HL , α _HR for the front left wheel, the rear left wheel, the front right wheel, and the rear right wheel of the vehicle are determined. A detailed description of how to determine the driving stability and the slip angles from the measured values of the sensors will be described later. The processing units 5 and 6 Of course, it can also be realized as a processing unit.

The slip angles and the value for the driving stability are determined by the device 2 to the processing unit 3 the device 1 transmitted to adjust the brake pressure. In the processing unit 3 the slip angles are compared with a maximum allowable slip angle and a brake pressure 7 that of the processing unit 3 to a braking system 8th of the vehicle is set depending on the determined slip angle. For example, the brake pressure 7 with the help of a regulator 9 the processing unit 3 be reduced as soon as one of the slip angle exceeds a predetermined maximum slip angle, for example, 6 °. In addition, with the help of the regulator 9 and that of the device 2 certain value χ the driving stability of the brake pressure 7 set so that a current value of driving stability χ _is smaller than a predetermined value χ _soll is. The predetermined maximum value for the driving stability χ _should be, for example, -0.5 or another vehicle-specific size.

The to the brake system 8th the vehicle output brake pressure 7 For example, can set a brake pressure in the master cylinder of the vehicle. The brake system 8th The vehicle may further comprise an anti-lock device, a so-called anti-lock braking system (ABS). With the help of the anti-lock brake the brake pressures at the individual wheels are then further reduced upon detection of a wheel lock.

With reference to the 2 - 9 Below is the operation of the device 2 for determining the driving stability of the vehicle will be described in more detail. After that, referring to the 10 - 14 the operation of the device 1 for setting the brake pressure for the vehicle will be described in more detail.

in the Following are a condition of driving stability of a vehicle when braking and their determination in real driving described. To one to ensure stable braking must have this stability condition always fulfilled become.

Equations of motion of motor vehicles when braking

First, referring to 2 considered a minimum two-lane overall vehicle model to determine overall vehicle behavior during braking.

With ψ the yaw angle of the vehicle relative to a fixed coordinate system x ₀ , y ₀ is called. An angle β between a vehicle longitudinal axis 10 and a direction of travel speed ν at the vehicle's center of gravity 11 is called slip angle β. An angle ψ + β between a parallel to the x ₀ axis and the vehicle speed direction is called the course angle. Accordingly, the vector of velocity ν rotates at an angular velocity ψ. + β. in the spatially fixed coordinate system x ₀ , y ₀ . An acceleration of the vehicle's center of gravity 11 in the spatially fixed coordinate system, ie the derivation of the velocity vector of the vehicle's center of gravity 11 in the spatially fixed coordinate system, is thus composed of a so-called centripetal acceleration ν (ψ. + β.) and a relative acceleration ν. together. These accelerations are in 2 located.

Angle α _VL , α _VR , α _HL , α _HR between Radmittelebenen and the respective speed directions of the wheels 12 - 15 are called slip angle. Because of the kinematic constraints let It is characterized by the slip angle β and the yaw rate ψ. express by equations (1) to (4):

It is assumed that the wheels 12 . 13 a steerable axle (in this case, the front axle) with a same steering angle δ _{V are taken in} parallel.

As a rule, half-track widths b _V and b _{H are} small compared to a course radius ρ = ν / (ψ. + Β.), Ie, b _V << ρ ≈ ν / ψ. and b _H << ρ ≈ ν / ψ., ie b _V ψ. << ν, b _H ψ. << ν. The terms b _V ψ. and b _H ψ. in equations (1) to (4) can thus be neglected. The slip angles at the wheels of an axle are practically the same in this case and can thus be determined from equations (5) and (6):

Since the angles δ _V - α _V , α _H, and β are small during normal driving, linearization of equations (5) and (6) is allowed. Thus, equations (7) and (8) result:

During a general braking operation, the vehicle acts in addition to the braking forces (circumferential forces) F U VL , F U VR , F U HL and F U MR still the lateral forces F S VL , F S VR , F S HL and F S MR , These forces are also in 2 located. The air forces are neglected here.

With the mass of the vehicle m and a moment of inertia about the vehicle vertical _axis J _Z are set up kinetic equations for the vehicle model:
The momentum balance (force equilibrium) in the vehicle longitudinal direction yields equation (9): mν (ψ. + β.) sinβ - mν .cosβ - (F U HL + F U MR ) - (f U VL + F U VR ) cosδ V - (f S VL + F S VR ) sinδ V = 0, (9)

From the set of impulses (equilibrium of forces) in the vehicle transverse direction, equation (10) results: mν (ψ. + β.) cosβ - mν.sinβ - (F S HL + F S MR ) - (f S VL + F S VR ) cosδ V - (f U VL + F U VR ) sinδ V = 0, (10)

From the spin set (moment equilibrium) around the vehicle vertical axis results equation (11) J Z ψ .. - l V (F S VL + F S VR ) cosδ V + l V (F U VL + F U VR ) sinδ V + l H (F S HL + F S MR ) + b V (F U VR cosδ V - F U VL cosδ V + F S VR sinδ V - F S VL sinδ V ) + b H (F U MR - F U HL ) = 0. (11)

Since the angle quantities are small during a normal braking operation, the equations (9) to (11) are simplified without much deviation from equations (12) to (14): mν. + (F U HL + F U MR ) + (F U VL + F U VR ) = 0, (12) mν (ψ. + β.) + mν .β - (F S HL + F S MR ) - (f S VL + F S VR ) + (F U VL + F U VR ) δ V = 0, (13) J Z ψ .. - l V (F S VL + F S VR ) + l V (F U VL + F U VR ) δ V + l H (F S HL + F S MR ) + b V (F U VR - F U VL ) + b H (F U MR - F U HL ) = 0. (14)

Equations (13) and (14) are relevant to driving stability and are considered in more detail. The lateral forces F S VL , F S VR , F S HL , F S MR can be expressed with the _{slip angles} α _V , α _H and the lateral force _{coefficients of} the wheels c _αVL , c _αVR , c _αHL , c _αHR in the following linearized forms as equations (15) to (18): F S VL = c αVL α V , (15) F S VR = c αVR α V , (16) F S HL = c αHL α H , (17) F S MR = c αHR α H , (18)

If these relationships and equations (7) and (8) are used in equations (13) and (14), equations (19) and (20) are obtained:

Here, C _αV = C _αVL + C _αVR and C _αH = C _αHL + C _{αHR are} the lateral force _{coefficients of} all wheels of the front and rear axles. Equations (19) and (20) thus essentially correspond to a one-track model with the addition of an additional yaw moment, which will arise with asymmetric braking forces.

oder in Matrixschreibweise die Gleichung (23): ẋ = Ax + bδV + υ (23) mit dem Zustandsvektor

der Systemmatrix

der Eingangsmatrix

und dem Vektor der Störgrößen

A corresponding state space representation of equations (19) and (20) yields equations (21) and (22):

or in matrix notation the equation (23): ẋ = Ax + bδ V + υ (23) with the state vector

the system matrix

the input matrix

and the vector of the disturbances

you recognizes that this is a linear time-varying system acts as the velocity ν in the system and input matrix while a braking process constantly changes. Accordingly the characteristics of the system are also above the driving speed mutable. However, in the following investigations, the speed becomes first for simplicity "frozen". This is also allowed because the longitudinal dynamics the vehicle according to equation (12) during a normal braking operation practically can be considered decoupled from the lateral dynamics. Become such quasi-stationary Transfer studies to other speeds, you get one Overall picture of the system properties, such. As the controllability and stability.

Controllability of motor vehicles brakes

The controllability matrix of the system according to equation (23) is:

Since the lateral force _coefficient c _αV usually much higher than the braking forces F U VL + F U VR the latter can be neglected. The controllability matrix is thus reduced to equation (24):

The system is controllable if and only if the matrix Q is regular, that is, equation (25) is satisfied

Since in a car approximately J _Z ≈ ml _V l _H holds, the term in brackets J Z (l V + l H ) c αH - ml V l H (l V + l H ) c αH + m 2 l 2 V ν 2 usually a positive value. The necessary condition for the controllability of the vehicle is thus: c _αV # 0, ie the lateral force _{coefficient of} the front axle must have a nonzero value (in practice a sufficiently large value because of the simplification assumptions made above). For this reason, the steering front wheels should not block when braking.

Stability condition of motor vehicles when braking

The ABS system prevents the wheels from locking. Thus, the controllability of the vehicle is ensured. Theoretically, steering can compensate for the disturbances on the vehicle and even correct the skidding of the stern. The driver acts in this case as a state controller of the form of equation (26). δ V = Rx. (26)

there R is a 1 × 2 feedback matrix.

If equation (26) is used in (23), the differential equation of the state control (equation of state of the closed-loop system) according to equation (27) results: ẋ = (A + bR) x + υ. (27)

The System matrix used for the system properties prevail is changed by the return. The is called, By a suitable choice of the feedback matrix, one can actually become unstable Stabilize vehicle. A trained Driver can do that most of the time, a normal driver (and that's the most) however, it can be common Not.

investigations have shown that a normal driver in a skid mostly not correct and fast enough. It also has to always be expected that the driver only after a period of time, which corresponds approximately to its reaction time, corrective action can. For these reasons will at the following stability study the native behavior of the vehicle, without driver intervention, closer look. This is done by the homogeneous state differential equation ẋ = Ax expressed according to equation (28).

The solution of this equation (28) for z. For example, the yaw rate describes Equation (29):

The coefficients ζ ₁ , ζ _{2 are} determined by initial conditions of the state variables β (t = 0) and ψ. (T = 0). λ ₁ , λ ₂ are the eigenvalues of the system matrix A, ie the solutions of the characteristic equation of the system according to equations (30) to (32): det (λI-A) = λ 2 + 2σλ + ω 2 = 0 (30) With

It follows immediately equation (33)

From the solution of the homogeneous equation (29) it can be seen that the stability requirement is satisfied if the real parts of the eigenvalues λ ₁ and λ _{2 are} negative, ie equation (34) is satisfied: Re (λ 1.2 ) <0. (34)

Exactly then namely the system aims for a disruption always against a stationary Status. Otherwise, no equilibrium position (steady state) reached.

The eigenvalues are not only decisive for the stability but also largely influence the time behavior of the system. The more "negative" Re (λ _1,2 ) is, the faster a transition process will sound. As a driver, you immediately notice how easily the vehicle can be controlled.

For real vehicles, σ is almost always a positive quantity. On the other hand, ω ² can take both a positive and a negative value and therefore represents a characteristic variable for the stability.

For the case ω ² > 0, Re (λ _1,2 ) <0 always applies, so the vehicle is stable. If σ ² - ω ² > 0, λ ₁ and λ _{2 are} negatively real. One has in this case a monotonous time process. At σ ² - ω ² <0, λ ₁ and λ _{2 are} conjugate complex. Such a conjugate complex eigenvalue pair includes a decaying vibrational process.

For the case ω ² <0, one of the eigenvalues becomes positive. As a result, the stability condition (34) is no longer satisfied. This situation can occur if the term l _H c _αH - l _V c _{αV falls below} a certain negative value (in this case, the vehicle is overdriven because of 1 _H c _αH - 1 _V c _αV <0). The term mn. (l 2 V c αV + l 2 H c αH ) Although the braking takes a comparatively small negative value, but leads to further aggravation of the situation.

Since the term l _H c _αH - L _V c _{αV is multiplied} by ν ² , instability at higher speeds can already be caused by braking, because of the load on the front axle and the relief of the rear axle in the braking maneuver increases the Seitenkraftbeiwert the front axle and the lateral force coefficient of the rear axle. If a lateral acceleration also acts on the vehicle, the wheel loads will shift between left and right.

Wheel load change of motor vehicles when braking

The following are with reference to 3 Wheel load changes during braking and their influence on the stability of the vehicle with the help of a simple model considered qualitatively. The vehicle of the 3 includes a rear axle 16 , a front axle 17 and wheels 12 - 15 ,

To 3 let the wheel loads F Z VL , F Z VR , F Z HL , F Z MR expressing longitudinal and lateral acceleration in the first food by equations (35) to (38):

It is assumed simplifying that the gauges of the front and rear axles are identical, namely b _V = b _H = b. With ε the differences of the Aufbaufeder- and the stabilizer hardness between the front and the rear axle are considered. By adjusting the Aufbaufeder- and the stabilizer hardness, the lateral Radlastverlagerung can be distributed due to the lateral acceleration targeted to the front and rear axles.

It can be seen from equations (35) to (38) that the wheel loads are significantly influenced by the center of gravity position L _V / II _H / l, h / l and h / 2b. This is primarily due to the vehicle concept and changes after load level. A higher ratio of the center of gravity height to the wheelbase h / l requires a greater wheel load displacement from rear to front wheels during braking. In the presence of a lateral acceleration, a higher ratio of the center of gravity height to the track h / 2b leads to a larger wheel load shift between the left 12 . 15 and right wheels 13 . 14 , On a one-sided slippery road surface (μ-split), such a shift will strongly influence the lateral force coefficients of the axles. Too much relief of the wheels on the grippier side can z. B. lead to the loss of lateral guidance of the axes.

Next the wheel load and the coefficient of friction depend on the lateral force coefficients still from the circumferential slip of the wheels from. The tire properties are considered in more detail below.

Tire properties and determination the lateral force coefficients

to The tire characteristics will be described by the HSRI tire model used, because this based on vehicle technology fundamentals Give an insight into the relationships and dependencies between the individual Sizes (forces, slip angles, Circumferential slippage, etc.).

The calculation is based on the deformations of the tire tread particles and the resulting shear stresses in the laces. Whether the profile particles in the landslide already partially reach the adhesion limit is determined by an auxiliary size S characterized according to equation (39).

S denotes the circumferential slip, α the slip angle and μ the friction coefficient of a wheel. Further is c 0 s the zero point tangent of the circumferential force-circumferential slip curve at slip angle α = 0. Analogous c 0 α the zero point tangent of the lateral force skew angle curve with circumferential slippage S = 0. The sizes c 0 s and c 0 α depend primarily on the wheel load according to equations (40) and (41):

In the case of S ≤ 0.5, all profile particles in the landslide are still in the adhesion area, so the adhesion limit is not yet reached. The forces result from the integration of the voltages across the Laces and can be expressed in the following way:
A circumferential force is described by Equation (42) F U = c 0 s S, (42)

A lateral force is described by Equation (43) F S = c 0 α tanα. (43)

In the case of S> 0.5, the profile particles slide partially or even completely in the laces. By integrating the stresses in the adhesion and sliding area over the Laces, the forces are as follows:
The circumferential force is given by equation (44).

The Lateral force results in equation (45).

folglichIt should be noted that equations (42) and (43) or (44) and (45) show a simple relationship between the circumferential and lateral forces according to equations (46) and (47):

consequently

This relationship states that the lateral force coefficient c _α can be determined during braking by the circumferential force F ^U and the corresponding circumferential slip S. According to equations (40) and (41), the coefficient depends c 0 α / c 0 s from the wheel load according to equation (48):

und ist in der Regel eine gute Nahrung, weil in diesem Fall κ_α1 für den Zähler der Gleichung (48) maßgebend ist. Somit wird der Aufwand zur Radlastschätzung erspart. Gleichung (47) zur Berechnung des Seitenkraftbeiwerts kann dann durch Gleichung (50) ausgedrückt werden:

If the wheel load F ^{Z is} not very strong from its face value F Z nominal deviates, equation (49) applies

and is usually a good food, because in this case κ _α1 is decisive for the numerator of equation (48). Thus, the effort for wheel load estimation is spared. Equation (47) for calculating the lateral force coefficient can then be expressed by equation (50):

Of the Coefficient κ must be determined in advance by measurements.

The circumferential force (braking force in this case) F ^U is not measured directly in the real vehicle and must be calculated via the brake pressure according to equation (51):

Here, p _{B is} the brake pressure, A the piston surface of the wheel brake cylinder, r the mean friction radius of the brake pad on the brake disc and C _B the brake characteristic. With ω. becomes the angular acceleration of the wheel. Further, J _{Rad is} the moment of inertia of the wheel and all associated rotational masses, R _dyn the dynamic tire radius.

If not disengaged during braking, the required brake pressure of a drive wheel because of the acting thereon motor drag torque M _motor at the same slip is smaller. The higher the vehicle speed and the lower the engaged gear, the stronger the effect of the engine braking torque.

Of the above presented approach for calculating the lateral force coefficient considered Reibbeiwert- and wheel load changes automatic and also works with combined maneuvers, eg. B. with the simultaneous occurrence of the circumferential slip and the slip angle. However, it is sensitive to very small circumferential slip values. This restriction but is for the real use not serious, since the braking stability only at larger circumferential slip values becomes a topic.

Determination of the stability condition in real driving

With the approach presented above, lateral force coefficients of the wheels during braking can be determined. Based on this, the quantity ω ² characteristic of the stability or the eigenvalues of the system λ _1,2 can be calculated. The following is a concrete example. This is the straight braking of a vehicle on a one-sided smooth road (ice on the left side and concrete on the right side) with an initial speed of 85 km / h. The vehicle has a high center of gravity and is equipped with an unmatched ABS. A human driver must try to drive the vehicle straight ahead.

The Vehicle behaves while This braking process is restless and difficult to get from the driver dominate. This maneuver becomes in the computer with the help of a multi-body total vehicle model reconstructed, so metrologically elaborate variables such as wheel loads, slip angle and lateral forces for further Investigations or for the validation of the presented method for the determination of the driving stability accessible be made.

In 4 the wheel loads reconstructed by simulation are shown. The graph 18 shows the wheel load on the left front wheel, the graph 19 the wheel load on the right front wheel, the graph 20 the wheel load on the left rear wheel and the graph 21 the wheel load on the right rear wheel.

It can be seen clearly from this figure that the deceleration leads to wheel load shifting from the rear to the front axle, while the lateral acceleration caused by the yawing leads to wheel load shifting between the left and right wheels. The Radlastverlagerungen are pronounced in this case because of the high center of gravity of the vehicle. The rear wheel is particularly relieved on the grippier side of the road when the unequal braking forces turn the vehicle to this side and the driver does not initiate a corresponding correction by means of steering (eg by the second or the fourth second in FIG 4 ).

In this case, it is also to be expected that the rear axle loses much of its cornering ability. In fact, this can be seen from the lateral force coefficients calculated using the method described above. 5 shows the calculated lateral force coefficients for the individual wheels of the vehicle. graph 22 shows the lateral force coefficient of the left front wheel, graph 23 the lateral force coefficient of the right front wheel, graph 24 the lateral force coefficient of the left rear wheel and graph 25 the lateral force coefficient of the right rear wheel.

To validate the calculated lateral force coefficients, they are multiplied by the wheel slip angles reconstructed by simulation. 6 shows the reconstructed lateral forces for each wheel 26 . 28 . 30 . 32 and the lateral forces calculated according to the above method 27 . 29 . 31 . 33 , 6 shows that the calculated lateral forces are in good agreement with the reconstructed lateral forces.

According to equations (31), (32) and (33), the quantities σ and ω ² and the eigenvalues (poles) λ _{1,2 are} calculated. The results are in 7 . 8th and 9 shown.

While the quantity σ always remains positive in this braking operation, the quantity ω ² becomes smaller by the second second 8th partially negative. Accordingly, the first eigenvalue (see 9 ) in this case a positive real part, which indicates instability of the vehicle. Due to the unexpected drivability change, the driver has difficulty capturing the turning of the vehicle. A common consequence of this is The overriding on the part of the driver, which partially amplifies the problem.

In 5 The constellation of lateral force coefficients did not improve after the fourth second. Consequently, the vehicle remains oversteering, ie, L _H c _{α H} <1 _V c _αV . To 8th Nevertheless, the vehicle has a stable behavior, since the driving speed in this case is not so high and an oversteering vehicle is unstable even at a certain speed. It follows that the braking forces can be increased accordingly with decreasing driving speed in order to achieve the shortest possible braking distance.

As described above, a method for determining a stability condition in braking has been derived. Here, ω ^{2 represents} a characteristic quantity and correlates well with the subjective perception of the driver of the controllability of the vehicle.

Furthermore the method is suitable for determining the stability condition to allow braking different types, z. B. Straight brakes on homogeneous and heterogeneous road surfaces, braking in the curve etc.

It should be noted that the variables I _V , I _H , M, J _Z required in this case also depend on the loading state and are therefore variable. The variation of these quantities has a negative effect on the accuracy of the determination. With a certain amount of effort, these quantities can also be calculated. You can z. B. the vehicle so easily brakes straight that caused by the delay wheel load displacement remains negligible. If the rotational speeds of the front and rear wheels are regulated in the same way, ie if the circumferential slip values of the wheels are the same, the ratio is set F U V / F U H According to equations (35), (36), (37), (38) is a good estimate of the ratio l _V / l _H. Since the wheelbase l _V + l _{H is} constant, l _V and l _H can be calculated.

On the other hand, the ranges of variation of the quantities I _V , I _H , M and J _{Z are} generally not significantly large. The resulting inaccuracies or deviations in the specific values of ω ² or Re (λ _1,2 ) will thus practically not prevent the use of the stability condition.

With Usage is here meant not only to determine the stability condition, but also used in the control of brake pressures targeted how will be described below. The goal is the liability of Wheels on the roadway at fulfillment the stability condition optimally exploit.

Method for setting a Brake pressure for a vehicle

At the Change brakes the vehicle parameters, which are decisive for the driving behavior. With too much change this parameter can be an undesirable Driving behavior, in the extreme case even instability occur. A normal driver is usually surprised and overwhelmed in such situations. Around to avoid this certain conditions are met during braking. The fulfillment of these conditions Can be achieved by a targeted regulation of the brake pressures. The goal The regulation is in addition to the controllability of the vehicle also a preferably short braking distance. The following are the conditions to be met and the corresponding control strategies are presented.

Stability condition of the whole vehicle

The stability of vehicles when braking was previously based on the differential equations (23).

The stability of the vehicle is decisively determined by the eigenvalues of the system matrix A from equations (52) to (54):

In order to ensure the stability of the vehicle, the real part of the first eigenvalue should assume a negative value (the real part of the second eigenvalue is always negative), namely Re (λ 1 ) <0 (55) or in other words ω 2 > 0. (56)

With the method described above for determining the stability of a vehicle, the variables ω ² or λ ₁ can be determined in real driving operation. Therefore, condition (55) or (56) is included in the control of brake pressures. If the braking pressures are controlled so that the condition (55) or (56) is always maintained, the vehicle remains theoretically stable. However, one must still make sure that a stable vehicle for the driver is not necessarily easy to control.

At the Braking (eg on heterogeneous road, in the curve or under other disorders) is often one Correction required by steering, otherwise the vehicle will be fast leaving the right lane. An average driver is mostly only with the driving behavior in normal driving situations familiar. Too strong a change Driving behavior during braking might surprise the driver and possibly lead to a wrong driver reaction. For characterization Driving behavior can frequency responses be used.

Assessment of driving behavior by means of of the yaw frequency response

The yaw frequency response is a valuable tool for assessing driving behavior. From differential equations (23), the yaw transmission function (57) can be derived by means of the Laplace transformation:

Where l = 1 _V + 1 _H.

If the complex frequency j2πf is used for s in the yaw transfer function (57), the yaw frequency response is obtained:

Of the Frequency response thus represents a section of the transfer function namely, the totality of their functional values on the imaginary axis.

The yaw frequency response (60) is followed by an amplitude response | F (f) | and a phase response ∠ F (f). They describe the amplitude and the phase of the yaw rate after the decay of the transient (which requires stability) against a harmonious excitation on the steering wheel. At a very low frequency, ie f → 0, F (0) = K / ω ² corresponds to the so-called yaw amplification factor, namely the ratio between the yaw rate and the steering wheel angle in a stationary circular drive.

Of the Yaw frequency response should be during the braking process as possible do not change too much, so that the driver is not overwhelmed becomes.

Both the amplitude response and the phase response of the yaw frequency response fall off very early and very steeply, especially at higher speeds (indicating a large change in drivability) when the quantity Re (λ ₁ ) is negative but not small enough. It therefore makes sense to limit Re (λ ₁ ) as follows: Re (λ 1 ) <τ, (τ <0) (61) or alternatively ω 2 > ξ, (ξ> 0). (62)

The Limit values τ and ξ are appropriate by Set applications, so that the inaccuracies in the estimates and above all the perception of the driving behavior of the driver considered can be.

The Limits should not be too generous, thus a normal driver with the change of driving behavior while braking can still cope. On the other hand lead to conservatively elected Values for reducing the brake pressures and consequently a longer braking distance.

The quantity Re (λ ₁ ) decreases rapidly as the vehicle speed decreases. The brake pressures can be increased accordingly without violating the stability condition. However, the braking pressures must be limited because of the tire characteristics, so that the stability of the wheels is ensured both in the circumferential direction (not blocked) and in the lateral direction.

Limiting the slip angle

Similar to the circumferential force over the circumferential slip, the lateral force can only increase up to a certain limit with the skew angle. If this limit is exceeded, the lateral force will not increase or decrease, although the skew angle continues to increase. In this case, the vehicle gets into an unstable area, ie no stationary state is reached. This situation can occur especially when braking on one-sided slippery roads. In 10 is the quasi-stationary (by "quasi" is meant that the driving speed is still changing) state of a straight-braking on such a roadway exemplified. In this case the vehicle drives straight ahead with a slip angle β.

That by the asymmetrical braking forces F U VL <F U VR , F U HL <F U MR caused Störgiermoment must be compensated by a counteracting moment, by the side forces F S VL , F S VR , F S HL , F S MR is produced. These lateral forces in turn lead to slip angles α _VL , α _VR , α _HL , α _HR . It is easy to see that the slip angles increase in this case with increasing braking power. The braking power must therefore be limited so that these angles do not exceed a certain limit. It is generally sufficient to use the quasi-stationary slip angles.

in the quasi-stationary Condition applies

Differential equations (23) are thus reduced to the following algebraic equations 0 = Ax + bδ V + υ. (64)

From this, the quasi-stationary slip angle and the required steering angle can be determined at a measured yaw rate:

ergeben sich quasi-stationäre Schräglaufwinkel der Vorder- und Hinterräder.Due to the following relationships

result in quasi-stationary slip angle of the front and rear wheels.

control strategy

• 1. Die Stabilitätsbedingung des Gesamtfahrzeugs nach (61) bzw. (62) muss erfüllt werden;
• 2. Die Schräglaufwinkel der Räder dürfen eine bestimmte Grenze nicht überschreiten;
• 3. Die Räder dürfen nicht blockieren.

A stable and controllable braking operation therefore requires three conditions:

• 1. The stability condition of the entire vehicle according to (61) or (62) must be met;
• 2. The slip angles of the wheels must not exceed a certain limit;
• 3. The wheels must not lock.

Under Under these conditions, the adhesion of the wheels on the road should be optimal be used to one as possible short braking distance to achieve. This can be achieved through targeted regulation the brake pressures or the slip values are achieved.

In principle, many control strategies are conceivable. One embodiment is in 1 shown. The locking of the wheels is as usual by a conventional anti-lock 8th prevented. However, the brake pressure in the master cylinder is controlled under conditions 1 and 2 above. An advantage of this strategy is that braking forces of the left and right wheels are approximately the same even on one-sided slippery roads, as long as the anti-lock 8th not yet active, z. B. at a light braking. Although the driver is not informed about the road condition in this case, he also does not need to counter-steer.

This control strategy is now being investigated with the help of a multi-body complete vehicle model. As a controlled variable, Re (λ ₁ ) is used. Alternatively, the size ω ² can be used.

The presented control strategy works differently when braking Kind, z. B. Straight braking on a homogeneous and heterogeneous road surface, Brakes in the curve, etc. Exemplary in the following only some simulation results during straight braking on one side (left in this case) smooth roadway shown.

As 11 shows, the default τ = -0.5 was well maintained during the braking process. Condition 1 is thus fulfilled.

Since Re (λ ₁ ) at the beginning of the braking process is significantly smaller than the default, the brake pressure in the master cylinder is built up quickly. The rotational speed of the wheels on the slippery side of the road decreases rapidly. In this case, the anti-lock device responds so that the brake pressure in the respective wheel cylinders does not increase any further and blocking is prevented as in 12 shown. The graph 34 shows the brake pressure on the left front wheel, the graph 35 the brake pressure on the right front wheel, the graph 36 the brake pressure on the left rear wheel and the graph 37 the brake pressure on the right rear wheel.

Since the wheels on the grip road side (right) can transmit even more braking forces, the brake pressure under the stability conditions 1 and 3 is further increased until the slip angle of a wheel (in this case on the rear axle) the predetermined limit (in this case 6 ° ) reached. The course of the slip angle is in 13 shown.

The Driving behavior in higher Speed ranges, ie at the beginning of the braking, changes relatively strong. To improve this, instead of a constant one is with the driving speed variable limit τ conceivable.

The required steering wheel angle during braking is in 14 shown. It can be seen that this control strategy allows a smooth steering correction.

1, 2

contraption

3

processing unit

4

sensors

5, 6

processing unit

7

brake pressure

8th

Braking system, anti-lock

9

regulator

10

vehicle longitudinal axis

11

Center of gravity

12-15

wheel

16

rear axle

17

Front

18-37

graph

Claims (19)

Method for determining a driving stability of a vehicle during braking, comprising: determining a center of gravity ( 11 ) of the vehicle, - determination of lateral force coefficients of wheels ( 12 - 15 ) of the vehicle, and - determining a value for the driving stability of the vehicle from a speed of the vehicle, the center of gravity ( 11 ) of the vehicle, the lateral force coefficients of the wheels ( 12 - 15 ) of the vehicle, a vehicle mass and a vehicle inertia about a vehicle vertical axis. A method according to claim 1, characterized in that the value χ for the driving stability from the speed v of the vehicle, a distance l _{V of} a center of gravity ( 11 ) of the vehicle from the front axle ( 17 ), a distance l _{H of} the center of gravity ( 11 ) from the rear axle ( 16 ), the lateral force _coefficients front left c _αVL , front right c _αVR , rear left c _αHL , rear right c _{αHR of} the wheels ( 12 - 15 ), the vehicle mass m and the vehicle moment of _inertia J _{Z are} determined about a vehicle vertical axis as follows:

applies. Method according to claim 2, characterized in that determining a lateral force coefficient of the lateral force coefficients for a wheel ( 12 - 15 ) of the vehicle comprises: determining a circumferential force of the wheel ( 12 - 15 ), - detecting a slip of the wheel ( 12 - 15 ), and - determining the lateral force coefficient of the wheel ( 12 - 15 ) from the circumferential force, the slip and wheel-specific constants. Method according to Claim 3, characterized in that the lateral force coefficient Ca for a wheel ( 12 - 15 ) is determined from the circumferential force F ^U , the slip S and the wheel-specific constant κ as follows:

Method according to claim 3 or 4, characterized in that the determination of the circumferential force of the wheel ( 12 - 15 ) comprises: - detecting a brake pressure of a wheel brake cylinder of a brake of the wheel ( 12 - 15 ), - detecting an angular velocity of the wheel ( 12 - 15 ), - determining an angular acceleration of the wheel ( 12 - 15 ) from the angular velocity, and - determining the circumferential force from the brake pressure, the angular acceleration and vehicle-specific quantities. A method according to claim 5, characterized in that the vehicle-specific variables - a piston surface of the wheel brake cylinder, - a mean friction radius of a brake pad of a brake disc of the brake, - a brake characteristic of the brake, - an inertia of the wheel ( 12 - 15 ) and all masses associated with it, and - comprise a dynamic tire radius. Method according to claim 6, characterized in that the determination of the peripheral force of the wheel ( 12 - 15 ) further comprises: - detecting on the wheel ( 12 - 15 ) acting engine drag torque and - Determining the circumferential force in addition from the engine drag torque. Method according to claim 7, characterized in that the circumferential force F ^{U of} the wheel ( 12 - 15 ) From the brake pressure p _B , the angular acceleration ω., The piston surface A of the wheel brake cylinder, the mean friction radius r of the brake pad of the brake disc, the brake characteristic C _{B of} the brake, the moment of inertia J _{wheel of} the wheel and all masses associated therewith, the dynamic Tire radius R _dyn and that on the wheel ( 12 - 15 ) acting engine drag M _engine is determined as follows:

Method according to one of claims 5-8, characterized in that the center of gravity ( 11 ) of the vehicle from the peripheral forces of the wheels ( 12 - 15 ) and the wheelbase of the vehicle is determined. Method according to claim 9, characterized in that the distance l _{V of} the center of gravity ( 11 ) of the vehicle from the front axle ( 17 ) and the distance l _{H of} the center of gravity ( 11 ) from the rear axle ( 16 ) out of proportion F U V / F U H the peripheral force of the front wheels ( 12 . 13 ) to the peripheral force of the rear wheels ( 14 . 15 ) and the wheelbase l is determined as follows: l V / l H = F U V / F U H and l V + l H = l. A method of adjusting brake pressure for a vehicle, comprising: determining wheel slip angles ( 12 - 15 ) of the vehicle, determining a value for driving stability of the vehicle during braking, and adjusting the brake pressure ( 7 ) on the wheels ( 12 - 15 ) of the vehicle as a function of the determined slip angle and the determined driving stability such that a predetermined slip angle is not exceeded and that a predetermined range of values for the driving stability is maintained. Method according to claim 11, characterized in that that the value for the driving stability according to one of the claims 1-10 determined becomes. Method according to claim 12, characterized in that that the predetermined value range for the driving stability a Range from -∞ to -0.5. Method according to one of claims 11-13, characterized in that further a yaw rate of the vehicle is detected, and that the slip angle of a wheel ( 12 - 15 ) of the vehicle is determined from the yaw rate and other variables, wherein the further variables include the speed of the vehicle, lateral force coefficients of the wheels of the vehicle, circumferential forces of the wheels of the vehicle, a center of gravity of the vehicle, a vehicle mass and a vehicle inertia about a vehicle vertical axis. Method according to one of Claims 11-14, characterized that the predetermined slip angle 6 °. Device for determining a driving stability of a vehicle during braking, comprising a processing unit ( 5 . 6 ), which with sensors ( 4 ) of the vehicle, the sensors ( 4 ) provide the following measurements: an angular velocity of each wheel ( 12 - 15 ) of the vehicle and - a brake pressure for each wheel ( 12 - 15 ) of the vehicle, the processing unit ( 5 . 6 ), a value for the driving stability of the vehicle from a speed of the vehicle, the angular speeds of each wheel ( 12 - 15 ) of the vehicle, the brake pressures for each wheel ( 12 - 15 ) of the vehicle and vehicle-specific information. Device according to claim 16, characterized in that the device ( 2 ) is designed for carrying out the method according to one of claims 1-10. Device for setting a brake pressure for a vehicle, comprising a processing unit ( 3 ), which with sensors ( 4 ) and an actuator ( 8th ) of the vehicle, the sensors ( 4 ) provide the following measurements: an angular velocity of each wheel ( 12 - 15 ) of the vehicle, - a yaw rate and - a brake pressure for each wheel ( 12 - 15 ) of the vehicle, wherein the actuator ( 8th ) for adjusting one of the processing unit ( 3 ) certain brake pressure ( 7 ) is configured for the vehicle, wherein the processing unit ( 3 ), slip angle of the wheels ( 12 - 15 ) of the vehicle and a value for driving stability of the vehicle when braking from the measured values of the sensors ( 4 ) and vehicle-specific information and the brake pressure ( 7 ) for the vehicle depending on the determined slip angle and the particular driving stability to be set such that a predetermined slip angle is not exceeded and that a predetermined range of values for the driving stability is maintained. Device according to claim 18, characterized in that the device ( 1 ) for carrying out the method according to any one of claims 11-15 is configured.