DE4218034A1 - Measuring frictional connection potential of motor vehicle - involves measuring and smoothing vehicle parameters, e.g. speed and acceleration, and deriving vehicle state and road conditions - Google Patents

Abstract

The method involves detecting and smoothing measurement values, deriving the vehicle's state from them, identifying the road conditions from the measurement values and vehicle state, predicting a prevailing friction coefficient from the road conditions and vehicle state and deriving the force connection potential from the frictional coefficient. The vehicle parameters smoothed by an exponential filter include the speed, longitudinal and lateral acceleration, yaw angle and steering wheel angle. The road condition is identified as dry, wet or icy. USE/ADVANTAGE - Enables continuous measurement of frictional connection potential of motor vehicle.

Description

The operating range of a passenger car is determined by the conditions in the contact zone between Tires and road surface significantly affected. Forces that have to be transmitted in this zone arise when cornering, accelerating and braking. The power transmission takes place through Non-positive, that is, by friction. As with all friction processes, the friction resistance is dependent on the properties of the two friction partners, in this case tires and road surface, as well as on the Conditions in the contact area, e.g. B. dry, wet or winter smooth. In particular the conditions in the contact area changes while a vehicle is traveling, sometimes suddenly, e.g. B. through puddles or through slippery roads on bridges. This also changes the Limits of power transmission between the vehicle and the road. For the safe operation of one Motor vehicle, however, it is always necessary to the current adhesion limits of the Knowing the vehicle / lane combination.

The only indications of road surfaces with potentially dangerous reduced grip So far, the driver has received traffic signs in addition to his own sensory organs. This kind However, the information is very general and rarely adapted to individual circumstances. As a result the driver is inclined to ignore such signs.

But even under the condition that the driver with the help of his personal sensors (e.g. the Eyesight) receives full information about the condition of the road and the course of the road, it is not always able to evaluate the information correctly. That is, he can under the circumstances associate the driving limits of his vehicle inaccurately and thus make mistakes that again endanger the traffic system. This is made clear by the not inconsiderable Proportion of solo accidents due to unmatched driving speed.

If one assumes that in particular the association skills of the human being also more intensive training can only be improved insignificantly Vehicle technology remedy. The basic prerequisite for this is the existence of a system which the current driving limits of the vehicle continuously recorded. Such a system must be able to do this be to accomplish three main major tasks, namely

• - the detection of the current frictional connection between the tire and the road,
• - the determination of the forces that can be transmitted between the tire and the road, taking into account the current engagement conditions and
• - the association of the vehicle's driving limits valid under the current adhesion conditions.

It is therefore an object of the invention to provide a method which enables a continuous determination of the Grip potential of a motor vehicle enables.  

This object is achieved in that the one driving state of the vehicle Descriptive sizes are determined and brought into a form that can be further processed. From these The current driving state is then determined from measured values. In the next step, the measured values and determines a road condition from the driving condition and then from driving condition and Road condition predicts an instantaneous prevailing coefficient of friction. From the An existing adhesion potential can now be derived from the coefficient of friction.

For this purpose, the variables vehicle speed, vehicle slip angle, Vehicle acceleration in the longitudinal and transverse directions, yaw angle of the vehicle and steering wheel angle. The driving state is determined by the variables determined from this for the center of gravity of the vehicle Floating angle, vehicle speed in the longitudinal and transverse directions and vehicle acceleration in Longitudinal and transverse directions described. The driving state and a signal from a wetness sensor become then differentiate between the road conditions dry, wet and winter smooth.

In a further two steps, there is first a prevailing coefficient of friction and then the values for maximum Longitudinal acceleration, minimum longitudinal acceleration and maximum lateral acceleration are determined. These values can then be used to determine the adhesion potential in a standardized representation.

These steps are essentially polynomial calculations using the coefficients of the polynomials depending on the tire design and condition of the road surface (for calculating the coefficient of friction) or Coefficient of friction and vehicle design (for the calculation of the acceleration values) in tests were determined and stored in a memory. Therefore, a closed calculation of the Non-positive potential is possible.

The process according to the invention is characterized in particular by the fact that it is continuously in the Vehicle can be carried out. The determined adhesion potential is only low Delay for display or further use in vehicle-related control devices for Available.

An embodiment of the invention is described below.

Show it:

Fig. 1 shows a first flowchart of a method for determining a power circuit potential,

Fig. 2 is a sketch of a vehicle,

Fig. 3 shows diagrams of a step response and a frequency response of a low pass filter,

Fig. 4 in a vector diagram of a transformation of speeds,

Fig. 5 in a vector diagram of the relationship between measured and actual lateral accelerations,

Fig. 6 is a flowchart for detecting a road condition,

Fig. 7 is a flowchart of a prediction coefficient of friction,

Fig. 8 is a diagram of a coefficient of friction on dry roads as a function of vehicle speed,

Fig. 9 is a diagram of a coefficient of friction on wet roads as a function of vehicle speed,

Fig. 10 is a graph of a predicted coefficient of friction on wet roads as a function of vehicle speed,

Fig. 11 is a sketch of a three-zone model of a wheel footprint,

Fig. 12 is a diagram a diagram of a predicted coefficient of friction on winter slippery road surface as a function of vehicle speed,

Fig. 13 is a diagram of a normalized power circuit potential while driving,

Fig. 14 is a diagram of a normalized power circuit potential during braking,

Fig. 15 is a diagram of a coefficient D as a function of the coefficient of friction,

Fig. 16 is a diagram of a coefficient e as a function of the coefficient of friction,

Fig. 17 is a diagram of a coefficient F as a function of the coefficient of friction,

Fig. 18 is a diagram of a coefficient A as a function of the coefficient of friction,

Fig. 19 is a diagram of a coefficient B as a function of the coefficient of friction,

Fig. 20 is a diagram of a coefficient C as a function of the coefficient of friction,

Fig. 21 is a diagram of a skew angle at the maximum side force as a function of coefficient of friction and vehicle speed,

Fig. 22 is a diagram of a cross slip over a circumferential slip,

Fig. 23 is a diagram of an approximated maximum longitudinal acceleration over an iteratively calculated maximum longitudinal acceleration and

Fig. 24 is a second flowchart for determining the frictional connection potential.

Fig. 1 shows the basic procedure for determining the adhesion potential. Here are the steps:

• - Acquisition and smoothing of measured values
• Determining a driving state from the measured values,
• - recognition of a road condition,
• - Predicting the coefficient of friction and
• - Calculation of the adhesion potential.

Acquisition and smoothing of measured values

The measured values are recorded by means of sensors arranged in a vehicle 1 outlined in FIG. 2, which measure the measured variables vehicle speed v, slip angle, longitudinal acceleration, lateral acceleration, yaw rate and steering wheel angle. These sensors are attached to the body of the vehicle 1 . The measurements are therefore carried out in a manner that is ready for installation.

The measured variables are defined in a center of gravity SP of vehicle 1 and should also be recorded here. However, if this is e.g. B. not possible for reasons of space, this must be taken into account when determining the sensors.

The driving speed v and the slip angle are measured by a correlation-optical sensor. This sensor is mounted in the front bumper (position O in FIG. 2) of the vehicle 1 . It measures two speeds v1 and v2, which occur in the +45 degree and -45 degree directions with respect to the vehicle longitudinal axis X. From these two speeds, the amount and the direction of the resulting speed with respect to the longitudinal axis X of the vehicle can be determined for the measuring location. Taking into account the yaw rate of the vehicle 1 , the speed and the slip angle in the vehicle center of gravity SP can be calculated therefrom.

The measurement of the yaw rate is absolutely necessary, because it is a characteristic is indispensable for the vehicle movement, and secondly for the transformation of some measured variables from the measuring point to the vehicle center of gravity SP is required. A serves as a sensor mechanical gyroscope. It is installed in the vehicle at the level of the left rear seat.

The vehicle accelerations in the longitudinal and transverse directions detect piezoelectric accelerometers. The longitudinal acceleration can be measured directly in the direction of the vehicle longitudinal axis X. The corresponding sensor is installed in a spare wheel well (position H in Fig. 2).

Since the position of the center of gravity SP in the longitudinal direction X of the vehicle is initially not clearly known, the lateral acceleration must be detected by two sensors. This is necessary because in order to transform the acceleration value measured at any point in the vehicle into the center of gravity SP, in addition to the yaw rate of the vehicle, the yaw angle acceleration must also be known. Since this is not measured directly, it is eliminated by taking into account the lateral accelerations measured at two points in the vehicle. For this reason, piezoelectric sensors for detecting the lateral acceleration are mounted both in the spare wheel well (position H in FIG. 2) and on the side wall of the cooler (position V in FIG. 2).

The steering wheel angle is finally detected using a measuring steering wheel Incremental transducer.

A smoothing of the measured values is necessary in order to convert the measured values into meaningful ones Shape. Most of the measurement signals are very noisy, which means that they contain random errors. Such disturbances can be eliminated by smoothing the sensor signals. Another Measure in the context of signal preprocessing is the transformation of the measured values into that for the further calculations relevant coordinate system. This is particularly important when determining the  Driving state required, because in this case the individual is not directly in the reference point for which they are defined can be detected.

The sensors available for equipping the vehicle 1 are for the most part universally usable measurement sensors. Therefore, their properties are not directly adapted to the special measuring task. This leads to a strong noise being superimposed on the useful signal. This effect arises from the fact that the respective sensor is able to detect temporal changes in the sensed variable which lie outside the actually relevant frequency range of the measured value. So z. B. a piezoelectric transducer, which is attached to the vehicle body for measuring the vehicle lateral acceleration, also very high-frequency accelerations that result from vibrations within the vehicle structure. The signals must be freed from interference of this type by low-pass filters.

This is a suitable means for digitally smoothing measured values with continuous evaluation exponential filter. The corresponding formula results from a control engineering consideration of the filter. For this it is assumed that the filter behaves like a proportional one Loop element should behave with a first-order delay. The relationship between filtered The value and unfiltered value x (t) of a time signal can then be determined by the differential equation

to be discribed. Approximately

set, where Δt corresponds to the reciprocal of the samples ATR, so the recursion formula results from (Eq. 1)

(t) = kx (t) + (1 - k) (t - Δt) (Eq. 3)

The smoothing factor k is calculated from the sampling rate ATR and filter corner frequency f ₀ , according to

The step response and the frequency response of such a filter are shown in FIG. 2, for a corner frequency of f ₀ = 0.5 Hz and a sampling rate of ATR = 100 Hz, corresponding to the data rate of the A / D converter used. The result is a low-pass filter that reliably eliminates high-frequency noise.

Determining the driving condition from the measured values

Following the smoothing of the signals, the driving state is determined as part of the signal preprocessing. The driving state is characterized by the state of movement of the vehicle's center of gravity SP. However, as already mentioned, the corresponding speeds and accelerations are not recorded directly at the reference point (cf. FIG. 2). A transformation of the respective measured values from the location of the measurement into the coordinate origin is therefore necessary.

The driving speed v and the slip angle can be determined from the speed signals v1 and v2 of the correlation-optical sensor. For this purpose, the speed components v _{X, F, O} and v _{Y, F, O are first determined} at measuring point O (cf. FIG. 2). As shown in Fig. 3, these result in

v _{X, F, O} = 1/2 · · (v₁ + v₂) (Eq. 5)

and

v _{Y, F, O} = 1/2 · · (v₁ - v₂) (Eq. 6)

Taking into account the measured yaw rate, the speed components v _{X, F, SP} and v _{Y, F, SP of} the vehicle's center of gravity SP are calculated from this in the vehicle-fixed coordinate system, and the values sought for the vehicle speed v and the slip angle β are finally obtained. If one neglects the influences of roll and pitch movement of the superstructure, these values also correspond to the sizes in the horizontal coordinate system. Since mainly stationary driving conditions are examined, this neglect is permitted. Even in normal driving, the dynamics are very low-frequency (<0.5 Hz), i.e. quasi-stationary.

The conditions for determining the lateral acceleration a _y in the vehicle center of gravity SP are similar. The transformation of the lateral acceleration measured at a point fixed to the vehicle into the center of gravity requires not only the knowledge of the yaw rate, which is available as a measured value, but also the knowledge of the yaw acceleration. However, this is not recorded directly, but must be taken from the two measured lateral accelerations accordingly

be derived. The (measured) lateral acceleration in the vehicle's center of _gravity a _{Y, mess} now results from

with one of the two lateral acceleration signals a _{Y, V} or a _{Y, H} , taking into account the measured yaw rate and the yaw acceleration accordingly (Eq. 7).

However, the lateral acceleration a _{Y, mess} determined in this way does not correspond to the lateral acceleration a _Y resulting purely from the vehicle movement. Due to the roll angle ϕ, the measured values of the lateral acceleration sensors are falsified by a gravitational acceleration component. This systematic measurement error has to be eliminated.

There is a linear relationship for vehicle 1

ϕ = KW · a _y (Eq. 8)

between roll angle ϕ and lateral acceleration a _Y. KW achieved the value

Taking into account the geometric relationships, corresponding to FIG. 5, it finally results

if sin ϕ = ϕ and cos ϕ = 1 is set.

When determining the longitudinal acceleration a _x in the vehicle center of gravity SP, it must also be taken into account that the measurement value is recorded in position H (cf. FIG. 2). In addition, the longitudinal acceleration signal is also falsified by a component of the gravitational acceleration g, due to the pitch angle ϑ of the vehicle body. The transformation into the coordinate origin is therefore done with

the measured yaw rate and the yaw acceleration are used accordingly (Eq. 7) will.

The systematic measurement error resulting from the pitch angle ϑ is corrected analogously to Correction of the lateral acceleration signal. It follows

The pitch angle / longitudinal acceleration gradient KN has different values when driving and braking. When driving, the value results for vehicle 1

In the event that the vehicle 1 is braked, applies

Detect the road condition

Determining the current road condition is the most important part of the signal interpretation, since the Condition of the road surface has the greatest influence on the potential for adhesion to be predicted of the entire vehicle.

The strategy for recognizing the condition of the road is shaped by the available ones Measurands. A suitable sensor signal can be used to identify road wetness. The situation is different when it comes to detecting slippery roads. This road condition cannot directly to be sensed. However, slippery road surface significantly changes tire properties. This manifests itself also in the movement behavior of the entire vehicle. Identification of a winter slick The road surface is therefore based on an interpretation of the driving condition.

The condition of the road is recognized in three stages. As shown in Fig. 6, it is initially assumed that the road is dry. The next step is to check whether the road surface is slippery. If there is no slippery road, querying the wetness sensor signal provides information as to whether the road surface is wet. The results of both queries are finally combined, so that between the three road conditions

• - dry,
• - wet as well
• - winter smooth can be distinguished.

Prediction of the coefficient of friction

The adhesion potential of the vehicle can be approximately calculated if the current coefficient of friction is known. This is not measured directly, but is predicted taking into account the road condition (qualitative) and driving speed v (quantitative) (cf. FIG. 1). The quality of this prediction thus decisively influences the quality of the information derived from it. Since the vehicle 1 is equipped with mixed tires, a separate coefficient of friction must be forecast for the front and rear axles.

The structure of the steps for forecasting the coefficient of friction is illustrated in FIG. 7. The coefficient of friction, corresponding to the definition of the maximum braking force coefficient at a wheel load of 4 kN, is applied depending on the driving speed v. If one neglects the behavior of the adhesion coefficient at low speeds (<20 km / h), it can be seen that the dependence of the coefficient of friction on the vehicle speed v is fundamentally hyperbolic. This relationship can be approximated by the polynomial

μ = G2 · v² + G1 · v + G0 (Eq. 13)

to be discribed. It is of fundamental importance for this approach that the possibility through G0 is given to influence the level of adhesion. G1 and G2 allow the individual To define the dependence of the coefficient of friction on the vehicle speed v. The coefficients of the Polynomials depend on the condition of the road. They will match the current one Road condition retrieved from a data store. By inserting the driving speed v in Equation (Eq. 13) finally becomes the current coefficient of friction for the front and rear axles approximated.

The initial data when determining the memory content are friction coefficients from tire maps. These values have been determined on tire test benches.

As already mentioned, the vehicle 1 is equipped with differently dimensioned tires on the front and rear axles. Test bench measurements, as basic data for the prognosis of the coefficient of friction, are mainly only available for the narrower front tire (tire 1). In order to draw conclusions about the expected behavior of the wider rear tire (tire 3), the wheel contact areas of the two tires are determined as additional information. The front axle tire has an almost square contact patch. For the wider tire on the rear axle, on the other hand, there is mainly a cross-country tire. Compared to the tires on the front axle, the length of the tires in particular is significantly less. This must be taken into account when forecasting the speed dependence of the coefficient of friction.

The level of friction, characterized by GO, is finally tested on a principle Lane determined.

The dependency of the stored parabola coefficients ( Fig. 7) on the road condition is described below. A basic distinction is made between dry, wet and winter smooth roads.

To determine the coefficients for (Eq. 11) that are valid on dry roads, the test bench values of tires 1 and 3 are examined first. It can be seen ( FIG. 8) that the friction coefficients of both tires are above µ = 1.0 up to a speed of 180 km / h. It can also be seen that the coefficients of friction decrease with increasing speed. The values of the wider tire (tire 3) drop more strongly than those of the narrower tire (tire 1). Up to a speed of approx. 160 km / h, the coefficients of the wide tire are higher than the values of the narrow one. At a driving speed v in the range of 160 km / h, both tires achieve approximately the same maximum circumferential force coefficient. This behavior can be explained by the different shape of the wheel contact patch or tire construction.

Due to a significantly shorter pint, the wider tire becomes less strong when rolling deformed. This leads to a more homogeneous pressure distribution in the wheel contact area. Because of the degressive connection between surface pressure and adhesion coefficient is a homogeneous Pressure distribution optimal for the build-up of frictional forces between tires and road surface. Out of it this results in the higher coefficients of friction of the wider tire at low driving speeds. With increasing driving speed v, however, another influence becomes more important. The size of the Frictional force between the tire and the road is mainly determined by the adhesion component. However, it takes time to build up the molecular bonds required for this. It's easy understand that with increasing driving speed v the contact time between the individual Molecules of the tire and the road surface decrease, which is associated with the reduction in the coefficient of friction increasing driving speed v due. This effect is due to a smaller slit length wider tires reinforced. In addition, the wider tire due to its in the center of the tread reinforced carcass with increasing driving speed v a more inhomogeneous ground pressure distribution arises. This ultimately results in a greater drop in the coefficient of friction over the Driving speed v for the wider tire on the rear axle. This basic behavior of the Both tires, in particular the relationship to each other, must be used when forecasting the coefficient of friction for all road conditions are taken into account.

Additional tests are therefore carried out as a supporting measure for a realistic forecast of the coefficient of friction. The vehicle 1 is braked with maximum deceleration on a dry road 1 . By calculating back from the results of these tests, the coefficient of friction of the front axle tires can be determined as a function of the driving speed v. The parabola coefficients result for equation (Eq. 13)
G2, V = 0.000075 0.000075 S ² / m ² ,
G1, V = -0.00714 s / m and
G0, V = 1,192.

Taking into account the test bench results for tires 1 and 3 and the conclusions from the shape of the wheel contact patch or the tire construction, the parabolic coefficients for the rear axle tires become
G2, H = 0.0000771 s ² / m ² ,
G1, H = -0.007920 s / m and
G0, H = 1,223
fixed. These values are stored and are used on dry roads to predict the coefficient of friction of the respective tire on the front and rear axles in (Eq. 13).

Compared to the dry road surface, in the case of road wetness, the prediction of the coefficient of friction cannot theoretically be based on individual characteristics for the front and rear axles. The influence of the water height WH must be taken into account here. The points in FIG. 9 show the maximum circumferential force coefficients for tire 1 with a wheel load of P = 4000 N, plotted against the respective associated driving speed v. It is clear that at low water levels (WH = 0.2 mm) the coefficients decrease v degressively depending on the driving speed. The course of the curve is comparable to the speed dependency on dry roads. However, this characteristic changes with increasing water level WH. At high driving speeds, the coefficients decrease progressively above speed as the water level increases. The water level at low speeds (v <40 km / h) has practically no influence on the coefficient of friction. Nevertheless, the coefficients are generally smaller on wet roads than at dry ones, even at low driving speeds v.

The relationship between the coefficient of friction and the vehicle speed v can also be approximately described in the forecast on wet roads with (Eq. 13). In contrast to the dry roadway, the parabolic coefficients G2, G1 and G0 are not constants, but must be determined depending on the water height WH. The relationships for the measured values of tire 1 shown in FIG. 9 result from regression analysis

G2 = G22 · WH² + G21 · WH + G20 (Eq. 14)

With
G22 = -0.0001515 s ² / (),
G21 = 0.0001621 s ² / () and
G20 = 0.0000344 s ² / m ²
such as

G1 = G12 · WH² + G11 · WH · G10 (Eq. 15)

With
G12 = 0.0044326 s / (),
G11 = -0.0083232 s / () and
G10 = -0.0045210 s / m
and

G0 = G02WH² + G01WH + G00 (Eq. 16)

With
G02 = -0.0305470 1 / mm ² ,
G01 = 0.0724680 1 / mm and
G00 = 0.846.

On wet roads, the prognosis of the coefficient of friction requires knowledge of the current water level. However, the existing sensors only provide a qualitative statement about the presence of road wetness. The current water level cannot be measured. Also, when predicting the coefficient of friction, it cannot be assumed that the properties of the road surface in terms of micro-roughness and macro-roughness (drainage capacity) match the test bed road surface. As a supportive measure for a realistic forecast of the coefficient of friction, additional tests are therefore necessary even when wet. For this purpose, the vehicle 1 is braked with maximum deceleration on a wet roadway. Back calculation from the results of these tests shows that to predict the coefficient of friction of the front axle tires a water level of
WHV = 1.4 mm
must be applied. G00 is also open
G00, V = 1,126
to be set, because the level of the friction coefficients on wet roads is much higher than with the measurements on the test bench.

The predicted coefficient of friction of the tires on the front axle thus results in accordance with the characteristic curve shown in FIG. 10. The values for WHV and G00, V necessary for the calculation are stored in the memory for forecasting the coefficient of friction (cf. FIG. 7) and, in the case of a wet road, for determining the parabolic coefficients valid for the front wheels from (Eq. 13) in (Eq. 14) , (Eq. 15) and (Eq. 16) are used.

Comparable data for the rear wheels (tires 3) are not available for the measured values of the front wheels shown in FIG. 9. The prognosis of the coefficient of friction of the rear wheels of vehicle 1 is therefore based on test results and on theoretical considerations which allow a statement to be made about the expected adhesion behavior of the wider rear tire in relation to the narrower front tire. For this purpose, it is examined in particular how the tire width affects the build-up of force when the road is wet.

The build-up of force when the road surface is wet can be described with the help of a 3-zone model frequently used in the literature. It is characteristic of this approach that the contact area between the tire and the road is divided into three zones ( FIG. 11).

Zone I represents an area in which a water wedge forms due to hydrodynamic effects, which completely separates the tire from the road. Zone II is considered a transitional area in there is already local contact between the tire and the road. Zone III finally characterizes the area in which there is close contact almost undisturbed by the presence of water between molecules of the tire and the road surface. Accordingly, in particular Long from zone III decisive for the achievable adhesion. This applies provided that the road surface has a minimum level of micro-roughness. It is required in order to be able to operate in Zone III to penetrate the minimal water film still present.

The starting point of the considerations is therefore the fact that to generate the frictional force essential determining component is a direct contact between the molecules of Tires and road surface must exist. This is only possible on wet road surfaces if that Water is completely displaced from the contact area to the tire surface. That per time unit dt Water volume dV to be displaced can be approximated by the approach

to be discribed. It depends on the contact area width bL, driving speed v and water height WH. After all, how well the tire manages to push this water out of the wheel contact patch decisive for the maximum transferable friction force. In their investigations it was found that Tires with increasing width have more difficulty getting water from the contact patch oust. Accordingly, there are lower maximum circumferential forces for wider tires, if Driving speed v or water level increase. At speeds below 30 to 40 km / h the tire width has no influence on the coefficient of friction.

Even assuming that the drainage capacity of a tire is independent of the tire width is, from purely geometrical relationships, the worse with increasing tire width explain future adhesion behavior. This is approximated for the 3-zone model assuming that the dimensions of zone I and II are proportional to the volume flow. Is this Drainage capacity of the tire regardless of the tire width, it follows from (Eq. 17)

(l, + l ,,) = KPvW WH (Eq. 18)

with KP as a proportionality factor.

How large the transferable friction force FR ultimately depends on the contact width bL and length I _III ; area determined by Zone I _III . I _III results from the difference between the length of the original wheel contact area I _L and the sum of I and I _II . For the frictional force FR applies approximately

FR ∼ bL · l _L - (bL · KP · v · WH) (Eq. 19)

For a given mountain range width bL, the length of the mountain range is therefore mainly on wet roads determining the level of adhesion. Due to the presence of water on the carriageway, consequently the area required for the build-up of power is reduced more percentage-wise in the case of the wider tire. Because of The shorter track length must therefore be for the wider rear tire compared to the narrower one A lower level of traction can be applied to the front tires. For force build-up in Zone III apply in addition to the considerations described above, those described for dry roads Connections. After that, at low speeds, the disadvantages of the wider tire partially in wet conditions due to the more homogeneous pressure distribution in zone III of the wheel contact patch be balanced again. At speeds below 40 km / h, there are therefore no differences Coefficients of friction to be expected on front and rear tires. With increasing driving speed v however, it also applies that, with smaller slit lengths, less time is required to build molecular bonds Available. This exacerbates the disadvantages of the wider tire when building power on wet Roadway. For the wider tire on the rear axle, a must Friction coefficient / vehicle speed gradient are used, which is in relation to the gradient of the The front tire is even steeper than on a dry road.

Analogous to the test results and the theoretical considerations, the friction coefficient for the tires of the rear axle is forecast. The parabola coefficients of (Eq. 13) are calculated as for the front tires with (Eq. 14), (Eq. 15) and (Eq. 16). The level of the friction coefficients at low driving speeds is largely determined by G00 in (Eq. 16). Since the rear tire should not differ from the front tire here,
G00, H = G00, V = 1,126
set. A higher friction coefficient / vehicle speed gradient than at the front axle can be generated by the water height parameter. It is therefore set to a fictitious value WHH for calculating the parabolic coefficients G2, G1 and G0 for the tire on the rear axle. This results from the water height WHV used for the front wheels, which corresponds to the actual road conditions

WHH = WAV + 0.2 mm (Gl.20)

The characteristic curve shown in FIG. 10 therefore applies to the predicted coefficient of friction of the tires on the rear axle. The values for WHH and G00, H necessary for the calculation are stored in the memory for forecasting the coefficient of friction (cf. FIG. 7) and, in the case of a wet road, for determining the parabolic coefficients valid for the rear wheels from (Eq. 13) in (Eq. 14) , (Eq. 15) and (Eq. 16) are used.

As a basis for the prediction of the coefficient of friction on winter slippery roads, there are no data directly available for the tires mounted on vehicle 1 .

First of all, it can be said that the manifestations of winter smoothness are extremely diverse. With terms such as snow, ice, ice or frost, the history and the Structure of the winter slippery road described. Typical for all winter smooth road surfaces is the very low level of adhesion. This is due to the presence of water in the contact zone between the tire and the road. It also forms at temperatures well below 0 Degrees from frictional heat and pressure melting. By melting the road surface at The micro-roughness is largely resolved during power transmission. It can only be a minor one Form the adhesion component. It is also important to note that when there is no contact between Rubber sample and ice surface with increasing contact time the initial friction increases. At Measurements on ice show that the maximum circumferential force coefficients are very small Maximum speed (approx. 5 km / h). After exceeding the maximum, the maximum braking force coefficient decreases slightly progressively with increasing driving speed v. So that leaves the following conclusion: Even on a slippery road surface, the length of time affects one Element of the tire surface in the contact zone to the road surface significantly the coefficient of friction.

For the power build-up on the tire, the conditions are similar to those in the wet road in Zone III of the wheel contact patch. This becomes analogous to the conclusions drawn above The level of traction on winter slippery roads is largely determined by the size of the wheel contact area embossed. In addition, there is the negative influence of the higher surface pressure on the wider tires, which are due to the larger tire pressure. So is for the wider tire on the rear axle use a lower coefficient of friction than for the front tire. Due to the time required to set up the adhesion component is a decrease in the maximum braking force coefficient for both tires to predict increasing driving speed v. Due to the smaller length, the Decrease steeper with wider tires.

As a supportive measure for a realistic forecast of the coefficient of friction, principle tests were also carried out on slippery roads. The vehicle 1 is accelerated or braked while driving straight ahead. The results of the braking tests allow conclusions to be drawn about the level of the coefficient of friction of the front axle tires. For (Eq. 13) the parabolic coefficients are set to
G2, V = -0.00002s ² / m ² ,
G1, V = -0.0015 s / m and
G0, V = 0.20
set. The parabolic coefficients for the rear axle tires become by back calculation from the acceleration tests
G2, H = -0.00004 s ² / m ² ,
G1, H = -0.005 s / m and
G0, H = 0.19
fixed. The friction coefficients shown in Fig. 12 thus result from (Eq. 13). It can be seen that the tendencies of the predicted friction coefficients are in line with the theoretical considerations. The parabola coefficients are stored in the memory for forecasting the coefficient of friction. They are used on slippery roads to calculate the maximum braking force coefficient of the tires on the front and rear axles in (Eq. 13).

Calculation of the adhesion potential

In the next step, the frictional engagement potential is to be determined from the coefficient of friction determined. The aim of the approximation leading to this is to find a closed approximation solution derive the adhesion potential. The maximum transferable forces between are decisive Tires and road surface, as well as the vehicle concept. Basis for the derivation of the algorithms for Approximate calculation of the driving limits are those that result from a simulation calculation Adhesion potentials.

The standardization of the envelopes of the adhesion potential has proven to be a significant relief in finding a solution. It is carried out for the individual tire maps by dividing the coordinates of the individual potential profiles by the respective extreme values of the accelerations. These result from the points of intersection of the adhesion potentials with the coordinate axes of the a _X / a _Y diagram. Due to the different longitudinal acceleration potential when braking or driving, the normalized adhesion potential of the vehicle is composed of two halves. In the manner described above, curve points of the normalized potentials derived from the simulation results are shown for all the tire maps examined in FIG. 13 for the case of driving and in FIG. 14 for brakes. It turns out that within the respective potential ranges (driving or braking) the contour of the standard potentials is very similar. This leads to the conclusion that the frictional engagement between the tire and the road only has an insignificant effect on the curve of the normalized potential. The contour of the standardized adhesion potential can thus be described independently of the road condition, driving speed v and tire type. However, a different course of the curve must be taken into account when driving or braking. With regression calculation, the ellipse equation can be used to approximate the normalized adhesion potential when driving

With
KX2 = 1.19058,
KX1 = -0.19058,
KY2 = 0.73819 and
KY1 = 0.26181
can be derived as an approximation. As a boundary condition, it is required that the approximation in both coordinate directions reach the intercept value one.

Even when approximating the normalized potential when braking, the requirement for intercept one in both coordinate directions can be met. As the best approximation, the regression calculation provides the 4th degree polynomial entered in FIG . The approximation equation is

With
K4 = -3.54984,
K3 = 4.60826,
K2 = -2.10140,
K1 = 0.04298 and
K0 = 1.0.

With (Eq. 21) and (Eq. 22), the maximum possible lateral acceleration of the entire vehicle can be as Longitudinal acceleration function can be calculated with good approximation if the intercepts in Shape of the extreme values of the accelerations in the longitudinal and transverse directions are known. This too Values can be determined with a closed solution if knowledge of the maximum transmissible forces between the tire and the road surface.

The following considerations about the maximum transferable forces between tire and road surface based on the hypothesis that there is basically a dependency between the tire properties in Longitudinal and transverse direction must exist, since the substances in contact with the power transmission are always the same and the mechanisms of rubber friction are not directional. It correlations between the extreme values of the tire characteristics for the Frictional forces exist in the longitudinal and transverse directions. The connections are however due to the structure of the tire, the tread pattern and the different mechanisms of formation Sliding speeds in the longitudinal and transverse directions are affected. It will surely be the characteristic the dependencies between the frictional forces in the longitudinal and transverse directions of the tire are not affected but their existence. For the approximate determination of the adhesion potential, the Knowing the maximum transferable circumferential and lateral forces as a function of the wheel load. The Relationships are determined depending on the maximum circumferential force coefficient with a wheel load of P = 4000 N determined. This factor represents the characteristic for the respective Frictional engagement in the contact zone between tire and road surface. He is here as Coefficient of friction defined.  

The maximum transferable circumferential forces can be calculated as a function of the tire characteristics Wheel load P can be derived. The resulting relationships are known to be degressive the individual characteristic curves in the entire wheel load range cannot be described simply mathematically are. For the calculation of the adhesion potential, however, there is only a limited range of the respective Characteristic curve of interest for the example vehicle between a wheel load of P = 3000 N and P = 5000 N. In this wheel load interval, the dependence of the maximum circumferential force Umax on the wheel load P by the parabola equation

U _max = D · P² + E · P + F (Eq. 23)

be approximated. Precondition is the exact knowledge of the coefficients D, E and F, which are strongly dependent on the frictional connection. With these values, the coefficients D, E and F can be calculated for each characteristic. In addition, the coefficient of friction at a wheel load of 3500 N is determined for each tire map. It is now assumed that there is as simple a connection as possible in the form of a first or second degree polynomial between the coefficients of (Eq. 23) and the coefficient of friction. The coefficient equations are determined by regression calculation. The relationship between the coefficient D and the coefficient of friction is shown in FIG. 15. The values derived directly from the tire characteristics are plotted. In addition, the is through

D = D₂ · μ² + D₁ · μ + D₀ (Eq. 24)

With
D2 = -0.00000523 1 / N,
D1 = -0.00002869 1 / N and
D0 = 0.00001103 1 / N

approximation curve described. It turns out that the coefficient D increases with increasing Coefficient of friction becomes smaller. In addition, D is always negative except for a very low level of friction. This results in a degressive relationship between maximum circumferential force and wheel load. The Degressivity increases with the increasing coefficient of friction. Overall, the influence of the coefficient D falls on the maximum circumferential force very small. The proportion of (. 23) The product of D and the square of the wheel load P at the maximum circumferential force remains relevant Wheel load range between 3000 N and 5000 N below 10%. This means that the context between maximum circumferential force and wheel load only slightly from that mainly due to E certain linear dependency deviates.

Fig. 16 shows the relationship between friction coefficient and E of the circumferential force / wheel load - parabola (eq. 23). The ones derived from the tire maps and those with a linear approach are plotted

E = E1μ + E0 (Eq. 25)

approximated values, where

E1 = 1.1337 and
E0 = -0.0355

make a good approximation of the relationship in the entire value range. The order of magnitude of E causes this coefficient to determine approximately 90% of the maximum circumferential force.

The relationship between the coefficient of friction and the coefficient F is finally shown in FIG. 17. This also turns out to be very small. The approximation equation is

F = F1μ + F0 (Eq. 26)

With
F1 = 45.38 N and
F0 = -73.04 N.

With a very low coefficient of friction and at the same time a low wheel load (e.g. 3000 N), the in (Eq. 23) share of the total circumferential force determined by F maximum 10%. With increasing The coefficient of friction makes the influence of F negligible, especially with high wheel loads.

Also for the creation of the equations for the approximation of the maximum lateral forces available tire maps, the maximum transferable lateral forces at the Wheel loads 3000, 4000 and 5000 N determined. The relationship between maximum transferable Lateral force and wheel load is also degressive and is for the wheel load range from P = 3000 N to P = 5000 N according to the parabola equation

S _max = A · P² + B · P + C (Eq. 27)

scheduled. In analogy to the determination of the parabola coefficients of (Eq. 23), in a first First step the coefficients A, B and C using the data from the individual tire maps maximum transferable lateral forces determined. Based on the one formulated above Hypothesis, the coefficients A, B and C are approximated depending on the coefficient of friction. The The coefficient equations are again determined by regression calculation. It shows that in addition to the coefficient equation for A, also for the coefficient B only a dependence on Friction coefficient in the form of a second degree polynomial leads to a satisfactory overall solution. The approximation of the coefficients A, B and C finally results as follows. Coefficient A can approximately by

S = A2μ² + A1μ + A0 (Eq. 28)

With
A2 = -0.00005312 1 / N
A1 = 0.00004481 1 / N
A0 = -0.00001489 1 / N

be calculated. In Fig. 18, out of the tires maps directly derived values of A as well as the approximation are (Eq. 28) as a function, the friction coefficient. A is always negative. Its amount increases progressively as the coefficient of friction increases. This means that the relationship between maximum lateral force and wheel load becomes increasingly degressive as the coefficient of friction µ increases. The influence of A on the maximum lateral force is basically small. The share of the product of A and the square of the wheel load on the maximum lateral force calculated accordingly (Eq. 27) remains below 10% in the relevant wheel load range between 3000 N and 5000 N. This means that the relationship between maximum lateral force and wheel load is almost linear. The linear dependency is determined by the parabola coefficient B. Fig. 19 shows the relationship between the coefficient B and the coefficient of friction. The values derived directly from the tire characteristics and the values approximated with (Eq. 29) are both plotted, both as a function of the coefficient of friction. The regression calculation provides the approximation equation for the coefficient B the parabola equation

B = B2 · μ² + B1 · μ + B0 (Eq. 29)
With
B2 = 0.4794,
B1 = 0.2667 and
B0 = 0.1788.

It shows that the coefficient B increases with the coefficient in the considered range of the coefficient of friction progressively increases. As a result, the maximum achievable lateral force increases disproportionately with the Coefficient of friction. The order of magnitude of B means that the maximum calculated with (Eq. 27) Lateral force results to over 90% from the product of B and wheel load P.

Coefficient C ( Fig. 20) approximated by

C = C1μ + C0 (Eq. 30)

With
C1 = -30.86 N and
C0 = 23.80 N,

is due to its small amount without any significant influence on the relationship between maximum lateral force and wheel load.  

In addition to the maximum transferable forces, the slip angle α _{S, max} with maximum lateral force (circumferential slip s = 0) is of interest for the algorithms for calculating the maximum lateral acceleration. The investigation of the relationships shows that the slip angle at maximum lateral force is dependent in particular on three sizes, namely

• - wheel load P,
• - coefficient of friction µ and
• - driving speed v.

It becomes clear that larger slip angles occur with increasing wheel load, the influence being more pronounced with larger coefficients of friction. The wheel load is, however, much less influential overall than the coefficient of friction and driving speed v. In order to enable a closed solution for the calculation of the maximum lateral acceleration of the entire vehicle _, the influence of the wheel load is therefore neglected in the approximate calculation of α _{S, max} . The wheel load P is set to P = 4000 N, corresponding to the average of the data available. 4000 N wheel load also correspond to the value on which the definition of the coefficient of friction is based. For the approximation of the slip angle at maximum lateral force, only the influence of the coefficient of friction and the driving speed v are taken into account. The approximation equation finally results from regression analysis

α _{s, max} = (L₂ · v² + L1 · v + L0) · µ² + (M2 · v² + M1 · v + M0) μ + (N2 · v² + N1 · v + N0) (Eq. 31)

with the coefficients
L2 = 0.0176 degrees s ² / m ² , M2 = -0.0190 degrees s / m, N2 = 0.0034 degrees,
L1 = -1.6960 degrees s ² / m ² , M1 = 2.0155 degrees s / m, N1 = -0.5015 degrees,
L0 = 55.315 degrees s ² / m ² , M0 = -63.063 degrees s / m, N0 = 21.059 degrees.

The slip angle calculated with (Eq. 31) for the constant wheel load P = 4000 N at maximum lateral force α _{S, max} are shown in FIG. 21 as a function of the driving speed v and the coefficient of friction. It can be seen that α _{S, max is} parabolic depending on the coefficient of friction. A pronounced minimum arises, which shifts toward smaller friction coefficients with increasing driving speed v. The dependence on the driving speed v is almost linear with small friction coefficients. With a large coefficient of friction, the slip angle increases progressively with maximum lateral force α _{S, max} with decreasing driving speed v.

If you want to consider the forces that can be transferred between the tires and the road surface as a friction cake, then that is an equivalent scale for slip angle and circumferential slip λ is required. For this the Slip angle can be converted into cross slip. A more balanced relationship between Circumferential slip and transverse slip result if the latter according to

λ = sin (α _{s, max} ) (Eq. 32)

it is determined what Fig. 22 should clarify. Here the values of the transverse slip at maximum lateral force calculated with (Eq. 32) are plotted against the circumferential slip at maximum circumferential force determined under the same boundary conditions. It can be seen that despite the considerable spread, there is a connection that is true in the trend.

Algorithms for calculating the extreme values of the accelerations still have to be derived will. These acceleration values are required as scale factors in order to derive from the Coordinate equations of the standardized driving limits (Eq. 21) and (Eq. 22) the absolute values of the To be able to determine the adhesion potential. For the calculation of extreme accelerations provided that the maximum transferable forces occur on the respective determining axis.

Determining the maximum longitudinal acceleration in the case of a vehicle with rear-wheel drive is the sum of the maximum transmissible circumferential forces on both wheels of the rear axle U _{H, max} . However, it must be taken into account that this force is not fully available to accelerate the vehicle, since part of the circumferential force is required to overcome the driving resistance FW. When viewed at a level, FW sits down accordingly

composed of air resistance and rolling resistance. Provided that there is no steering wheel lock d when driving straight ahead and the vehicle has 1 rear-axle drive, the relationship arises for the longitudinal acceleration when the vehicle is viewed as a single-track model

ma _{x, max} = U _{H, max} - F _w (Eq. 34)

where m represents the vehicle mass. The sum of the maximum propulsive _forces on the rear axle U _Hmax can be calculated with (Eq. 23) if the wheel loads of the rear wheels are known. When determining the wheel loads, it must be taken into account that when accelerating due to the high center of gravity, an axle load is shifted from the front axle to the rear axle. This results accordingly

as a function of the achievable longitudinal acceleration. The relevant rear axle load PH thus consists of the static rear axle load P0, H and the dynamic axle load DP. At maximum Acceleration therefore applies to the respective wheel loads on the rear wheels

The maximum propulsive force on the rear axle UH, max required to solve (Eq. 34) results finally from the sum of the maximum circumferential forces of the individual rear wheels. These can be by inserting (Eq. 36) and (Eq. 37) into (Eq. 23). This is how (Eq. 34) arises quadratic equation with which the maximum longitudinal acceleration corresponds

can be determined. The coefficients of the parabola depend on driving resistance and Vehicle concept, as well as the coefficients D (Eq. 24), E (Eq. 25) and F (Eq. 26) of the relationship between maximum transferable circumferential force and coefficient of friction. The parabola coefficients are for (Eq. 38) the values of

to use.

The minimum longitudinal acceleration a _{X, min} is a negative acceleration value. For reasons of clarity, therefore, the maximum braking deceleration is usually considered, which corresponds to the amount of the minimum longitudinal acceleration. Determining the minimum longitudinal acceleration is the sum of the maximum transferable braking forces on the wheels of the front axle U _{V, max} and rear axle U _{H, max} . It should be noted that the maximum transmissible forces may only be used on the front axle. For reasons of driving stability, only part of the maximum transmissible circumferential force is applied to the rear axle. The power transmission potential of the front axle thus determines the maximum achievable braking deceleration. This ensures that in addition to braking forces, lateral forces can also be transmitted to the rear wheels, which ensure a stable driving condition when braking. The braking force on the rear axle results from this

U _{H, max} = BA₁ · U _{v, max} + BA₀ · m · g (Eq. 39).

In addition to the braking forces, there is also the driving resistance FW, which is reflected accordingly (Eq. 33) Air resistance and rolling resistance combine to delay the vehicle. Under the The prerequisite that there is no steering wheel lock δ when driving straight ahead, results when viewed of the vehicle as a single-track model for the minimum longitudinal acceleration of the vehicle context

_{max x, min} = - (1 + BA₁) U _{v, max} - (BA₀mg + FW) (40).

The maximum circumferential force on the front axle U _{V, max} can be calculated with (Eq. 23) if the wheel loads of the front wheels are known. When determining the wheel loads, it must be taken into account that when braking due to the high center of gravity, an axle load shift DP arises from the rear axle to the front axle. This results accordingly

as a function of the achievable longitudinal acceleration. The relevant front axle load PV thus settles from the static front axle load P0, V and the dynamic axle load DP. At maximum Braking deceleration therefore applies to the respective wheel loads of the rear wheels

The maximum braking force on the front axle U _{V, max} required to solve (Eq. 40) ultimately results from the sum of the maximum circumferential forces of the individual front wheels. These can be calculated by inserting (Eq. 42) and (Eq. 43) into (Eq. 23). From (Eq. 40) a quadratic equation arises, which corresponds to the minimum longitudinal acceleration

delivers. The coefficients of the parabola depend on driving resistance and vehicle concept, and the coefficients D (Eq. 24), E (Eq. 25) and F (Eq. 26) of the relationship between maximum transferable circumferential force and coefficient of friction. Surrender

The chassis of modern passenger cars are tuned so that the vehicles turn understeering behavior. It means that the maximum lateral acceleration during stationary circular travel is reached when the maximum transferable cornering forces on the wheels of the front axle occur. However, it is also possible for a vehicle to oversteer. This can e.g. B. by a extreme loading condition. In this case, the cornering potential of the Rear axle the maximum achievable lateral acceleration of the vehicle. The following are both Considered cases.

With understeering characteristics, the achievable lateral acceleration is determined by the maximum transferable lateral forces on the front axle. It is called a _{Y, max, V.} The simultaneous cornering forces on the rear axle can be determined using the swirl set for the single-track vehicle. By definition, the yaw acceleration disappears during a stationary circular drive. This results in the lateral force SH on the rear axle for the single-track vehicle

The circumferential force UV on the front axle results from the rolling resistance of the front wheels during stationary circular driving and rear wheel drive. From the condition for the equilibrium of forces in the transverse direction of the vehicle, the maximum lateral acceleration a _{Y, max, V} for stationary circular travel can be determined accordingly (Eq. 45)

can be determined as a function of the maximum transferable cornering force S _{V, max} and wheel lock angle d. The maximum transferable cornering force S _{V, max} results accordingly

S _{v, max} = S _{1, max} + S _{4, max} (Eq. 47)

as the sum of the maximum forces given by (Eq. 27) of the two front wheels (index 1 and 4). In the Determination of the wheel loads required for (Eq. 27) takes into account that by the Center of gravity hSP creates a rolling moment proportional to the lateral acceleration. This leads to a shift in the wheel load from the wheels on the inside of the curve to the outside of the curve. For the The wheel load shift on the front axle applies

where WAV defines the percentage of the rolling moment that is supported on the front axle. This results in the wheel loads on the front wheels

In addition to the maximum transferable cornering force there is also the solution to (Eq. 46) Determine the steering angle δ of the front axle. This must be chosen so that the individual wheels the slip angle sets, which to generate the maximum transferable Cornering force is needed. If one neglects the influence of the wheel load on the slip angle to generate the lateral force maxima, this can be done with (Eq. 31) as a function of the coefficient of friction and the driving speed v can be determined. So there is no oblique sound angle Differentiation between inside and outside wheel is necessary. If you neglect that due to the track gauge influence on the direction of speed on the individual wheels of the Front axle of the vehicle, the vehicle can be viewed as a single-track vehicle. The The steering angle of the front wheels is then calculated if the slip angle is neglected

The calculation of α _{S, max} is done with (Eq. 31). In addition, the relationship between yaw rate and lateral acceleration is approximately

provided. This results from the rotary movement of the vehicle in the earth-fixed coordinate system during a stationary circular drive. The float angle is neglected so that the normal path acceleration a _{N can be set} equal to the lateral acceleration a _{Y of} the vehicle. Assuming that the steering angle δ is small so that sin (δ) = δ and cos (δ) = 1 can be set, the result of inserting (Eq. 47) and (Eq. 51) in (Eq . 46) a quadratic equation for the maximum lateral acceleration. Their solution is

The parabola coefficients become corresponding

certainly. They are only dependent on the vehicle speed v and the coefficient of friction µ, because both A (Eq. 28), B (Eq. 29) and C (Eq. 30) and α _{S, max} are known as functions of the same. The maximum lateral acceleration with understeering vehicle characteristics can thus be approximated.

If the characteristic oversteers, the achievable lateral acceleration is determined by the maximum transmissible lateral forces on the rear axle. The simultaneously occurring Cornering forces on the front axle can be adjusted again using the swirl set for the Determine single-track vehicle. By definition, it also disappears in the event of oversteer stationary round trip the yaw acceleration. This results in the for the single-track vehicle Total lateral force on the front axle too

From the condition for the equilibrium of forces in the transverse direction of the vehicle, the maximum lateral acceleration a _{Y, max, H} can be determined with (Eq. 41) during a stationary circular drive

as a function of the maximum transmissible cornering force of the rear axle S _{H, max} . For this, the maximum transferable side force S _{H, max is} corresponding

scheduled. It is the sum of the maximum cornering forces of the two rear wheels reduced by the power SU. The force SU takes into account that with driven rear wheels The cornering potential of the axle is impaired by circumferential forces that are needed to overcome the Driving resistances FW (corresponding (Eq. 33)) are required. The relationship between Circumferential force and lateral force per rear wheel set as an ellipse, so that applies

In order to enable a closed solution for (Eq. 55), it is assumed that to calculate the Axis sections of this ellipse (Eq. 57) with (Eq. 23) or (Eq. 27) the required wheel loads P0.2 or P0.3 correspond to half the static axle load (P0, H / 2). The resulting error in the Overall result is considered low. The loss of cornering power of the rear axle as a result This results in circumferential forces for overcoming driving resistance

In addition to SU, the maximum lateral forces on the two rear wheels are also to solve (Eq. 47) required. These can be calculated by inserting the dynamic wheel loads Pi in (Eq. 27). It must be taken into account that due to the high point of focus hSP one of the Rolling force proportional to lateral acceleration occurs. This leads to a shift in the wheel load of the inside wheels towards the outside. The following applies to the wheel load shift on the rear axle

where (1-WAV) describes the percentage of the rolling moment on the rear axle is supported. This results in the wheel loads on the rear wheels

By inserting (Eq. 60) and (Eq. 61) in (Eq. 27), the maximum cornering forces of the two rear wheels can now be formulated. Together with (Eq. 58), this gives (Eq. 55) a quadratic equation for the maximum lateral acceleration a _{Y, max, H.} The solution is

The parabola coefficients become corresponding

certainly. They are only dependent on the vehicle speed v and the coefficient of friction µ, because both A (Eq. 28), B (Eq. 29), C (Eq. 30) and SU (Eq. 58) are known as functions of the same. So that maximum lateral acceleration can also be approximated in the event that they are caused by the Cornering potential of the rear axle is determined.

Using the derived relationships, the maximum achievable stationary accelerations of a vehicle can initially only be determined in the direction of the horizontal coordinate axes (longitudinal or transverse direction) of the horizontal coordinate system (X, Y, Z). The calculation of the driving limits with superimposed longitudinal and lateral acceleration is finally carried out with the help of the normalized adhesion potential halves. The potential of the entire vehicle results for positive longitudinal accelerations by inserting a _{X, max} from (Eq. 38) and a _{Y, max} from (Eq. 53) or (Eq. 62) in the equation for the normalized potential when driving ( Eq. 21). The adhesion potential when braking is calculated accordingly by inserting a _{X, min} from (Eq. 44) and a _{Y, max} from (Eq. 53) and (Eq. 62) in (Eq. 22). Both potential halves together give the current driving limits of the entire vehicle when driving on a left turn on a homogeneous road. The adhesion potential of the corresponding right-hand curve arises from reflection on the a _X axis.

Fig. 24 illustrates the relationship again. Following the forecast of the current coefficient of friction on the front and rear axles, the adhesion potential is calculated. This can be derived from the coefficients of friction µ _V and µ _H with the dependencies described.

According to Fig. 24 are initially (Eq. 24) (Eq. 25) and (Eq. 26), the coefficients D, E, F max. Circumferential force / wheel load - parabola (Eq. 23) and (Eq. 28), (Eq. 29) and (Eq. 30) determine the parabolic coefficients A, B and C of the relationship (Eq. 27) between maximum lateral force and wheel load. In addition, the slip angle α _{S, max} occurring at maximum lateral force is determined with (Eq. 31).

In the next level (cf. FIG. 24) the extreme values of the achievable accelerations are calculated. If the respective parabolic coefficients A, B and C are determined for the front and rear axles, then (Eq. 53) and (Eq. 62) the maximum accelerations a _{Y, max, V} and a _Y determined by the cornering potential of the individual axles can be determined _{, H} can be calculated. The maximum lateral acceleration then corresponds to the smaller of the two values. The coefficients D, E and F can be used to determine the maximum longitudinal acceleration a _{X, max} with (Eq. 38) and the maximum braking deceleration a _{X, min} with (Eq. 44). When calculating a _{X, min} , however, it must also be taken into account that vehicle 1 is equipped with an ABS system. As is known, this system regulates the slip in the area of the maximum circumferential force. Losses are caused by the regulatory activity. Thus, only a certain percentage of the maximum circumferential force approximated with (Eq. 23) may be used to calculate the maximum braking deceleration. The efficiency is 95% on dry roads, 89% on wet roads and 98% on winter roads.

The ABS efficiency is in reality dependent on the driving speed v. He's going with decreasing speed progressively worse. This can be neglected because the Prediction of the coefficient of friction the progressive increase in the coefficient with decreasing speed is insufficiently pronounced. Both neglect cancel each other out.

The adhesion potential finally results for positive longitudinal accelerations by inserting a _{X, max} and a _{Y, max} into the equation for the normalized potential when driving (Eq. 21). The potential for braking is calculated accordingly by inserting a _{X, min} and a _{Y, max} in (Eq. 22). Both potential halves give the current driving limits of the entire vehicle when driving on a left turn on a homogeneous road. The adhesion potential of the corresponding right-hand curve arises from reflection on the aX axis.

The result of these calculations is stored in the form of a result vector and passed on to other control devices for data output or further processing (see FIG. 1).

Claims (2)

1. Method for determining the adhesion potential of a motor vehicle, consisting of the following steps:

• - Acquisition and smoothing of measured values
• Determining a driving state from the measured values,
• Recognizing a road condition from the measured values and the driving status,
• - Predicting a prevailing coefficient of friction from the road condition and the driving condition and
• - Determination of a adhesion potential from the coefficient of friction.

2. The method of claim 1, wherein

• in the step of acquiring and smoothing measured values, the variables of vehicle speed, vehicle slip angle, vehicle acceleration in the longitudinal and transverse directions, yaw angle of the vehicle and steering wheel angle are recorded and subsequently smoothed using an exponential filter,
• - in the step of determining the driving state, the variables float angle, vehicle speed in the longitudinal and transverse directions and vehicle acceleration in the longitudinal and transverse directions, in each case for the center of gravity, are determined from the measured values,
• - in the step of recognizing the roadway condition, it is recognized whether the roadway is dry, wet or wintery,
• - In the step Predicting a prevailing coefficient of friction depending on the condition of the road from a memory, a first set of coefficients (A, B, C, D, E, F, L, M, N) for polynomials for calculating the coefficient of friction is determined, into which the vehicle speed as Variable arrives, whereby the first set of coefficients from tire maps and tests was determined depending on the tire design and road condition and is stored in the memory and
• - In the step of determining a adhesion potential depending on the coefficient of friction from a memory, a second set of coefficients (K) is determined, from which, in conjunction with the value of the driving speed in polynomials, a maximum longitudinal acceleration, a minimum longitudinal acceleration and a maximum lateral acceleration are calculated, which in turn are calculated in Further polynomials are used to standardize the adhesion potential, the second set of coefficients being determined from the values determined for maximum transferable peripheral force, maximum transferable lateral force and slip angle at maximum lateral force for the tire design and stored in the memory.