DE102020112487A1 - Method for determining a developing expansion of a tire contact patch and a developing ground pressure distribution in the tire contact patch, method for calculating tire forces and torques in the tire contact patch, method for designing a component of a vehicle, method for operating a driving simulator, computer program, computer-readable medium and driving simulator - Google Patents

Abstract

The present invention relates to various methods in connection with a determination of a developing expansion of a tire contact area and a developing ground pressure distribution in the tire contact area of a tire subject to a defined load, as well as a computer-implemented method for calculating tire forces and torques arising in the tire contact area, a method for design at least one component of a vehicle as a function of a resulting tire force and / or a resulting tire torque, a method for operating a driving simulator, an actuator device of the driving simulator being controlled as a function of a calculated tire force and / or a calculated tire torque, a computer program, a computer-readable Medium and a driving simulator.

Description

FIELD OF THE INVENTION

A first aspect of the present invention relates to a method for determining at least one circumferential contour parameter of a parameterized tire contact area circumferential contour function, by means of which a circumferential contour of a tire contact area that occurs under a defined load for a tire can be described, in particular a circumferential contour of a tire contact area that changes during steering when standing and / or when maneuvering, preferably depending on a load on the tire, in particular also depending on a tire condition and / or one or more tire properties, the parameterized tire contact patch circumferential contour function in relation to a circumferential contour function coordinate system with a circumferential contour function Origin of coordinates and is defined by at least one independent variable and at least one parameter. At least one circumferential contour parameter is determined from a tire contact area imprint of a tire contact area, which has set or is to be expected as a function of a defined load on the tire, in particular also as a function of a tire condition and / or one or more tire properties .

A second aspect of the present invention relates to a method for determining at least one ground pressure distribution parameter of a parameterized ground pressure distribution function, by means of which a ground pressure distribution that occurs for a tire under a defined load can be mathematically described in an associated tire contact area that sets itself under the defined load, in particular a Ground pressure distribution that occurs when steering while stationary and / or when maneuvering, preferably as a function of the load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, the parameterized ground pressure distribution function in relation to a tire contact coordinate system originates with a tire trailing coordinates and is defined by at least one independent variable and at least one soil pressure distribution parameter. At least one ground pressure distribution parameter is determined from a ground pressure distribution in a tire contact patch, which has set or is expected as a function of a defined load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, with For defined points of the tire contact area, which are each clearly defined by their coordinates in relation to the tire contact coordinate system, an associated ground pressure value is available.

A third and a fourth aspect of the present invention each relate to a computer-implemented method, in particular a simulation method, for determining, in particular for predicting, an expansion of a tire contact area of a defined stressed tire, in particular for determining when steering when stationary and / or when Maneuvering adjusting expansion of the tire contact patch, preferably depending on a tire condition and / or one or more tire properties, wherein the expansion is determined with the help of a parameterized tire contact patch circumferential contour function, which describes a circumferential contour of the tire contact patch mathematically, preferably depending on a load on the tire and in particular further dependent on a tire condition and / or one or more tire properties, wherein the tire footprint circumferential contour function that is used in relation to a Perimeter contour function coordinate system with a circumferential contour function coordinate origin and is defined by at least one independent variable and at least one circumferential contour parameter.

• - Auswählen definierter Punkte, die innerhalb der Reifenaufstandsfläche liegen,
• - Bestimmen der Koordinaten der ausgewählten Punkte in einem definierten Koordinatensystem,
• - gegebenenfalls umrechnen der Koordinaten der ausgewählten Punkte in das Koordinatensystem, auf welches sich die definierte Bodendruckverteilungsfunktion bezieht, die zum Bestimmen der Bodendruckverteilung verwendet wird, und
• - Ermitteln eines zugehörigen Bodendruckwertes für jeden der ausgewählten Punkte mithilfe der definierten Bodendruckverteilungsfunktion,

wobei die Bodendruckverteilungsfunktion, die zur Ermittlung der Bodendruckverteilung in der Reifenaufstandsfläche verwendet wird, eine parametrisierte Bodendruckverteilungsfunktion ist, die in Bezug auf ein Reifenlatsch-Koordinatensystem mit einem Reifenlatsch-Koordinatenursprung und durch mindestens eine unabhängige Variable und wenigstens einen Bodendruckverteilungs-Parameter definiert ist.A fifth and a sixth aspect of the present invention each relate to a computer-implemented method, in particular a simulation method, for determining, in particular for predicting, a ground pressure distribution that occurs in a tire contact area of a tire subject to a defined load, in particular for determining a steering while stationary and / or When maneuvering in the tire contact area adjusting ground pressure distribution, preferably as a function of a tire condition and / or one or more tire properties, the ground pressure distribution is determined with the aid of a defined ground pressure distribution function, which describes the ground pressure distribution in the tire contact area of the tire, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties. The process comprises the following steps:

• - Selecting defined points that lie within the tire contact area,
• - Determination of the coordinates of the selected points in a defined coordinate system,
• - if necessary, convert the coordinates of the selected points into the coordinate system to which the defined soil pressure distribution function relates, which is used to determine the soil pressure distribution, and
• - Determination of an associated ground pressure value for each of the selected points using the defined ground pressure distribution function,

wherein the ground pressure distribution function, which is used to determine the ground pressure distribution in the tire contact patch, is a parameterized ground pressure distribution function which is defined in relation to a tire contact coordinate system with a tire contact coordinate origin and by at least one independent variable and at least one ground pressure distribution parameter.

A seventh and eighth aspect of the present invention each relate to a computer-implemented method for calculating at least one resulting tire force and / or at least one resulting tire torque generated by frictional forces in a tire contact area of a tire, in particular when a tire is mounted on a rim and is supported on a flat surface Tire that is forced to move, in particular via the rim, in particular when steering while stationary and / or when maneuvering, preferably depending on a load on the tire, in particular also depending on a tire condition and / or one or more tire properties, the tire force and or the tire torque is determined numerically with the aid of a tire model, which the properties of the tire, in particular a contact of the tire with a ground, among other things with the aid of a large number of massless rubber brush elements in the tread of the tire n achforms. The tire force and / or the tire torque arising in the tire contact area due to frictional forces are determined in one step, initially at least for each rubber brush located within the tire contact area, the respective rubber brush in the tire contact area as a result of the forces and moments applied between the tire and the underlying friction which are combined in a further step via all rubber brushes located within the tire contact area to form the resulting tire force and / or the resulting tire torque, each rubber brush element being assigned a reference point with associated coordinates, which clearly defines the position of the rubber brush element is.

A ninth aspect of the present invention relates to a computer-implemented method for designing at least one component of a vehicle, preferably for designing a steering arrangement, in particular for designing a rack of a steering gear, with at least one value of a design variable relevant for designing the component depending on the design of the component is determined by a resulting tire force and / or at least one resulting tire torque resulting from frictional forces in a tire contact patch of a tire.

A tenth aspect of the present invention relates to a method for operating a driving simulator, the driving simulator having at least one controllable actuator device.

An eleventh aspect of the present invention relates to a computer program which comprises instructions which, when executed by a computer, cause the computer to carry out a specific method.

A twelfth aspect of the present invention relates to a computer-readable medium, in particular a computer-readable storage medium, which comprises instructions which, when executed by a computer, cause the computer to carry out a specific method.

A thirteenth aspect of the present invention relates to a driving simulator.

BACKGROUND AND PRIOR ART

It is known that in a vehicle with a conventional steering system, for example with rack and pinion steering, the greatest forces act on the steering system during steering maneuvers at a standstill, in particular when parking (steering while stationary). But also when maneuvering (steering when rolling slowly up to a maximum walking speed) high forces occur. Above all, the forces that occur and act on the rack and pinion steering (rack and pinion forces) represent a decisive factor in the design of the steering, whereby tire forces and torques (scaled via axle kinematics and weight) are the The main influencing factors on the rack force are. In particular, for a suitable steering design, which nowadays is usually carried out to a large extent with the help of suitable simulation methods, as well as for precise vehicle dynamics simulations, it is therefore important to know as precisely as possible the tire forces and torques that occur in the individual driving states. The tire forces and torques that occur when steering while stationary and when maneuvering depend in particular on a distribution of ground pressure in the contact area between the tire and the ground, for example the roadway. Consequently, it is particularly important for a suitable steering design, especially if this is essentially carried out by simulation, as well as for precise driving dynamics simulations, that the contact area between the tires and the ground in the individual driving states and the respective soil pressure distribution in the contact area are established to know exactly. To determine this by means of a simulation method, a model is therefore required which depicts the contact surface and the soil pressure distribution that is established as precisely and realistically as possible.

Current models, especially current tire models, are usually only calibrated with a low camber and high speeds and therefore only depict low camber values and high speeds in a satisfactory manner. However, high camber values when the bike is stationary or slowly rolling, such as those that occur when maneuvering and / or steering while stationary, are generally only inadequately represented. This results, among other things, in inaccurate forecasts of the tire forces and torques occurring in the contact area between the tire and the ground, especially the frictional forces, especially in simulations during early development stages. As a result, in many cases, an optimal steering design is not yet possible or the steering design is made more difficult at this point in time. In addition, some of the tire models known from the prior art are difficult to parameterize and thus difficult to adapt to different tires and / or tire loads and / or driving conditions, e.g. to different camber values or different tire inflation pressures. This means that the influence of various variables such as wheel load, tire inflation pressure, camber and, for example, the tire dimensions can only be forecast with difficulty or hardly at all, especially in an early development phase, when this is precisely what is desired.

Generic, computer-implemented methods, in particular simulation methods for calculating the tire forces and torques occurring in the contact surface, in particular the occurring frictional forces, as well as associated methods for parameter identification of the simulation models, associated computer programs and corresponding computer-readable media are basically known from the prior art.

On the one hand, there are known simulation methods for calculating expected, occurring circumferential contours of tire contact areas of a tire subject to a defined load, as well as simulation methods for calculating expected, occurring ground pressure distributions within the tire contact area.

A wide variety of methods for parameter identification of generic peripheral contour and ground pressure distribution functions are also known.

In particular, it is known, for example from Weinberger, M., Becker, J., Schramm D .: “Tire contact patch pressure distribution model for the static parking maneuver”, published in “18. International Stuttgart Symposium “, Proceedings, Ed .: M. Bargende, H.-C. Reuss, J. Wiedemann, Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2018, https://doi.org/10.1007/978-3-658-21194-3-95, this calculation is based on mathematical, parameterized circumferential contour and soil pressure distribution functions the parameters of which have been determined with the help of real recorded measurement data, in particular from real recorded tire contact patch imprints.

On the other hand, simulation methods for calculating the resulting tire forces and torques arising in a tire contact patch are known, which are generally based on a corresponding tire model for mapping the tire properties or “FTire” (Cosin Scientific Software), “MF-Tire” and “MF-Swift” (both Delft-Tire) tire models sold under these names.

Methods for designing vehicle components based on the methods described above are also known in principle. Driving simulators and corresponding methods for controlling them are also known in principle from the prior art.

TASK AND SOLUTION

Against this background, it is therefore an object of the present invention to provide an alternative method, in particular an improved method for determining at least one circumferential contour parameter of a parameterized circumferential contour function and an alternative method, in particular an improved method for determining at least one soil pressure distribution parameter of a parameterized soil pressure distribution function , which in particular each allow a simple further use of an associated circumferential contour function or a ground pressure distribution function, for example to determine, in particular to predict, a tire contact area resulting, ie established, under a defined load on a tire and / or a resulting, ie established, ground pressure distribution in a tire contact area and / or for calculating tire forces arising in a tire contact area.

In addition, it is an object of the present invention to provide an alternative method, in particular an improved method, in particular a simulation method, for determining, in particular for predicting, an expansion of a tire contact area that occurs when a tire is subjected to a defined load, with which in particular a tire contact area Steering while stationary and / or when maneuvering adjusting expansion of the tire contact area can be determined, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, preferably with a high degree of accuracy and in particular taking into account a changing camber angle during a steering angle.

Furthermore, it is an object of the present invention to provide an alternative method, in particular an improved method, in particular a simulation method, for determining, in particular for predicting, a ground pressure distribution that is established in a tire contact patch with a defined load on a tire, with which, in particular, a When steering while stationary and / or when maneuvering, ground pressure distribution can be determined, preferably as a function of a load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, preferably with a high degree of accuracy and in particular taking into account a self camber angle changing during a steering angle.

In addition, an object of the present invention is to provide an alternative method, in particular an improved method, for calculating at least one resulting tire force and / or at least one resulting tire torque resulting from frictional forces in a tire contact patch, in particular when steering while stationary and / or when maneuvering, preferably as a function of a load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, preferably with a high degree of accuracy and in particular taking into account a camber angle that changes during a steering angle.

Furthermore, it is still an object of the present invention to provide an alternative, in particular improved method for designing at least one component of a vehicle, preferably for designing a steering arrangement, in particular for designing a rack of a steering gear, which in particular enables the most precise dimensioning possible, as well as a to provide an alternative, in particular advantageous method for operating a driving simulator, an alternative, in particular advantageous computer program, an alternative, in particular advantageous computer-readable medium and an alternative, in particular improved, driving simulator.

These objects are achieved by the various subjects of the invention according to the respective independent claims, in particular by a method with the features of claim 1, by a method with the features of claim 2, by a method with the features of claim 3, by a method with the Features of claim 4, by a method having the features of claim 5, by a method having the features of claim 6, by a method having the features of claim 7, by a method having the features of claim 8, by a method having the Features of claim 9, by a method with the features of claim 10, by a computer program with the features of claim 11, by a computer-readable medium with the features of claim 12 and by a driving simulator with the features of claim 13. Advantageous and preferred embodiments of the invention are the subject of the further claims and will be described in the following n explained later. The wording of the claims is made part of the content of the description by express reference.

TO THE FIRST ASPECT

ist, welcher eine zugehörige Koordinatentransformation für eine Verschiebung des Umfangskonturfunktion-Koordinatenursprungs des Umfangskonturfunktion-Koordinatensystems SE in einen Reifenlatsch-Koordinatenursprung eines Reifenlatsch-Koordinatensystems LR definiert.A method according to the first aspect of the present invention for determining at least one circumferential contour parameter of a parameterized tire contact patch circumferential contour function is characterized in that at least one circumferential contour parameter that is determined is a coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

which is an associated coordinate transformation for a shift of the circumferential contour function coordinate origin of the circumferential contour function coordinate system SE into a tire contact coordinate origin of a tire contact coordinate system LR Are defined.

The tire contact patch circumferential contour function is a function by means of which a circumferential contour is set under a defined load for a tire, in particular for a defined tire, preferably for a tire supported on a flat surface, in particular for a tire mounted on a rim Tire contact area can be described, in particular a circumferential contour of a tire contact area that occurs when steering while stationary and / or when maneuvering, preferably as a function of a load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, the parameterized Tire footprint circumferential contour function in relation to a circumferential contour function coordinate system with a circumferential contour function coordinate origin and defined by at least one independent variable and at least one parameter, and wherein at least one circumference Contour parameter is determined from a tire contact area imprint of a tire contact area of a tire, which has set itself or is to be expected as a function of a defined load on the tire, in particular as a function of a tire condition and / or one or more tire properties.

ermöglicht zum einen eine einfache Beschreibung einer Reifenaufstandsflächen-Umfangskonturfunktion, und zwar in Bezug auf ein zugehöriges, insbesondere entsprechend für die jeweilige, verwendete Reifenaufstandsflächen-Umfangskonturfunktion geeignetes Umfangskonturfunktion-Koordinatensystem, und zum anderen auf einfache Art und Weise eine Weiterverwendung der Reifenaufstandsflächen-Umfangskonturfunktion, beispielsweise zur Ermittlung einer sich abhängig von der Umfangskontur einstellenden Bodendruckverteilung und/oder zur Ermittlung von in der Reifenaufstandsfläche entstehenden Reifenkräften, da durch den ermittelten Koordinatentransformationsvektor ${}_{LR}{\overrightarrow{r}}_{SE}$

auf einfache Art und Weise ein Bezug zum Reifenlatsch-Koordinatensystem LR hergestellt werden kann, welches sich als Bezugs-Koordinatensystem hierfür besonders gut eignet, insbesondere für eine Ermittlung einer sich einstellenden Umfangskontur der Reifenaufstandsfläche und/oder einer sich einstellenden Bodendruckverteilung und/oder für eine Ermittlung von in der Reifenaufstandsfläche entstehenden Reifenkräften.The determination of the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

enables on the one hand a simple description of a tire contact area circumferential contour function, namely in relation to an associated circumferential contour function coordinate system that is particularly suitable for the respective tire contact area circumferential contour function used, and on the other hand it allows further use of the tire contact area circumference contour function in a simple manner, for example to determine a ground pressure distribution that is established as a function of the circumferential contour and / or to determine tire forces that arise in the tire contact patch, since by the determined coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

a reference to the tire contact coordinate system in a simple manner LR can be produced, which is particularly well suited as a reference coordinate system for this, in particular for determining a circumferential contour of the tire contact patch that is established and / or a soil pressure distribution that is established and / or for determining tire forces arising in the tire contact patch.

auf den Reifen wirken, d.h. wenn gilt ${\overrightarrow{F}}_y=0$

und ${\overrightarrow{F}}_x=\mathrm{0,}$

mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt. The tire contact coordinate system LR is preferably a right-handed, Cartesian, latsch-fixed coordinate system, the coordinate origin of which is in a latsch reference point LR where the Laces reference point LR is preferably chosen such that it is at a camber angle of γ = 0 °, with a straight-ahead position of the tire, ie with a toe angle of δ _v =: 0 °, and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_y=0$

and ${\overrightarrow{\mathrm{F.}}}_x=\mathrm{0,}$

coincides with a tire center projected onto a road surface.

${\overrightarrow{F}}_x$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt.The Latsch coordinate system is particularly preferred LR In particular, it is selected in such a way that with a camber angle of γ = 0 °, with a straight ahead position of the tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,$

${\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results.

In the context of the present invention, the term “tire contact area” is understood to mean the contact area between the tire and the roadway or ground, ie the tire contact area, which is the actual contact area of the tire with the ground, the associated contact area of the tire in particular through a part of a tread of the tire is formed (as long as the tire does not sink into the ground, which is assumed here), and with which the tire rests on the ground. If, on the other hand, the tire sinks into the ground, part of the contact area of the tire, i.e. the tire contact area, is formed by the side wall of the tire, but this is not considered here.

The geometry of the tire contact patch, in particular its extent, and thus in particular its circumferential contour, depends on the condition of the tire (e.g. the tire inflation pressure), one or more tire properties (e.g. the tire size) and the load on the tire (especially the wheel load as well as a steering angle and / or a camber angle).

A tire subjected to a defined load is a tire subjected to a defined wheel load with a defined steering angle and a defined camber angle, with the wheel load, steering angle and camber angle being able to be changed over time.

dabei mithilfe einer oder mehrerer Profilgeometrieinformationen ermittelt, welche ein Profil des jeweiligen Reifens charakterisieren, insbesondere mithilfe einer oder mehrerer Rilleninformationen.In an advantageous embodiment of a method according to the first aspect of the present invention, the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

determined with the help of one or more profile geometry information that characterizes a profile of the respective tire, in particular with the help of one or more groove information.

verwendet werden.However, profile geometry information can also be a defined stamp pattern incorporated into the profile of the tire or a defined marking incorporated into the tire profile or the like, provided that the position of the profile geometry information is relative to the contact point reference point LR is known. That is, instead of one or more groove items of information, such as a groove width, a groove spacing or certain features of a groove pattern or the like, other profile geometry information can also be used to determine the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

be used.

auf den Reifen wirken, d.h. wenn gilt ${\overrightarrow{F}}_y=0$

und ${\overrightarrow{F}}_x=0$

, mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt.Via one or more profile geometry information, in particular by means of at least one groove information item of the associated tire, for example by means of one or more pieces of information that characterize the number of grooves and / or a distance between two grooves and / or a distance to a sidewall of the tire, which in particular is relative can be easily extracted from a tire contact area imprint, for example by means of a corresponding image data analysis, a defined contact area reference point can be determined in a particularly simple manner, in particular the contact area reference point LR , which is at a camber angle of γ = 0 °, with a straight-ahead position of the tire, ie at a toe angle of δ _v = 0 °, and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_y=0$

and ${\overrightarrow{\mathrm{F.}}}_x=0$

, coincides with a tire center projected onto a road surface.

kann insbesondere durch eine geometrische Analyse des Profils des zugehörigen Reifenaufstandsflächen-Abdrucks, beispielsweise durch eine Messung der Breite einer oder mehrerer Rillen, eines Abstands einer Rille zu einem Rand des Reifenflächen-Abdrucks oder zu einem anderen charakteristischen Punkt im Reifenaufstandsflächen-Abdruck, der beispielsweise bei real erfassten Reifenaufstandsflächen-Abdrücken auch wie vorstehend erläutert, durch ein definiertes, in das Profil des Reifens eingebrachtes Stempelmuster definiert sein kann, d.h. durch eine andere Profilgeometrieinformation als eine Rilleninformation, ermittelt werden.The coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

can in particular by a geometric analysis of the profile of the associated tire footprint, for example by measuring the width of one or more grooves, a distance of a groove to an edge of the tire footprint or to another characteristic point in the tire footprint, which is for example Really recorded tire contact patch marks can also be defined, as explained above, by a defined stamp pattern introduced into the profile of the tire, ie determined by profile geometry information other than groove information.

einfach ermittelt werden, vor allem auch bei Slick-Reifen oder bei Reifen mit einem wenig charakteristischen Rillenprofil. Grundsätzlich kann das Stempelmuster dabei in einem Randbereich eingebracht sein. In jedem Fall sollte allerdings sichergestellt sein, dass das Stempelmuster derart positioniert bzw. an einer Stelle eingebracht ist, welche stets innerhalb der Reifenaufstandsfläche liegt, damit z.B. auch bei hohen Sturzwinkeln sichergestellt ist, dass das Stempelmuster innerhalb der Reifenaufstandsfläche liegt und erfasst wird.In particular, with a stamp pattern introduced into the tire tread, which can particularly preferably be as small as possible and as little as possible influencing the ground pressure distribution and / or resulting tire forces, the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

can be easily determined, especially in the case of slick tires or tires with an uncharacteristic groove profile. In principle, the stamp pattern can be introduced in an edge area. In any case, however, it should be ensured that the stamp pattern is positioned or placed at a point that is always within the tire contact area, so that it is ensured, for example, even at high camber angles, that the stamp pattern is within the tire contact area and is detected.

relativ einfach bestimmen, was im weiteren Verlauf dieser Anmeldung noch erläutert wird.But even without such a stamp pattern or such a marking introduced into the profile and only from the profile information of a tire, the coordinate transformation vector can generally be determined ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

determine relatively easily what will be explained in the further course of this application.

vorzugsweise ein oder mehrere weitere Umfangskontur-Parameter erfasst, wobei insbesondere der Umfangskonturfunktions-Koordinatenursprung ermittelt wird und vorzugsweise ein oder mehrere Umfangskontur-Parameter jeweils mit Bezug auf das Umfangskonturfunktions-Koordinatensystem. Dazu wird bevorzugt wenigstens einer der folgenden Schritte durchgeführt, besonders bevorzugt sämtliche der folgenden Schritte:

1. (a) Bestimmen einer, insbesondere maximalen, Erstreckung des Reifenaufstandsflächen-Abdrucks in einer ersten Reifenlatscherstreckungs-Richtung, welche bezogen auf einen funktionsgemäßen Einbauzustand des Reifens in einem Fahrzeug vorzugsweise einer Fahrzeuglängsrichtung entspricht,
2. (b) Bestimmen einer, insbesondere maximalen, Erstreckung des Reifenaufstandsflächenabdrucks in einer sich senkrecht zur ersten Reifenlatscherstreckungs-Richtung erstreckenden zweiten Reifenlatscherstreckungs-Richtung, welche bezogen auf einen funktionsgemäßen Einbauzustand des Reifens in einem Fahrzeug vorzugsweise einer Fahrzeugquerrichtung entspricht,
3. (c) Ermitteln des Umfangskonturfunktion-Koordinatenursprungs in Abhängigkeit von der Erstreckung des Reifenaufstandsflächen-Abdrucks in der ersten Reifenlatscherstreckungs-Richtung und in Abhängigkeit von der Erstreckung des Reifenaufstandsflächen-Abdrucks in der zweiten Reifenlatscherstreckungs-Richtung,
4. (d) Ermitteln wenigstens eines Umfangskontur-Parameters der parametrisierten Reifenaufstandsflächen-Umfangskonturfunktion in Abhängigkeit von einem Abstand eines Umfangskonturpunktes des Reifenaufstandsflächen-Abdrucks zum Umfangskonturfunktion-Koordinatenursprung in der ersten Reifenlatscherstreckungs-Richtung und/oder der zweiten Reifenlatscherstreckungs-Richtung, und/oder
5. (e) Ermitteln wenigstens eines weiteren Umfangskontur-Parameters der parametrisierten Reifenaufstandsflächen-Umfangskonturfunktion, insbesondere wenigstens eines Krümmungs-Parameters, mithilfe eines Optimierungsverfahrens.

In a particularly advantageous embodiment of a method according to the first aspect of the present invention, in addition to the coordinate transformation vector $\mathrm{L.}{\mathrm{R.}}^{\overrightarrow{r}}\mathrm{S.}\mathrm{E.}$

preferably one or more additional circumferential contour parameters are recorded, with the circumferential contour function Origin of coordinates is determined and preferably one or more circumferential contour parameters each with reference to the circumferential contour function coordinate system. For this purpose, at least one of the following steps is preferably carried out, particularly preferably all of the following steps:

1. (a) Determination of an, in particular maximum, extension of the tire contact patch imprint in a first tire contact extension direction, which, based on a functional installation state of the tire in a vehicle, preferably corresponds to a vehicle longitudinal direction,
2. (b) Determining a, in particular a maximum, extension of the tire contact patch in a second tire contact extension direction extending perpendicular to the first tire contact extension direction, which, based on a functional installation state of the tire in a vehicle, preferably corresponds to a transverse direction of the vehicle,
3. (c) determining the circumferential contour function coordinate origin as a function of the extent of the tire contact area imprint in the first direction of tire contact area and as a function of the extent of the tire contact area imprint in the second direction of tire contact area extent,
4. (d) determining at least one circumferential contour parameter of the parameterized tire contact patch circumferential contour function as a function of a distance of a circumferential contour point of the tire contact patch to the circumferential contour function coordinate origin in the first tire contact extension direction and / or the second tire contact extension direction, and / or
5. (e) Determining at least one further circumferential contour parameter of the parameterized tire contact patch circumferential contour function, in particular at least one curvature parameter, with the aid of an optimization method.

In a particularly advantageous embodiment of a method according to the first aspect of the present invention, the steps a ) until e ) carried out one after the other, in particular in the order given above.

In a further development of a method according to the first aspect of the present invention, at least one independent variable particularly preferably defines a distance from a reference point in a defined direction, in particular a distance from the circumferential contour function coordinate origin in a defined direction.

wobei der Index i einen zugehörigen Funktionsabschnitt indiziert, wobei der Index SE das Umfangskonturfunktion-Koordinatensystem mit seinem Umfangskonturfunktion-Koordinatenursprung indiziert, wobei das Umfangskonturfunktion-Koordinatensystem ein kartesisches, rechtshändiges Superellipsen-Koordinatensystem ist, dessen Ursprung im Schnittpunkt der Halbachsen der zugehörigen Superellipse liegt, wobei eine Abszisse x_SE des rechtshändigen Superellipsen-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeughinten zeigt, eine zugehörige Applikate z_SE in Fahrzeughochrichtung nach unten und ein zugehörige Ordinate y_SE jeweils senkrecht auf der Abszisse x_SE und der Applikate z_SE steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, und wobei der Parameter a_i eine erste Halbachsenlänge in x_SE-Richtung der zugehörigen Superellipse definiert, der Parameter b_i eine zweite Halbachsenlänge in y_SE-Richtung der zugehörigen Superellipse und die beiden übrigen Parameter n_i, m_i jeweils Krümmungsparameter zur Parametrisierung einer Krümmung der Superellipse sind.The parameterized tire contact patch circumferential contour function is preferably a two-dimensional function defined in Cartesian coordinates, in particular as described below in connection with a method according to the fourth aspect of the present invention and defined at least in sections by a 4-parameter superellipse. The parameterized tire contact patch circumferential contour function is particularly preferably defined by: $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0},$$

where the index i indexes an associated functional section, the index SE the circumferential contour function coordinate system is indexed with its circumferential contour function coordinate origin, the circumferential contour function coordinate system being a Cartesian, right-handed superellipse coordinate system, the origin of which lies at the intersection of the semiaxes of the associated superellipse, with an abscissa x _{SE of} the right-handed superellipse coordinate system in the longitudinal direction of the vehicle shows, an associated applicate z _SE in the vertical direction of the vehicle downwards and an associated ordinate y _SE each perpendicular to the abscissa x _SE and the applicate z _SE , in particular in such a way that a right-handed, Cartesian coordinate system results, and the parameter a _{i is} a first semiaxis length in x _SE direction of the associated superellipse, the parameter b _i defines a second semiaxis length in y _SE direction of the associated superellipse and the two remaining parameters n _i , m _i each have curvature parameters for parameterization r are the curvature of the superellipse.

If the circumferential contour function is defined, for example, as described above or as in a method according to the fourth aspect of the present invention, at least in sections by a 4-parametric superellipse, it is advisable to determine the circumferential contour function coordinate origin, for example, by initially determining the maximum extent of the tire contact area in a first To determine the tire contact extension direction, which preferably corresponds to a vehicle longitudinal direction based on a functional installation state of the tire in a vehicle, and the maximum extent of the tire contact patch in a second tire contact extension direction, which preferably corresponds to a vehicle transverse direction based on a functional installation state of the tire in a vehicle , and to define the point of intersection of the two lines along the respective maximum extensions as the circumferential contour function coordinate origin. At least one parameter of the 4-parametric superellipse can then be determined, for example, by determining a distance between the circumferential contour and the circumferential contour function coordinate origin along one of the routes along the maximum extent, in particular the parameters a _i and b _i , respectively.

For the determination of at least one further circumferential contour parameter of the parameterized tire contact patch circumferential contour function according to step e ) With the aid of an optimization method, in particular at least one curvature parameter, for example one of the parameters n _i, m _i , the most varied of mathematical optimization methods or algorithms known from the prior art can be used. However, the use of an optimization method based on minimizing the distance squares has proven to be particularly advantageous for this purpose.

In a particularly advantageous embodiment of the method according to the first aspect of the invention, at least one further circumferential contour parameter, in particular at least one curvature parameter, for example one of the parameters n _i, m _i , is preferably determined by a mathematical optimization method that is based in particular on a minimization a distance of an envelope contour function to the circumferential contour of the tire contact area imprint, the envelope contour function being determined in particular with the aid of an image data analysis from recorded tire contact imprints. The mathematical optimization method is preferably carried out with the aid of the parameterized tire contact patch circumferential contour function and in particular only after the steps a ) until d ) have been carried out, with particular preference being given to assuming a reasonable start value for the at least one parameter to be determined by optimization, and for the other parameters in particular the values obtained by executing the steps a ) until d ) have been determined. This enables a particularly simple and thus particularly efficiently realizable optimization.

In a method according to the first aspect of the present invention, at least one circumferential contour parameter is particularly preferably determined by means of image data analysis from a tire contact area imprint of a tire contact area of a tire, which is determined as a function of a defined load on the tire, preferably also as a function of a tire condition and / or one or more tire properties. This enables a relatively simple parameter identification.

For the identification of the parameters of the circumferential contour function, it is not absolutely necessary to use actually recorded tire contact area imprints. In principle, tire footprint imprints calculated on the basis of simulation methods can also be used for parameter identification for determining the circumferential contour parameters. However, the model on which the respective simulation is based should be sufficiently precise for this purpose in order to obtain a correspondingly precise and sufficiently usable circumferential contour function as a result. This enables a particularly flexible application of the method for parameter identification.

In a further, particularly advantageous embodiment of a method according to the first aspect of the present invention, one or more circumferential contour parameter data sets are determined for at least one circumferential contour parameter, in particular for all circumferential contour parameters, the respective circumferential contour parameter preferably in each case is determined from various tire contact patch imprints (recorded in real terms or as the result of a simulation process) that have occurred (real) or are expected (simulation) as a function of various, defined loads on the tire, in particular as a function of various wheel loads, tire inflation pressures and / or camber angles, and / or for different tires with different tire properties.

This makes it possible, in particular in a simple manner, to determine for each circumferential contour parameter a corresponding set of parameters from tire contact area imprints at different, defined loads and / or for different tire conditions and / or tire properties. In this way, a parameterization of the circumferential contour function can be achieved in a simple manner as a function of different wheel loads, tire inflation pressures and / or camber angles, and / or for different tires with different tire properties. As a result, the number of possible uses of the circumferential contour function, in which one is established by this Tire contact patch circumferential contour can be written with sufficient accuracy, can be increased. In particular, if one or more of the parameters are determined as a function of different camber angles or for different camber angles, this opens up the possibility of a suitably selected circumferential contour function, for example such as a circumferential contour function defined according to the fourth aspect of the present invention, even when steering while standing and / or to describe or predict an emerging circumferential contour reliably and with a high degree of accuracy when maneuvering.

ON THE SECOND ASPECT

1. (a) Unterteilen der Reifenaufstandsfläche in einer ersten Bodendruckverteilungs-Richtung in mehrere Abschnitte, vorzugsweise in mehrere, zumindest teilweise äquidistante Abschnitte, wobei die erste Bodendruckverteilungs-Richtung vorzugsweise bezogen auf einen funktionsgemäßen Einbauzustand des Reifens in einem Fahrzeug einer Fahrzeugquerrichtung entspricht, und
2. (b) Ermitteln eines statistisch repräsentativen, Bodendruckwertes, insbesondere eines mittleren Bodendruckwertes, für wenigstens einen der Abschnitte, vorzugsweise für jeden Abschnitt, aus wenigstens zwei definierten Punkten der Reifenaufstandsfläche, die innerhalb dieses Abschnitts liegen und jeweils einen gleichen Koordinatenwert in einer zweiten Bodendruckverteilungs-Richtung aufweisen, insbesondere aus sämtlichen definierten Punkten der Reifenaufstandsfläche, die innerhalb dieses Abschnitts liegen und jeweils einen gleichen Koordinatenwert in der zweiten Bodendruckverteilungs-Richtung aufweisen, wobei die zweite Bodendruckverteilungs-Richtung vorzugsweise bezogen auf einen funktionsgemäßen Einbauzustand des Reifens in einem Fahrzeug einer Fahrzeuglängsrichtung entspricht.

A method according to the second aspect of the present invention for determining at least one soil pressure distribution parameter of a parameterized soil pressure distribution function is characterized according to the invention by the steps:

1. (a) Subdivide the tire contact patch in a first direction of ground pressure distribution into several sections, preferably into several, at least partially equidistant sections, the first direction of soil pressure distribution preferably corresponding to a transverse direction of the vehicle in relation to a functional installation state of the tire in a vehicle, and
2. (b) Determination of a statistically representative ground pressure value, in particular a mean ground pressure value, for at least one of the sections, preferably for each section, from at least two defined points of the tire contact patch that lie within this section and each have the same coordinate value in a second direction of ground pressure distribution in particular from all defined points of the tire contact area that lie within this section and each have the same coordinate value in the second ground pressure distribution direction, the second ground pressure distribution direction preferably corresponding to a vehicle longitudinal direction based on a functional installation state of the tire in a vehicle.

The ground pressure distribution function is a function by means of which a ground pressure distribution, which occurs under a defined load for a tire, in particular for a defined tire, preferably for a tire supported on a flat surface, in particular a tire mounted on a rim, in an associated, is mathematically describable under the defined load setting tire contact area, in particular a ground pressure distribution that occurs when steering while stationary and / or when maneuvering, preferably as a function of the load on the tire, in particular also as a function of a tire condition and / or one or more Tire properties, wherein the parameterized ground pressure distribution function is defined in relation to a tire contact coordinate system with a tire contact coordinate origin and by at least one independent variable and at least one ground pressure distribution parameter rt, where at least one ground pressure distribution parameter is determined from a ground pressure distribution in a tire contact patch, which has set or is expected as a function of a defined load on the tire, in particular also as a function of a tire condition and / or one or more tire properties and an associated ground pressure value is present for defined points of the tire contact area, each of which is clearly defined by its coordinates in relation to the tire contact coordinate system.

A method according to the second aspect of the invention enables a particularly simple and thus efficiently realizable parameter identification for the identification of parameters of a parameterized ground pressure distribution function for the mathematical description of a ground pressure distribution in a tire contact patch of a tire, the method according to the invention also having the advantage that it is particularly sufficiently accurate Provides parameter values in order to describe the resulting soil pressure distribution with sufficient accuracy in many applications.

In a particularly advantageous embodiment of a method according to the second aspect of the invention, for at least one of the sections, in particular for each section, for at least two different coordinate values, in particular for all coordinate values, in the second soil pressure distribution direction, for each of which at least one defined point Within the tire contact area, each with an associated ground pressure value, exists, as described above, in each case a statistically representative ground pressure value, in particular a mean ground pressure value, is determined. In this way, the parameter values can be identified particularly precisely, since as a result more statistically representative ground pressure values are available for the parameter identification, which in turn enables a particularly precise, partially improved description of the ground pressure distribution in the tire contact area in many applications. In particular, this gives a vector of statistically representative ground pressure values for the Parameter identification, in particular for the respective coordinate values for which a statistically representative ground pressure value has been determined.

A statistically representative ground pressure value can in principle be both a mean ground pressure value, which in particular can be determined arithmetically or geometrically, but alternatively also a median value or another statistically representative variable.

The tire contact coordinate system is particularly preferably defined as described above in connection with a method according to the first aspect of the invention, with this explicitly referring to the above statements on the tire contact coordinate system in order to avoid repetitions LR is referred. The ground pressure distribution function is particularly preferably also defined in relation to such a coordinate system, in particular to the above-described tire contact coordinate system LR .

In a method according to the second aspect of the present invention, at least one soil pressure distribution parameter is particularly preferably determined by means of an image data analysis from a soil pressure distribution in a tire contact patch, which is dependent on a defined load on the tire, preferably also dependent on a tire condition and / or one or more tire properties.

For the identification of the parameters of the soil pressure distribution function, however, it is not absolutely necessary to use real recorded soil pressure distributions. In principle, soil pressure distributions calculated on the basis of simulation methods can also be used to identify parameters for determining the soil pressure distribution parameters. However, the model on which the respective simulation is based should be sufficiently precise in order to obtain a correspondingly precise and sufficiently usable soil pressure distribution function as a result.

The parameterized soil pressure distribution function is preferably also a two-dimensional function defined in Cartesian coordinates.

In a further advantageous embodiment of a method according to the second aspect of the invention, at least one soil pressure distribution parameter of the soil pressure distribution function is preferably a parameterized regression function, by means of which a course of the determined, statistically representative soil pressure values in the first soil pressure distribution direction or the second soil pressure distribution direction is mathematical can be described, at least one regression parameter, in particular all regression parameters, of the parameterized regression function preferably being determined by a mathematical optimization method. This enables a particularly advantageous, particularly precise mathematical description of the ground pressure distribution that is established in the tire contact patch.

wobei die Bodendruckverteilungsfunktion insbesondere in Bezug auf das eingangs im Zusammenhang mit dem ersten Aspekt der Erfindung beschriebene Reifenlatsch-Koordinatensystem definiert ist, welche ein definiertes, rechtshändiges, kartesisches, latschfestes Koordinatensystem ist, dessen Koordinatenursprung in einem Latsch-Referenzpunkt LR liegt, wobei der Latsch-Referenzpunkt LR vorzugsweise derart gewählt ist, dass er bei einem Sturzwinkel von γ = 0° und bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x$

auf den Reifen wirken, mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt, und wobei das Latsch-Koordinatensystem insbesondere derart gewählt ist, dass bei einem Sturzwinkel von γ = 0°, bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x,$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt. Dabei ist x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x -Koordinate eines Punktes der Lauffläche des Reifens, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist. N_x(y_LR ) ist dabei eine Normierungsfunktion zur Normierung des Koordinatenwertes von x_LR auf eine Länge einer Erstreckung der Reifenaufstandsfläche in x-Richtung, insbesondere in Abhängigkeit von dem Koordinatenwert y_LR , N_y(x_LR ,y_LR ) eine Abbildungsfunktion zur Abbildung des Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, insbesondere in Abhängigkeit von dem Koordinatenwertepaar (x_LR , y_LR ), A(ŷ_LR) eine Skalierungsfunktion, die einen ersten Bodendruckverteilungs-Parameter, insbesondere einen Skalierungsparameter, in Abhängigkeit von y_LR definiert, und B(ŷ_LR) eine Krümmungsfunktion, die einen zweiten Bodendruckverteilungsparameter, insbesondere einen Krümmungsparameter, in Abhängigkeit von y_LR definiert.In a particularly preferred embodiment, the soil pressure distribution function is defined in particular as described in connection with a method according to the sixth aspect of the present invention. The soil pressure distribution function is particularly preferably defined by: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right],\\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

wherein the ground pressure distribution function is defined in particular with reference to the tire contact coordinate system described at the beginning in connection with the first aspect of the invention, which is a defined, right-handed, Cartesian, non-slip coordinate system whose coordinate origin is in a contact point reference point LR where the Laces reference point LR is preferably selected such that it is at a camber angle of γ = 0 ° and with a straight ahead position of the tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that with a camber angle of γ = 0 °, with a straight-ahead position of the tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x,$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle pointing to the front of the vehicle and an associated applique z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results. It is x _LR one on the tire contact coordinate system LR Relative x -coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR is. N _x ( y _LR ) is a normalization function for normalizing the coordinate value of x _LR to a length of an extension of the tire contact patch in the x direction, in particular as a function of the coordinate value y _LR , N _y ( x _LR , y _LR ) a mapping function for mapping the coordinate value of y _LR to a defined range of values depending on a length of an extension of the tire contact patch in the y-direction, in particular depending on the coordinate value pair ( x _LR , y _LR ), A (ŷ _LR ) is a scaling function which a first soil pressure distribution parameter, in particular a scaling parameter, as a function of y _LR defines, and B (ŷ _LR) a curvature function which a second soil pressure distribution parameter, in particular a curvature parameter, as a function of y _LR Are defined.

wobei N_y (x_LR , y_LR ) wie vorbeschrieben eine Abbildungsfunktion ist zur Abbildung eines Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, wobei die Länge der Erstreckung der Reifenaufstandsfläche abhängig von x_LR ist, jeweils bezogen auf das Latsch-Koordinatensystem LR. Hierdurch lässt sich eine besonders vorteilhafte und genaue, aber dennoch einfache mathematische Beschreibung der Bodendruckverteilung in der ersten Bodendruckverteilungs-Richtung erreichen.In a particularly advantageous embodiment of a method according to the second aspect of the invention, a course of the determined, statistically representative soil pressure values in the first soil pressure distribution direction is described mathematically by means of a soil pressure distribution parameter of the soil pressure distribution function, which is determined, in particular by means of a first soil pressure distribution parameter , wherein the first soil pressure distribution parameter is preferably the scaling parameter defined by the scaling function A (ŷ _LR ) as a function of a mapping variable ŷ _LR , and wherein the scaling function A (ŷ _LR ) is preferably a parameterized regression function, in particular a sixth degree polynomial , which is defined by: $$\begin{array}{l}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{a1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{6th}}+p_{a2}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^5+p_{a3}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{4th}}+p_{a\mathrm{4th}}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^3+p_{a5}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+p_{a\mathrm{6th}}\cdot {\widehat{y}}_{\mathrm{L.}\mathrm{R.}}+p_{a\mathrm{7th}}\\ \text{with}{p}_{a\mathrm{1..7}}\in \square \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

where N _y ( x _LR , y _LR ) as described above is a mapping function for mapping a coordinate value of y _LR to a defined range of values as a function of a length of an extension of the tire contact patch in the y-direction, the length of the extension of the tire contact patch depending on x _LR is based on the Laces coordinate system LR . This makes it possible to achieve a particularly advantageous and precise, but nevertheless simple mathematical description of the soil pressure distribution in the first soil pressure distribution direction.

In a particularly preferred embodiment of a method according to the invention according to the second aspect of the present invention, the regression parameters of the parameterized regression function A (ŷ _LR ) are determined by a mathematical optimization method, the optimization method used in particular on minimizing a distance between the associated regression function and the determined , statistically representative ground pressure values are based in the first ground pressure distribution direction.

wobei N_y(x_LR ,y_LR ) insbesondere dieselbe Abbildungsfunktion ist, welche bereits mehrfach eingehend beschrieben worden ist zur Abbildung des Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, wobei die Länge der Erstreckung der Reifenaufstandsfläche abhängig von x_LR ist, jeweils bezogen auf das Latsch-Koordinatensystem LR. Damit ist B(ŷ_LR) im Ergebnis auch von x_LR und damit der ersten Richtung abhängig.In a particularly advantageous embodiment of a method according to the second aspect of the invention, a course of the determined, statistically representative soil pressure values in the second soil pressure distribution direction is mathematically determined by means of a further soil pressure distribution parameter of the soil pressure distribution function, which is determined, in particular by means of a second soil pressure distribution parameter The second soil pressure distribution parameter is preferably the curvature parameter defined by the curvature function B (ŷ _LR) as a function of the mapping variable ŷ _LR , the curvature function B (ŷ _LR) preferably (also) being a parameterized regression function, in particular a Second degree polynomial defined by: $$\begin{array}{l}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{b1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\cdot {\widehat{y}}_{\mathrm{L.}\mathrm{R.}}+{\mathrm{<figure-callout\; id="3"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\\ \text{with}{\mathrm{<figure-callout\; id="1"\; label="p\; b"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\in \square \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

where N _y ( x _LR , y _LR ) is in particular the same mapping function that has already been described in detail several times for mapping the coordinate value of y _LR to a defined range of values in Dependence on a length of an extension of the tire contact patch in the y-direction, the length of the extension of the tire contact patch depending on x _LR is based on the Laces coordinate system LR . Hence B (ŷ _LR ) is also of as a result x _LR and thus dependent on the first direction.

In a particularly preferred embodiment of a method according to the invention according to the second aspect of the present invention, the regression parameters of the parameterized regression function B (ŷ _LR ) are preferably also determined by a mathematical optimization method, the optimization method used in particular on minimizing a distance between the associated regression function and the determined, statistically representative ground pressure values are based in the second ground pressure distribution direction.

In a further advantageous embodiment of a method according to the invention according to the second aspect of the present invention, in particular in a further development, one or more soil pressure distributions are used for at least one soil pressure distribution parameter, in particular for the first soil pressure distribution parameter and / or for the second soil pressure distribution parameter Parameter data sets and / or one or more regression parameter data sets are determined, in particular for each regression parameter of a soil pressure distribution parameter, the respective soil pressure distribution parameter and / or the respective regression parameter being determined from different soil pressure distributions that are dependent on have set or are expected to have different, defined loads on the tire, in particular as a function of different wheel loads, tire inflation pressures and / or camber angles, and / or for different tires with differing fine tire properties.

This makes it possible, in particular in a simple manner, to determine a corresponding set of parameters from soil pressure distributions at different, defined loads and / or for different tire conditions and / or tire properties for each soil pressure distribution parameter.

In a particularly advantageous embodiment of a method according to the invention according to the second aspect of the present invention, in particular in a further development, the soil pressure distribution parameters A (ŷ _LR ) and B (ŷ _LR ) are determined for each of the sections described above result in a series of parameters or several data sets of parameters. Depending on the number n of sections, n rows of parameters or n times several data sets of parameters then result for the tire contact area.

This allows the ground pressure distribution function to be parameterized in a simple manner as a function of different wheel loads, tire inflation pressures and / or camber angles, and / or for different tires with different tire properties. As a result, the number of possible applications of the ground pressure distribution function, in which a tire contact patch circumferential contour that is established can be described with sufficient accuracy by this function, can be increased. In particular, if one or more of the parameters are determined as a function of different camber angles or for different camber angles, this opens up the possibility of a suitably selected ground pressure distribution function, for example like a ground pressure distribution function defined according to the sixth aspect of the present invention, even when steering while standing and / or to describe or predict an established ground pressure distribution function reliably and with a high degree of accuracy when maneuvering.

ON THE THIRD ASPECT

A computer-implemented method according to the third aspect of the present invention, in particular a simulation method, for determining, in particular for predicting, an expansion of a tire contact area of a defined loaded tire, preferably a tire supported on a flat surface, in particular a tire mounted on a rim , in particular for determining a tire contact area that occurs when steering while stationary and / or when maneuvering, preferably as a function of a load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, is characterized in that at least one circumferential contour Parameters of the circumferential contour function used is or has been determined by a method according to the invention according to the first aspect of the invention, with particularly preferably all circumferential contour parameters of the tire contact area circumference ang contour function can be determined or have been determined by means of this method. This enables efficient Parameter identification and a particularly good, particularly precise description or prediction of the extent of the tire contact patch that is established.

The tire contact area circumferential contour function, by means of which the extent of a tire contact area is determined, is a parameterized tire contact area circumferential contour function, which describes a circumferential contour of the tire contact area in particular mathematically, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, wherein the tire contact patch circumferential contour function is defined in relation to a circumferential contour function coordinate system with a circumferential contour function coordinate origin and by at least one independent variable and at least one circumferential contour parameter.

In the context of the invention, the term “extension of the tire contact area” is understood to mean the areal extent of the tire contact area in the road plane, the tire contact area extending within an associated circumferential contour or being limited in its extent by the associated circumferential contour.

The circumferential contour function used to determine the extent of the tire contact area that is established is particularly preferably suitable for maneuvering (slow driving and steering up to the maximum possible steering angle) and / or when parking (steering while standing up to the maximum possible steering angle ), in particular to describe a circumferential contour that occurs during a stationary parking maneuver, preferably with sufficient accuracy for both braked steering (steering when the brake is applied) and for unbraked steering (steering when the brake is not applied).

Depending on the rolling portion of the tire, the respective tire contact areas and the frictional forces arising in the tire contact area differ in size. Since the tires cannot roll when the vehicle is stationary, especially when parking while stationary, the frictional forces generated in the tire contact are greatest here, especially when steering is braked. Thus, this maneuver usually represents the borderline case of the steering forces occurring in the tire contact and the tire forces occurring during this maneuver, in particular the friction forces occurring in the tire contact, form an important basis for the design of one or more vehicle components such as a steering system.

The more precisely and precisely the extent of the tire contact area that is established and the tire forces occurring in this in the tire contact area, in particular the friction forces occurring in the tire contact area, especially during maneuvering and / or parking, can be determined, in particular can be predicted, for example by a corresponding simulation, the better can a needs-based design be implemented, in particular a particularly targeted design that is as little oversized as possible, ie a design with as little as possible but sufficient safety reserve. This can be achieved particularly well with a method according to the invention in accordance with the third aspect of the invention, since the method according to the invention can achieve a particularly good and thus precise mathematical description of the circumferential contour of a tire contact patch that is being set, with the help of which, in turn, a particularly good and thus a precise mathematical description of a ground pressure distribution that is established in the tire contact area can be determined and, by means of this, the corresponding tire forces.

It is particularly advantageous if the circumferential contour function used is designed and suitable for setting a circumferential contour with sufficient accuracy as a function of camber angles of approximately -3 ° to 9 °, preferably -5 ° and / or up to 12 ° to describe. The circumferential contour function used is particularly preferably selected in such a way that the circumferential contour of the tire contact patch that is established can also be described mathematically with sufficient accuracy over a larger camber angle range.

The circumferential contour function used to determine the extent of the tire contact area that is established is also preferably selected or particularly suitable for describing the circumferential contour of the tire contact area that is established on paved ground, for example for a paved road such as an asphalt roadway, in particular with sufficient accuracy, ie for a ground which is so firm that the tire does not sink in and only the tread forms a contact surface with the ground, but not one of the sidewalls or sidewalls of the tire.

Preferably, the circumferential contour function used to determine the extent of the tire contact area that is established is also selected or particularly suitable for the extent of the tire contact area that is established to be sufficient for a radial tire, in particular for a tire of a two-lane vehicle, in particular for a tire of a passenger car to determine exactly.

wobei der Index i einen zugehörigen Funktionsabschnitt indiziert, wobei der Index SE ein kartesisches, rechtshändiges Superellipsen-Koordinatensystem indiziert, dessen Ursprung im Schnittpunkt der Halbachsen der zugehörigen Superellipse liegt, wobei eine Abszisse x_SE des rechtshändigen Superellipsen-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeughinten zeigt, eine zugehörige Applikate z_SE in Fahrzeughochrichtung nach unten und ein zugehörige Ordinate y_SE jeweils senkrecht auf der Abszisse x_SE und der Applikate z_SE steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, und wobei der Parameter a_i eine erste Halbachsenlänge in x_SE-Richtung der zugehörigen Superellipse definiert, der Parameter b_i eine zweite Halbachsenlänge in y_SE-Richtung der zugehörigen Superellipse und die beiden übrigen Parameter n_i, m_i jeweils Krümmungsparameter zur Parametrisierung einer Krümmung der Superellipse sind.The tire contact area circumferential contour function that is used is particularly preferred, in particular a circumferential contour function which describes the circumferential contour of the tire contact area in particular mathematically, and at least in sections, in particular in a functional section i , by a 4-parametric superellipse according to the following formula and as described in detail below in connection with a method according to the invention according to the fourth aspect, is defined by: $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0},$$

where the index i indexes an associated functional section, the index SE a Cartesian, right-handed superellipse coordinate system whose origin lies at the intersection of the semiaxes of the associated superellipse, with an abscissa x _SE of the right-handed super-elliptical coordinate system in the longitudinal direction of the vehicle towards the rear of the vehicle shows an associated applicate z _SE in the vehicle vertical direction downwards and an associated ordinate y _SE each perpendicular to the abscissa x _SE and the applicate z _SE stands, in particular such that a right-handed, Cartesian coordinate system results, and the parameter a _i defines a first semiaxis length in the x _SE direction of the associated superellipse, the parameter b _i a second semiaxis length in the y _SE direction of the associated superellipse and the the other two parameters n _i , m _{i are} each curvature parameters for parameterizing a curvature of the superellipse.

For the curvature parameters n _i , m _{i , n i} , m _i ∈ R ^{> 0} applies in particular. In a particularly advantageous embodiment of a method according to the invention, however, n _i , m _i ∈ R ^{> 1} applies.

ON THE FOURTH ASPECT

wobei der Index i einen zugehörigen Funktionsabschnitt indiziert, wobei der Index SE ein kartesisches, rechtshändiges Superellipsen-Koordinatensystem indiziert, dessen Ursprung im Schnittpunkt der Halbachsen der zugehörigen Superellipse liegt, wobei eine Abszisse x_SE des rechtshändigen Superellipsen-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeughinten zeigt, eine zugehörige Applikate z_SE in Fahrzeughochrichtung nach unten und ein zugehörige Ordinate y_SE jeweils senkrecht auf der Abszisse x_SE und der Applikate z_SE steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, und wobei der Parameter a_i eine erste Halbachsenlänge in y_SE-Richtung der zugehörigen Superellipse definiert, der Parameter b_i eine zweite Halbachsenlänge in x_SE-Richtung der zugehörigen Superellipse und die beiden übrigen Parameter n_i, m_i, jeweils Krümmungsparameter zur Parametrisierung einer Krümmung der Superellipse sind. Eine derartige Umfangskonturfunktion ermöglicht eine besonders einfache und ausreichend genaue mathematische Beschreibung der sich einstellenden Reifenaufstandsfläche.A computer-implemented method according to the fourth aspect of the present invention, in particular a simulation method, for determining, in particular for predicting, an expansion of a tire contact area of a defined loaded tire, preferably a tire supported on a flat surface, in particular a tire mounted on a rim , in particular for determining a tire contact area that occurs when steering while stationary and / or when maneuvering, preferably depending on the load on the tire, in particular also depending on a tire condition and / or one or more tire properties, is characterized in that the tire contact area Perimeter contour function that is used, at least in sections, in particular in a functional section i , is defined by a 4-parametric superellipse according to the following formula: $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0},$$

where the index i indexes an associated functional section, the index SE a Cartesian, right-handed superellipse coordinate system whose origin lies at the intersection of the semiaxes of the associated superellipse, with an abscissa x _SE of the right-handed super-elliptical coordinate system in the longitudinal direction of the vehicle towards the rear of the vehicle shows an associated applicate z _SE in the vehicle vertical direction downwards and an associated ordinate y _SE each perpendicular to the abscissa x _SE and the applicate z _SE stands, in particular in such a way that a right-handed, Cartesian coordinate system results, and the parameter a _i defines a first semiaxis length in y _SE direction of the associated superellipse, parameter b _i a second semiaxis length in x _SE direction of the associated superellipse and the the other two parameters n _i, m _{i are} each curvature parameters for parameterizing a curvature of the superellipse. Such a circumferential contour function enables a particularly simple and sufficiently precise mathematical description of the tire contact patch that is established.

The tire contact area circumferential contour function is, as in a method according to the third aspect of the present invention, a parameterized tire contact area circumferential contour function which mathematically describes a circumferential contour of the tire contact area, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, wherein the tire contact patch circumferential contour function is defined in relation to a circumferential contour function coordinate system with a circumferential contour function coordinate origin and by at least one independent variable and at least one circumferential contour parameter.

For the curvature parameters n _i , m _{i , n i} , m _i ∈ R ^{> 0} applies in particular. In a particularly advantageous embodiment of a method according to the invention, however, n _i , m _i ∈ R ^{> 1} applies.

In a further, particularly advantageous embodiment of a method according to the third or fourth aspect of the invention, at least one circumferential contour parameter of the circumferential contour function that is used is determined by a method according to the invention according to the first aspect of the invention or has been determined in this way. This enables a particularly simple and sufficiently precise mathematical description of the tire contact patch that is established.

In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, the extent of the tire contact area that is established is determined by using the tire contact area circumferential contour function used to determine a circumferential contour of the tire contact area, in particular the coordinates of the the circumferential contour represent points of a tread of the tire are determined, and / or by using the tire contact area circumferential contour function used for a plurality of selected points of a tread of the tire is determined in each case whether the selected point is inside or outside the circumferential contour of the tire contact patch being established and thus inside or outside of the tire contact area. This enables the extent of the tire contact area to be determined, in particular to determine the area over which the tire contact area extends, in a particularly simple manner.

• - Bestimmen der Koordinaten des ausgewählten Punktes in einem definierten Koordinatensystem,
• - gegebenenfalls Umrechnen der Koordinaten des ausgewählten Punktes in das Koordinatensystem, auf welches sich die definierte Reifenaufstandsflächen-Umfangskonturfunktion bezieht, die zum Bestimmen, ob der ausgewählte Punkt der Lauffläche des Reifens innerhalb oder außerhalb einer Reifenaufstandsfläche liegt, verwendet wird, und
• - Prüfen mithilfe der verwendeten Reifenaufstandsflächen-Umfangskonturfunktion, ob der ausgewählte Punkt innerhalb oder außerhalb der Reifenaufstandsfläche liegt,

wobei sich der ausgewählte Punkt innerhalb der sich einstellenden Reifenaufstandsfläche befindet, wenn die Bedingung U_i(x_SE, y_SE) ≤ 1 erfüllt ist, und
wobei sich der ausgewählte Punkt außerhalb der sich einstellenden Reifenaufstandsfläche befindet, wenn die Bedingung U_i(x_SE, y_SE) > 1 erfüllt ist.In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, it is determined whether a selected point of a tread of the tire is inside or outside of the tire contact patch being established by performing the following steps will:

• - Determination of the coordinates of the selected point in a defined coordinate system,
• - if necessary, converting the coordinates of the selected point into the coordinate system to which the defined tire contact area circumferential contour function relates, which is used to determine whether the selected point of the tread of the tire is inside or outside a tire contact area, and
• - Check with the help of the tire contact patch circumferential contour function whether the selected point is inside or outside the tire contact patch,

wherein the selected point is located within the tire contact patch that is established if the condition U _i (x _SE , y _SE ) 1 is met, and
wherein the selected point is located outside the tire contact patch that is being established if the condition U _i (x _SE , y _SE )> 1 is met.

eingesetzt werden, wobei sich der ausgewählte Punkt innerhalb der sich einstellenden Reifenaufstandsfläche befindet, wenn die Bedingung U_i(x_SE, y_SE) ≤ 1 erfüllt ist, und sich der ausgewählte Punkt außerhalb der sich einstellenden Reifenaufstandsfläche befindet, wenn die Bedingung V_i(x_SE, y_SE) > 1 erfüllt ist.Checking whether a point is inside or outside the resulting tire contact patch can be done, for example, by entering the x and y coordinates of the selected point in the formula $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0}$$

can be used, where the selected point is located within the tire contact patch that is being established if the condition U _i (x _SE , y _SE ) ≤ 1 is met, and the selected point is outside the tire contact patch that is being established if the condition V _i ( x _SE , y _SE )> 1 is fulfilled.

• - Auswählen eines auf das Reifenaufstandsflächen-Umfangskonturfunktion-Koordinatensystem bezogenen Koordinatenwerts des Punktes,
• - Ermitteln eines zugehörigen Umfangskonturwerts in Abhängigkeit von dem ausgewählten Koordinatenwert des Punktes mithilfe der definierten Reifenaufstandsflächen-Umfangskonturfunktion mit Hilfe der Formel

$$U_i\left(x_{SE},y_{SE}\right):{\left(\frac{x_{SE}}{a_i}\right)}^{n_i}+{\left(\frac{y_{SE}}{b_i}\right)}^{m_i}=1\text{ mit }{a}_i,b_i\in {\text{R}}^{>0}\text{ und }{n}_i,m_i\in {\text{R}}^{>0},$$

welche die Umfangskontur der Reifenaufstandsfläche mathematisch näherungsweise beschreibt, und

• - Prüfen, ob der ausgewählte Punkt innerhalb oder außerhalb der Umfangskontur der Reifenaufstandsfläche liegt durch Vergleichen eines Betrags des ermittelten Umfangskonturwerts mit einem Betrag des anderen, nicht ausgewählten Koordinatenwerts des ausgewählten Punktes, wobei der Punkt innerhalb der Umfangskontur und damit innerhalb der Reifenaufstandsfläche liegt, wenn der Betrag des Koordinatenwerts kleiner ist als der Betrag des ermittelten Umfangskonturwerts ist.

Alternatively, checking whether a point is inside or outside the resulting tire contact area can also be carried out as follows, in particular with the following steps:

• - Selecting a coordinate value of the point that is related to the tire contact patch circumferential contour function coordinate system,
• Determination of an associated circumferential contour value as a function of the selected coordinate value of the point with the aid of the defined tire contact area circumferential contour function with the aid of the formula

$$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0},$$

which mathematically approximately describes the circumferential contour of the tire contact patch, and

• - Check whether the selected point is inside or outside the circumferential contour of the tire contact patch by comparing an amount of the determined circumferential contour value with an amount of the other, unselected coordinate value of the selected point, the point being within the circumferential contour and thus within the tire contact patch when the The amount of the coordinate value is smaller than the amount of the determined circumferential contour value.

For example, the x-coordinate of a point to be checked can be selected and the associated y-coordinate of the circumferential contour can be determined with the x-coordinate of the point, the formula for this preferably initially according to y _SE is converted, and then the for y _SE The determined value or the associated amount is compared with the value or the amount of the y-coordinate of the point. If the amount of the y-coordinate is smaller than the amount of y _SE If the point in question is within the tire contact area, if it is larger it is accordingly outside of it.

Alternatively, the y-coordinate of a point to be checked can also be selected and the associated x-coordinate of the circumferential contour can be determined for the y-coordinate of the point, the formula for this preferably initially according to x _SE is converted, and then the for x _SE will compare the determined value or the associated amount with the value or the amount of the y-coordinate of the point. If the amount of the y-coordinate is smaller than the amount of x _SE If the point in question is within the tire contact area, if it is larger it is accordingly outside of it.

eingesetzt werden, erfordert jedoch weniger Rechenoperationen und weist somit einen geringeren Ressourcenverbrauch auf und erscheint daher besonders vorteilhaft, insbesondere bei einer Verwendung des Verfahrens für eine Echtzeit-Simulation, insbesondere bei einer Verwendung des Verfahrens zur Berechnung von Reifenkräften in der Reifenaufstandsfläche in Echtzeit, wie beispielsweise in einem Fahrsimulator.The first variant, in which the x and y coordinates of the point in question are entered into the formula $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0}$$

are used, but requires fewer arithmetic operations and thus has lower resource consumption and therefore appears to be particularly advantageous, in particular when using the method for a real-time simulation, in particular when using the method for calculating tire forces in the tire contact patch in real time, such as in a driving simulator.

The result, whether a selected point is inside or outside the tire contact patch, is particularly preferably cached or stored and / or output as an output value assigned to the selected point, in particular as a characteristic property value of the point. This enables a simple and resource-saving further use of the result or the information resulting therefrom, in particular, for example, a resource-saving calculation of tire forces acting in the tire contact patch, since only the forces acting at points within the tire contact patch are relevant for these.

Preferably, several points of the tread are selected one after the other and checked to determine whether they are inside or outside the tire contact area, in particular so many points that the circumferential contour and / or the extent of the tire contact area is determined with sufficient accuracy, the tread preferably by means of a defined one Grid is divided, preferably evenly, and the selected points are in particular grid points of this grid. About the Resolution of the grid or the grid division can influence the accuracy with which the parameters for the circumferential contour can be determined and thus the accuracy of the circumferential contour function that is determined, in particular positively.

mit $$\left(\begin{array}{c}{x}_{SE}\\ y_{SE}\end{array}\right)=\left(\begin{array}{c}-x_{LR}\\ y_{LR}\end{array}\right){+}_{LR}{\overrightarrow{r}}_{SE}=\left(\begin{array}{c}-x_{LR}{+}_{LR}r{x}_{SE}\\ y_{LR}{+}_{LR}r{y}_{SE}\end{array}\right)$$

wobei der Koordinatentransformationsvektor ${}_{LR}{\overrightarrow{r}}_{SE}$

die zugehörige Koordinatentransformation für die Verschiebung des Koordinatenursprungs des Umfangskonturfunktions-Koordinatensystems bzw. in diesem Fall des Superellipsen-Koordinatensystems SE in den Koordinatenursprung des Latsch-Koordinatensystems LR definiert, und wobei der Latsch-Referenzpunkt LR vorzugsweise wie weiter oben beschrieben definiert ist. Mit einer derartigen Reifenaufstandsflächen-Umfangskonturfunktion lässt sich die Ausdehnung der sich einstellenden Reifenaufstandsfläche besonders vorteilhaft und genau beschreiben, auch in Abhängigkeit von einer Belastung des Reifens, einem Reifenzustand und einer oder mehreren Reifeneigenschaften.In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, the extent of the tire contact area that is established is determined in relation to a defined, right-handed, Cartesian, non-slip contact surface coordinate system, the origin of which is a contact point Reference point LR is, wherein the tire contact patch circumferential contour function that is used is particularly preferably defined at least in sections by: $$U_i\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\text{with}{a}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>1},$$

with $$\left(\begin{array}{c}{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{S.}\mathrm{E.}}\end{array}\right)=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}\\ y_{\mathrm{L.}\mathrm{R.}}\end{array}\right){+}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}\right)$$

where is the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

the associated coordinate transformation for the displacement of the coordinate origin of the circumferential contour function coordinate system or, in this case, the superellipse coordinate system SE in the coordinate origin of the Laces coordinate system LR defined, and where the Laces reference point LR is preferably defined as described above. With such a tire contact area circumferential contour function, the extent of the tire contact area that is established can be described particularly advantageously and precisely, also as a function of a load on the tire, a tire condition and one or more tire properties.

The tire contact area circumferential contour function used is preferably a continuous and closed function and, in particular, symmetrical to an axis of symmetry extending in the transverse direction of the tire.

The tire contact area circumferential contour function used is furthermore preferably composed of several sub-functions, ie it preferably has several functional sections i on. The tire contact area circumferential contour function is particularly preferably composed of a first sub-function and a second sub-function and in particular has two functional sections, the first sub-function and the second sub-function particularly preferably merging continuously. With such a tire contact area circumferential contour function, the extent of the tire contact area that is established can be described particularly advantageously and precisely, also as a function of a load on the tire, a tire condition and one or more tire properties.

The first partial function preferably describes, based on the circumferential contour function or superellipse coordinate system SE , part of the circumferential contour of the tire contact patch in the first and second quadrants of this coordinate system. In the case of a left tire, this corresponds to a part of the circumferential contour which encloses an inner part of the tire contact patch and, in the case of a right tire, it corresponds to a part of the circumferential contour which encloses an outer part of the tire.

The second sub-function preferably describes, based on the circumferential contour function or superellipse coordinate system SE , part of the circumferential contour of the tire contact patch in the third and fourth quadrants of this coordinate system. In the case of a left tire, this corresponds to a part of the circumferential contour which encloses an outer part of the tire contact patch and, in the case of a right tire, corresponds to a part of the circumferential contour which encloses an inner part of the tire.

However, both sub-functions are particularly preferred, in particular, each symmetrically to an axis of symmetry extending in the transverse direction of the tire. At least one of the two partial functions of the tire contact patch circumferential contour function is particularly preferably defined by a 4-parametric superellipse. With such a tire contact area circumferential contour function, the extent of the tire contact area that is established can be particularly simple, but nevertheless advantageously and precisely describe, also as a function of a load on the tire, a tire condition and one or more tire properties.

mit a, b₁₂,b₃₄ ∈ ⌷^>0 und n₁₂, n₃₄, m₁₂, m₃₄ ∈ ⌷^>1
und mit $$\left(\begin{array}{c}{x}_{SE}\\ y_{SE}\end{array}\right)=\left(\begin{array}{c}-x_{LR}\\ y_{LR}\end{array}\right){+}_{LR}{\overrightarrow{r}}_{SE}=\left(\begin{array}{c}-x_{LR}{+}_{LR}r{x}_{SE}\\ y_{LR}{+}_{LR}r{y}_{SE}\end{array}\right),$$

wobei insbesondere gilt: ${}_{LR}r{x}_{SE}=0$

wobei die Indizes 12 die erste Teilfunktion indizieren, welche die Umfangskontur in einem ersten Quadranten und in einem zweiten Quadranten des Superellipsen-Koordinatensystems SE sowie des Latsch-Koordinatensystems LR definiert, während die Indizes 34 die zweite Teilfunktion indizieren, welche die Umfangskontur im dritten und vierten Quadranten des Superellipsen-Koordinatensystems SE sowie des Latsch-Koordinatensystems LR definiert. D.h. es gilt: $$U\left(x_{SE},y_{SE}\right):\{\begin{array}{c}{U}_{12}\left(x_{SE},y_{SE}\right):\text{für }{y}_{SE}\ge 0\text{ bzw}.\text{ für }{y}_{LR}\ge {-}_{LR}r{y}_{SE}\\ U_{34}\left(x_{SE},y_{SE}\right):\text{für }{y}_{SE}<0\text{ bzw}.\text{ für }{y}_{LR}<{-}_{LR}r{y}_{SE}\end{array}$$

In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, the tire contact area circumferential contour function, which is used to determine the tire contact area, is composed of a first sub-function and a second sub-function, the first sub-function and the second sub-function are each defined by one half of a 4-parametric superellipse, the tire contact area circumferential contour function being defined in particular by: $$U\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):\{\begin{array}{c}{U}_{\mathrm{12th}}\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{\mathrm{12th}}}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{\mathrm{12th}}}\right)}^{m_{\mathrm{12th}}}=1\text{for}{y}_{\mathrm{S.}\mathrm{E.}}\ge 0\\ U_{34}\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{34}}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{34}}\right)}^{m_{34}}=1\text{for}{y}_{\mathrm{S.}\mathrm{E.}}<0\end{array}$$

with a, b ₁₂ , b ₃₄ ∈ ⌷ ^{> 0} and n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ ∈ ⌷ ^{> 1}
and with $$\left(\begin{array}{c}{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{S.}\mathrm{E.}}\end{array}\right)=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}\\ y_{\mathrm{L.}\mathrm{R.}}\end{array}\right){+}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}\right),$$

where the following applies in particular: ${}_{\mathrm{L.}\mathrm{R.}}r{x}_{\mathrm{S.}\mathrm{E.}}=0$

wherein the indices 12 indicate the first partial function which the circumferential contour in a first quadrant and in a second quadrant of the superellipse coordinate system SE as well as the Latsch coordinate system LR defines, while the indices 34 indicate the second partial function, which the circumferential contour in the third and fourth quadrants of the superellipse coordinate system SE as well as the Latsch coordinate system LR Are defined. That means: $$U\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\{\begin{array}{c}{U}_{\mathrm{12th}}\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\text{for}{y}_{\mathrm{S.}\mathrm{E.}}\ge 0\text{respectively}.\text{for}{y}_{\mathrm{L.}\mathrm{R.}}\ge {-}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\\ U_{34}\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\text{for}{y}_{\mathrm{S.}\mathrm{E.}}<0\text{respectively}.\text{for}{y}_{\mathrm{L.}\mathrm{R.}}<{-}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}$$

$$y_{SE34}=ƒ\left(x_{SE}\right)=-b_{34}\cdot {\left[1-{\left|\frac{x_{SE}}{a}\right|}^{n_{34}}\right]}^{\frac{1}{m_{34}}}$$

bzw. $$x_{SE12}=ƒ\left(y_{SE}\right)=\pm a\cdot {\left[1-{\left(\frac{y_{SE}}{b_{12}}\right)}^{m_{12}}\right]}^{\frac{1}{n_{12}}}.$$

$$x_{SE34}=ƒ\left(y_{SE}\right)=\pm a\cdot {\left[1-{\left|\frac{y_{SE}}{b_{34}}\right|}^{m_{34}}\right]}^{\frac{1}{n_{34}}}$$

Solving the equations results in each case $$y_{\mathrm{S.}\mathrm{E.}\mathrm{12th}}=ƒ\left(x_{\mathrm{S.}\mathrm{E.}}\right)=b_{\mathrm{12th}}\cdot {\left[1-{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{\mathrm{12th}}}\right]}^{\frac{1}{m_{\mathrm{12th}}}}$$

$$y_{\mathrm{S.}\mathrm{E.}34}=ƒ\left(x_{\mathrm{S.}\mathrm{E.}}\right)=-b_{34}\cdot {\left[1-{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{34}}\right]}^{\frac{1}{m_{34}}}$$

respectively. $$x_{\mathrm{S.}\mathrm{E.}\mathrm{12th}}=ƒ\left(y_{\mathrm{S.}\mathrm{E.}}\right)=\pm a\cdot {\left[1-{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{\mathrm{12th}}}\right)}^{m_{\mathrm{12th}}}\right]}^{\frac{1}{n_{\mathrm{12th}}}}.$$

$$x_{\mathrm{S.}\mathrm{E.}34}=ƒ\left(y_{\mathrm{S.}\mathrm{E.}}\right)=\pm a\cdot {\left[1-{\left|\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{34}}\right|}^{m_{34}}\right]}^{\frac{1}{n_{34}}}$$

In a further development, at least one circumferential contour value can be particularly dependent on a load on the tire, for example depending on a wheel load and / or a camber angle, and / or depending on a tire condition (e.g. a tire inflation pressure) and / or one or more tire properties can be determined (e.g. a tire size or the like), a tire contact area circumferential contour function being used for this purpose, which describes the circumferential contour of a tire contact area preferably as a function of one or more of these aforementioned influencing variables.

wobei C₁ ,...,C_n vorzugsweise jeweils eine Reifeneigenschaft definieren, ^LRF_f,z eine Radlast, p_R einen Reifenfülldruck und y einen Sturzwinkel.Therefore, in a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, the tire contact patch circumferential contour function is particularly preferably a function that is at least partially dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle For this purpose, preferably at least one circumferential contour parameter defining the tire contact patch circumferential contour function is stored as a circumferential contour parameter dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle, or as a function of at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle is determined, whereby preferably the following applies: $$\begin{array}{l}{U}_i\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...,{\mathrm{C.}}_n,{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\\ \text{with}{a}_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...,{\mathrm{C.}}_n,{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right),b_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...,{\mathrm{C.}}_n,{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>0}\\ \text{and}{n}_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...,{\mathrm{C.}}_n,{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right),m_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...,{\mathrm{C.}}_n,{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>1}\\ \text{and with}{x}_{\mathrm{S.}\mathrm{E.}}=-x_{\mathrm{L.}\mathrm{R.}}\text{and}{y}_{\mathrm{S.}\mathrm{E.}}=y_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}$$

whereby C ₁ , ..., C _n preferably each define a tire property, ^LR F _{f, e.g.} a wheel load, p _R a tire inflation pressure and y a camber angle.

This results in a tire contact area circumferential contour function which is dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle. As a result, the tire contact patch can thus be determined as a function of at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle.

A defined tire property can be, for example, a tire width, an aspect ratio, a load index, a speed index, a tire diameter (in inches), a tire stiffness variable, a profile parameter or the like.

In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, the method preferably comprises one or more steps with which at least one circumferential contour parameter of the tire contact patch circumferential contour function as a function of at least one predefined defined tire property , a predetermined wheel load, a predetermined tire inflation pressure and / or a predetermined camber angle is determined, this being carried out in particular before determining at least one circumferential contour value, in particular once at the beginning, for example in which a method according to the first aspect of the invention is carried out.

This then makes it possible to determine or predict the tire contact patch that is established in each case for various boundary conditions or as a function of the various aforementioned cases.

In a further advantageous embodiment of a method according to the third or fourth aspect of the invention, in particular in a further development, when the method according to the invention is carried out Method particularly preferably at least one circumferential contour parameter of the tire contact area circumferential contour function, in particular all circumferential contour parameters of the tire contact area circumferential contour function, is determined with the aid of a stored, associated artificial neural network or has been determined in this way, preferably with the aid of an artificial neural network that has two layers has, in particular a hidden layer and an output layer, wherein the stored, artificial neural network has been trained in particular with the aid of circumferential contour parameter data sets, preferably with the aid of several circumferential contour parameter data sets that have been determined from tire footprint imprints that are used for different tires with different tire properties depending on the wheel load, tire inflation pressure and / or camber angle have preferably been recorded in real life, in particular with the aid of image data analysis from real recorded travel footprints.

Input variables of the artificial neural network are preferably at least one tire property (tire dimension (tire width, aspect ratio, tire diameter), load index), a wheel load acting on the tire, a tire inflation pressure and / or a camber angle.

zur Umrechnung der auf das Superellipsen-Koordinatensystem bezogenen Koordinaten auf den Reifenmittelpunkt.The output variables of the artificial neural network are in particular the circumferential contour parameters a _i, b _i , n _i , m _{i of} the respective functional sections of the associated tire contact patch circumferential contour function and optionally one or more coordinate transformation parameters, in particular the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

to convert the coordinates related to the superellipse coordinate system to the tire center.

The real recording of corresponding circumferential contour parameter data sets that can be used to train the artificial neural network can be done, for example, with the help of pressure measurements with the help of a corresponding pressure measuring plate or with the help of a color print, as is fundamentally known from the prior art, in the tire contact area for different loads, tire conditions and / or tire properties take place, whereby the resulting circumferential contour can be determined from the respectively resulting pressure distribution or the respectively resulting tire contact area (color) imprint. In this way, corresponding circumferential contour parameter data sets for the circumferential contour function can be determined for various influencing variables such as wheel loads, camber angles, tire inflation pressures and tire sizes, etc. With these, a neural network can be trained in order to provide the corresponding circumferential contour parameters for determining, in particular for predicting, the circumferential contour for this state and to calculate the circumferential contour even for states for which no real circumferential contour has been recorded can.

Preferably, to determine at least one circumferential contour parameter, use is made of tire footprint imprints which have actually been recorded in a straight-ahead position of the tire, preferably in each case at different camber angles, wheel loads, tire inflation pressures and for different tires. However, tire footprint imprints can also be used which have been recorded at a defined steering angle or have been determined as a function of a defined steering angle.

Instead of using actually recorded tire footprint imprints, it is basically also conceivable to use tire footprint imprints generated by simulation to identify the circumferential contour function parameters, i.e. computer generated tire imprints, e.g. an imprint generated by means of a physical tire model or an imprint calculated by means of FEM analysis . This has the advantage that, as a rule, more data records are available or these can be generated more easily and more cost-effectively.

As an alternative to using an artificial neural network, one or more parameters of the tire contact patch circumferential contour function can also be determined by means of one or more other machine learning methods and / or by storing an associated, fixed parameter value for the respective parameter, in particular in In the form of a characteristic field or the like, the respective associated parameter value is read out, with in particular at least one stored parameter of the tire contact area circumference function having been determined with the help of image data analysis from actually recorded tire contact area imprints, in particular from tire contact area imprints that are available for different tires as a function of the wheel load , Tire pressure and / or camber angle have actually been recorded.

Alternatively, one or more parameters of the tire contact patch circumferential contour function can also be determined by storing the respective parameter in each case with the aid of an associated one Regression function is determined, wherein in particular at least one regression function has been determined with the help of image data analysis from actually recorded tire contact area imprints, in particular from tire contact area imprints that have actually been recorded for different tires as a function of wheel load, tire inflation pressure and / or camber angle.

Alternatively or additionally, one or more parameters of the tire contact patch circumferential contour function can also be determined with the aid of one or more interpolations and / or extrapolations, for example with the aid of a stored characteristic map or the like, and / or with the aid of one or more other machine learning methods. An artificial neural network, however, has the greatest flexibility and, in particularly many cases, enables an exact determination of the extent of the tire contact patch that is established or its circumferential contour.

The result, whether a selected point is inside or outside the tire contact patch, is particularly preferably cached or stored and / or output as an output value assigned to the selected point, in particular as a characteristic property value of the point. Likewise, preferably, in particular alternatively or additionally, at least one determined circumferential contour value and / or the determined circumferential contour function can be temporarily stored or stored and / or output. This enables a simple and resource-saving further use of the result or the information resulting therefrom, in particular, for example, a resource-saving calculation of tire forces acting in the tire contact patch, since only the forces acting at points within the tire contact patch are relevant for these.

ON THE FIFTH ASPECT

• - Auswählen definierter Punkte, die innerhalb der Reifenaufstandsfläche liegen,
• - Bestimmen der Koordinaten der ausgewählten Punkte in einem definierten Koordinatensystem,
• - gegebenenfalls Umrechnen der Koordinaten der ausgewählten Punktes in das Koordinatensystem, auf welches sich die definierte Bodendruckverteilungsfunktion bezieht, die zum Bestimmen der Bodendruckverteilung verwendet wird, und
• - Ermitteln eines zugehörigen Bodendruckwertes für jeden der ausgewählten Punkte mithilfe der definierten Bodendruckverteilungsfunktion.

A computer-implemented method according to the fifth aspect of the present invention, in particular a simulation method, for determining, in particular for predicting, a ground pressure distribution that occurs in a tire contact patch of a tire subject to a defined load, in particular for determining a ground pressure distribution when steering while stationary and / or when maneuvering in the Ground pressure distribution setting the tire contact area, preferably depending on the load, in particular also depending on a tire condition and / or one or more tire properties, in particular for a tire supported on a flat surface, preferably for a tire mounted on a rim, comprises the following steps :

• - Selecting defined points that lie within the tire contact area,
• - Determination of the coordinates of the selected points in a defined coordinate system,
• - if necessary, converting the coordinates of the selected point into the coordinate system to which the defined soil pressure distribution function relates, which is used to determine the soil pressure distribution, and
• - Determination of an associated ground pressure value for each of the selected points using the defined ground pressure distribution function.

The ground pressure distribution is determined with the aid of a defined ground pressure distribution function, which describes the ground pressure distribution in the tire contact patch, preferably as a function of the load on the tire and in particular also as a function of a tire condition and / or one or more tire properties Determination of the ground pressure distribution in the tire contact patch is used, a parameterized ground pressure distribution function which is related to a tire contact coordinate system LR , in particular as prescribed, is defined with a tire contact coordinate origin and by at least one independent variable and at least one soil pressure distribution parameter.

The method according to the fifth aspect of the present invention is characterized in that at least one soil pressure distribution parameter is determined or has been determined by a method according to the invention according to the second aspect of the invention.

This allows the soil pressure distribution, in particular at least one soil pressure parameter, to be determined in a particularly simple and advantageous manner. Furthermore, with such a method, the ground pressure distribution can also be determined efficiently, since the ground pressure values are only determined for points within the tire contact patch. In some cases, it can be advantageous to use the ground pressure values in the tire contact patch in particular only for required and / or specific and / or only for selected ones in a defined manner To determine points, also with different densities or resolutions for different areas of the tire contact patch.

wobei die Bodendruckverteilungsfunktion in Bezug auf ein definiertes, rechtshändiges, kartesisches, latschfestes Latsch-Koordinatensystem definiert ist, dessen Koordinatenursprung in einem Latsch-Referenzpunkt LR liegt, wobei der Latsch-Referenzpunkt LR vorzugsweise derart gewählt ist, dass er bei einem Sturzwinkel von γ = 0° , bei einer Geradeausstellung des Reifens, d.h. beim einem Spurwinkel von δ_v =0°, und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x$

auf den Reifen wirken, d.h. wenn gilt ${\overrightarrow{F}}_y=0$

und ${\overrightarrow{F}}_x=\mathrm{0,}$

mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt, und wobei das Latsch-Koordinatensystem insbesondere derart gewählt ist, dass bei einem Sturzwinkel von γ = 0°, bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x,$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x -Koordinate eines Punktes der Lauffläche des Reifens ist, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist, wobei N_x (y_LR ) eine Normierungsfunktion ist zur Normierung des Koordinatenwertes von x_LR auf eine Länge einer Erstreckung der Reifenaufstandsfläche in x-Richtung, wobei N_y (x_LR y_LR ) eine Abbildungsfunktion ist zur Abbildung des Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, wobei A(ŷ_LR) eine Skalierungsfunktion ist, die einen ersten Bodendruckverteilungs-Parameter, insbesondere einen Skalierungsparameter, in Abhängigkeit von x_LR und y_LR definiert, und wobei B(ŷ_LR) eine Krümmungsfunktion ist, die einen zweiten Bodendruckverteilungsparameter, insbesondere einen Krümmungsparameter, in Abhängigkeit von x_LR und y_LR definiert.In an advantageous embodiment of a method according to the fifth aspect of the present invention, the ground pressure distribution function, which is used to determine the ground pressure distribution in the tire contact patch, is defined in particular by: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right],\\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_x\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

wherein the ground pressure distribution function is defined in relation to a defined, right-handed, Cartesian, non-trailing laces coordinate system, the origin of which is in a laces reference point LR where the Laces reference point LR is preferably selected such that it is at a camber angle of γ = 0 °, with a straight ahead position of the tire, ie with a toe angle of δ _v = 0 °, and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_y=0$

and ${\overrightarrow{\mathrm{F.}}}_x=\mathrm{0,}$

coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that with a camber angle of γ = 0 °, with the tire in a straight position and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x,$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _{LR in the vertical direction of the} vehicle upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results, with x _LR one on the tire contact coordinate system LR is the related x -coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR where N _x ( y _LR ) a normalization function is used to normalize the coordinate value of x _LR to a length of an extension of the tire contact patch in the x-direction, where N _y ( x _LR y _LR ) a mapping function is used to map the coordinate value of y _LR to a defined range of values as a function of a length of an extension of the tire contact patch in the y-direction, where A (ŷ _LR ) is a scaling function that defines a first soil pressure distribution parameter, in particular a scaling parameter, as a function of x _LR and y _LR defined, and where B (ŷ _LR ) is a curvature function which a second soil pressure distribution parameter, in particular a curvature parameter, as a function of x _LR and y _LR Are defined.

Particularly preferably, A (ŷ _LR) > 0 and / or B (ŷ _LR )> 0 and / or N _x (y _LR ) _LR )> 0 applies in particular.

Such a soil pressure distribution function basically enables, in particular via a (even one-time) adaptation of the parameter functions A (ŷ _LR ) and B (ŷ _LR ), to determine, in particular to predict, a soil pressure distribution that is established as a function of several influencing variables, in particular one that is dependent on one another of at least one tire property, a wheel load, a tire inflation pressure and / or a camber angle setting ground pressure distribution, in particular a tire mounted on a rim.

Particularly preferably, a ground pressure value is temporarily stored or stored and / or output for at least one point within the tire contact patch as an output value assigned to the selected point, in particular as a characteristic property value of the point. Likewise, at least one determined ground pressure value and / or the determined ground pressure distribution function can be temporarily stored or stored and / or output. This enables a simple and resource-saving further use of the result or the information resulting therefrom, in particular, for example, a resource-saving calculation of tire forces acting in the tire contact patch.

TO THE SIXTH ASPECT

• - Auswählen definierter Punkte, die innerhalb der Reifenaufstandsfläche liegen,
• - Bestimmen der Koordinaten der ausgewählten Punkte in einem definierten Koordinatensystem,
• - gegebenenfalls Umrechnen der Koordinaten der ausgewählten Punktes in das Koordinatensystem, auf welches sich die definierte Bodendruckverteilungsfunktion bezieht, die zum Bestimmen der Bodendruckverteilung verwendet wird, und
• - Ermitteln eines zugehörigen Bodendruckwertes für jeden der ausgewählten Punkte mithilfe der definierten Bodendruckverteilungsfunktion.

A computer-implemented method according to the sixth aspect of the present invention, in particular a simulation method, for determining, in particular for predicting, a ground pressure distribution that occurs in a tire contact patch of a tire subject to a defined load, in particular for Determination of a ground pressure distribution that occurs in the tire contact patch when steering while stationary and / or when maneuvering, preferably as a function of a tire condition and / or one or more tire properties, in particular a tire supported on a flat surface, on a tire mounted on a rim, includes the following steps:

• - Selecting defined points that lie within the tire contact area,
• - Determination of the coordinates of the selected points in a defined coordinate system,
• - if necessary, converting the coordinates of the selected point into the coordinate system to which the defined soil pressure distribution function relates, which is used to determine the soil pressure distribution, and
• - Determination of an associated ground pressure value for each of the selected points using the defined ground pressure distribution function.

The ground pressure distribution is determined here and as in the above-described method according to the fifth aspect of the present invention with the aid of a defined ground pressure distribution function, which describes the ground pressure distribution in the tire contact patch, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, wherein the ground pressure distribution function that is used to determine the ground pressure distribution in the tire contact patch is a parameterized ground pressure distribution function that relates to a tire contact coordinate system LR , in particular as prescribed, is defined with a tire contact coordinate origin and by at least one independent variable and at least one soil pressure distribution parameter.

wobei die Bodendruckverteilungsfunktion in Bezug auf ein definiertes, rechtshändiges, kartesisches, latschfestes Latsch- γ= 0° Koordinatensystem definiert ist, dessen Koordinatenursprung in einem Latsch-Referenzpunkt LR liegt, wobei der Latsch-Referenzpunkt LR vorzugsweise derart gewählt ist, dass er bei einem Sturzwinkel von γ = 0° , bei einer Geradeausstellung des Reifens, d.h. beim einem Spurwinkel von δ_v =0° und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x$

auf den Reifen wirken, d.h. wenn gilt ${\overrightarrow{F}}_y=0$

und ${\overrightarrow{F}}_x=0$

mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt, und wobei das Latsch-Koordinatensystem insbesondere derart gewählt ist, dass bei einem Sturzwinkel von γ = 0°, bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_x,$

${\overrightarrow{F}}_x$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate γ_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x -Koordinate eines Punktes der Lauffläche des Reifens ist, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist, wobei N_x(y_LR ) eine Normierungsfunktion ist zur Normierung des Koordinatenwertes von x_LR auf eine Länge einer Erstreckung der Reifenaufstandsfläche in x-Richtung, wobei N_y(x_LR ,y_LR ) eine Abbildungsfunktion ist zur Abbildung des Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, wobei A(ŷ_LR) eine Skalierungsfunktion ist, die einen ersten Bodendruckverteilungs-Parameter, insbesondere einen Skalierungsparameter, in Abhängigkeit von ŷ_LR =f (x_LR, y_LR) definiert, und wobei B(ŷ_LR) eine Krümmungsfunktion ist, die einen zweiten Bodendruckverteilungsparameter, insbesondere einen Krümmungsparameter, in Abhängigkeit von ŷ_LR = f(x_LR, Y_LR) definiert.The method according to the sixth aspect of the present invention is characterized in that the ground pressure distribution function, which is used to determine the ground pressure distribution in the tire contact patch, is defined as in an advantageous embodiment of a method according to the fifth aspect of the invention by: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right],\\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_x\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

where the ground pressure distribution function is defined in relation to a defined, right-handed, Cartesian, non-trailing laces γ = 0 ° coordinate system, the origin of which is in a laces reference point LR where the Laces reference point LR is preferably chosen such that it is at a camber angle of γ = 0 °, with a straight ahead position of the tire, ie with a toe angle of δ _v = 0 ° and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_y=0$

and ${\overrightarrow{\mathrm{F.}}}_x=0$

coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that at a camber angle of γ = 0 °, when the tire is straight ahead and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_x,$

${\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate γ _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results, with x _LR one on the tire contact coordinate system LR is the related x -coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR where N _x ( y _LR ) a normalization function is used to normalize the coordinate value of x _LR to a length of an extension of the tire contact patch in the x-direction, where N _y ( x _LR , y _LR ) a mapping function is used to map the coordinate value of y _LR to a defined range of values as a function of a length of an extension of the tire contact patch in the y-direction, where A (ŷ _LR ) is a scaling function that defines a first soil pressure distribution parameter, in particular a scaling parameter, as a function of ŷ _LR = f (x _LR , y _LR ), and where B (ŷ _LR ) is a curvature function that defines a second soil pressure distribution parameter, in particular a curvature parameter, as a function of ŷ _LR = f (x _LR , Y _LR ).

With such a ground pressure distribution function, the ground pressure distribution in the tire contact patch can be particularly well described mathematically, in particular as a function of the load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, including when steering while stationary and / or when maneuvering .

At least one soil pressure distribution parameter of the soil pressure distribution function, in particular all soil pressure distribution parameters of the soil pressure distribution function, is particularly preferably determined by a method according to the second aspect of the present invention or has been determined by such a method.

durch y_LR verlaufenden Sekante einer zugehörigen Reifenaufstandsfläche, wobei die Sekante eine Umfangskontur der Reifenaufstandsfläche in zwei Schnittpunkten S₃ und S₄ schneidet, wobei die Normierungsfunktion N_x(y_LR ) besonders bevorzugt definiert ist durch: $$N_x\left(y_{LR}\right)=\left|\left({\overrightarrow{S}}_3\left(y_{LR}\right)-{\overrightarrow{S}}_4\left(y_{LR}\right)\right)\right|.$$

In an advantageous embodiment of a method according to the fifth and / or sixth aspect of the present invention, in particular in a further development, N _x ( y _LR ) a normalization function for normalizing the coordinate value of x _LR to a length one parallel to the unit vector ${\overrightarrow{e}}_{x,\mathrm{L.}\mathrm{R.}}$

by y _LR running secant of an associated tire contact area, the secant intersecting a circumferential contour of the tire contact area at two points of intersection S ₃ and S ₄ , where the normalization function N _x ( y _LR ) is particularly preferably defined by: $$N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)=\left|\left({\overrightarrow{\mathrm{S.}}}_3\left(y_{\mathrm{L.}\mathrm{R.}}\right)-{\overrightarrow{\mathrm{S.}}}_{\mathrm{4th}}\left(y_{\mathrm{L.}\mathrm{R.}}\right)\right)\right|.$$

In this way, a particularly good adaptation of the ground pressure distribution to the various states and load cases can be achieved.

In an advantageous embodiment of a method according to the fifth and / or sixth aspect of the present invention, in particular in a further development, N _y ( x _LR , y _LR ) a mapping function for mapping the coordinate value y _LR to a defined value range of [ L ₁ , L ₂ ] as a function of a length of a parallel to the unit vector e _y , LR by y _LR running secant of an associated tire contact area, preferably for linear mapping of the coordinate value y _LR , where the secant intersects a circumferential contour of the tire contact patch at two points of intersection S ₁ and S ₂ , where the mapping function N _y ( x _LR , y _LR ) is preferably defined by: $$\begin{array}{l}{N}_y\left(x_{\mathrm{L.}\mathrm{R.},}{y}_{\mathrm{L.}\mathrm{R.}}\right)={\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\\ =ƒ\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{L.}}_1,{\mathrm{L.}}_2,y_{\mathrm{L.}\mathrm{R.}}\right)\\ =N_y\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{L.}}_1,{\mathrm{L.}}_{\mathrm{2,}}{y}_{\mathrm{L.}\mathrm{R.}}\right).\\ =\frac{1}{2}\left[\left({\mathrm{L.}}_1+{\mathrm{L.}}_2\right)+\left({\mathrm{L.}}_2-{\mathrm{L.}}_1\right)\cdot \left[\frac{2\cdot y_{\mathrm{L.}\mathrm{R.}}+\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right)+{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right)\right)}{\left({\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right)-{\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right)\right)}\right]\right]\end{array}$$

In this way, a particularly good adaptation of the ground pressure distribution to the various states and load cases can be achieved.

In an advantageous embodiment of a method according to the fifth and / or sixth aspect of the present invention, in particular in a further development, at least one length of the extension of the tire contact patch in the x-direction and / or in the y-direction and / or at least one of the intersection points S ₁ , S ₂ , S ₃ , S ₄ , by means of which at least one mapping function value and / or at least one normalization function value for the determination of an associated ground pressure value is determined, with the aid of a tire contact area circumferential contour function which approximately describes the circumferential contour of the associated tire contact area, whereby preferably at least one of the intersection points S ₁ , S ₂ , S ₃ , S _{4 is determined} with the aid of a tire contact area circumferential contour function, as it is in a method for determining an expansion of a tire contact area of a tire subject to a defined load according to a method according to the third or much rth aspect is used.

By choosing the parameter functions A (ŷ _LR ) and B (ŷ _LR ), different load cases and the resulting soil pressure distributions can be mapped, in particular different dependencies of the soil pressure distribution in the y-direction. In particular, this approach enables the mapping of an influence of the camber angle, which in particular has a significant influence when maneuvering and steering while standing.

At least one of the soil pressure distribution parameters A (ŷ _LR ) and / or B (ŷ _LR ) is preferably a polynomial function, the scaling parameter A (ŷ _LR ) in particular being a scaling function in the form of a sixth degree polynomial, and the curvature parameter B (ŷ _LR ) is in particular a curvature function in the form of a polynomial of the second degree.

Particularly preferred is the scaling function A (ŷ _LR ), which defines the first soil pressure distribution parameter A (ŷ _LR ), as already described in connection with a method according to the second aspect of the invention, defined by: $$\begin{array}{l}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{a1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{6th}}+p_{a2}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^5+p_{a3}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{4th}}+p_{a\mathrm{4th}}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^3+p_{a5}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+p_{a\mathrm{6th}}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)+p_{a\mathrm{7th}}\\ \text{with}{p}_{a\mathrm{1..7}}\in \square \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.},}{y}_{\mathrm{L.}\mathrm{R.}}\right)\end{array}$$

The curvature function B (ŷ _LR ) which defines the second soil pressure distribution parameter B (ŷ _LR ) is, as already described in connection with a method according to the second aspect of the invention, particularly preferably defined by: $$\begin{array}{l}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{b1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b+{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}+{\mathrm{<figure-callout\; id="3"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\hfill \\ \text{with}{\mathrm{<figure-callout\; id="1"\; label="p\; b"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\in \square \hfill \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.},}{y}_{\mathrm{L.}\mathrm{R.}}\right)\hfill \end{array}.$$

und wobei insbesondere gilt: $$\begin{array}{l}A\left({\widehat{y}}_{LR}\right)=ƒ\left(x_{LR},y_{LR},C_1,C_2,C_3,C_4,\dots C_n{,}^{LR}{F}_{ƒ.z},p_R,\gamma \right)\\ {\text{mit p}}_{a1\dots 7}=ƒ\left(C_1,C_2,C_3,C_4,\dots C_n{,}^{LR}{F}_{ƒ.z},p_R,\gamma \right)\end{array}$$

und $$\begin{array}{l}B\left({\widehat{y}}_{LR}\right)=ƒ\left(x_{LR},y_{LR},C_1,C_2,C_3,C_4,\dots C_n{,}^{LR}{F}_{ƒ.z},p_R,\gamma \right)\\ {\text{mit p}}_{b1\dots 3}=ƒ\left(C_1,C_2,C_3,C_4,\dots C_n{,}^{LR}{F}_{ƒ.z},p_R,\gamma \right)\end{array}$$

und wobei C₁ ,..., C_n vorzugsweise jeweils eine Reifeneigenschaft definieren, ^LRF_f,z eine Radlast, p_R einen Reifenfülldruck und γ einen Sturzwinkel.In a particularly advantageous embodiment of a method according to the fifth and / or sixth aspect of the present invention, in particular in a further development, the ground pressure distribution function is a function dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle preferably at least one soil pressure distribution parameter defining the soil pressure distribution function and / or a regression parameter defining this is stored as a parameter dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle or depending on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle is determined, preferably the first ground pressure distribution parameter A (ŷ _LR ) and / or the second ground pressure distribution parameter B (ŷ _LR ), whereby preferably the following applies: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right]\\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)\text{and}\\ \text{with}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right).\\ \text{and}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)\end{array}$$

and in particular: $$\begin{array}{l}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)\\ {\text{with p}}_{a1...\mathrm{7th}}=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)\end{array}$$

and $$\begin{array}{l}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)\\ {\text{with <figure-callout id="1" label="p b" filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png" state="{{state}}">p</figure-callout>}}_b=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},...{\mathrm{C.}}_n{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ.z},p_{\mathrm{R.}},\gamma \right)\end{array}$$

and where C ₁ , ..., C _n preferably each define a tire property, ^LR F _{f, e.g.} a wheel load, p _R a tire pressure and γ a camber angle.

This results in a ground pressure distribution function that is dependent on at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle. As a result, the ground pressure distribution can thus be determined as a function of at least one defined tire property, a wheel load, a tire inflation pressure and / or a camber angle.

In a further advantageous embodiment of a method according to the fifth and / or sixth aspect of the invention, in particular in a further development, the method preferably comprises one or more steps with which at least one soil pressure distribution parameter of the soil pressure distribution function as a function of at least one predetermined defined tire property , a predetermined wheel load, a predetermined tire inflation pressure and / or a predetermined camber angle is determined, this being carried out in particular before determining at least one ground pressure value, in particular once at the beginning, for example in which a method according to the second aspect of the invention is carried out.

This then makes it possible to determine or predict the ground pressure distribution that occurs in each case in the tire contact area that is established for various boundary conditions or as a function of the various aforementioned cases.

In a further advantageous embodiment of a method according to the fifth and / or sixth aspect of the invention, in particular in a further development, when carrying out the method according to the invention, at least one soil pressure distribution parameter of the soil pressure distribution function, in particular all soil pressure distribution parameters of the soil pressure distribution function, is particularly preferred with the aid of a stored, associated artificial neural network is determined or has been determined in this way, preferably with the help of an artificial neural network that has two layers, in particular a hidden layer and an output layer, the stored, artificial neural networks in particular with the help of soil pressure distribution parameter data sets has been trained, preferably with the help of a plurality of ground pressure distribution parameter data sets that have been determined from ground pressure distributions in tire contact areas that are different for e tires with different tire properties depending on wheel load, tire inflation pressure and / or camber angle have preferably been recorded in real life.

Input variables of the artificial neural network are preferably at least one tire property (tire dimension (tire width, aspect ratio, tire diameter), load index), a wheel load acting on the tire, a tire inflation pressure and / or a camber angle.

The output variables of the artificial neural network are, in particular, the regression parameters p _{a1 ... 7} and p _b1..3 the scaling function A (ŷ _LR ) and / or the curvature function B (ŷ _LR ) of the associated soil pressure distribution function.

The real acquisition of corresponding soil pressure distribution parameter data sets or regression parameter data sets, which can be used to train the artificial neural network, can be done, for example, with the help of pressure measurements in the tire contact patch using a corresponding pressure measuring plate, as is fundamentally known from the prior art is made for different loads, tire conditions and / or tire properties. In this way, corresponding ground pressure distribution or regression parameter data sets for the ground pressure distribution function can be determined for various influencing variables such as wheel loads, camber angles, tire inflation pressures and tire sizes, etc. These can then be used to train a neural network in particular to provide the corresponding soil pressure distribution or regression parameters for determining, in particular for predicting, the ground pressure distribution that will arise for this state, even for conditions for which no real soil pressure distribution has been recorded to be able to calculate the ground pressure distribution.

Preferably, to determine at least one ground pressure distribution or regression parameter, use is made of ground pressure distributions which have actually been recorded in a straight-ahead position of the tire, preferably in each case at different camber angles, wheel loads, tire inflation pressures and for different tires. However, ground pressure distributions can also be used which have been recorded at a defined steering angle or have been determined as a function of a defined steering angle.

Instead of using real recorded soil pressure distributions, it is basically also conceivable to use simulated soil pressure distributions to identify the soil pressure distribution or regression parameters, i.e. computationally generated soil pressure distributions, e.g. a soil pressure distribution generated by means of a physical tire model or a soil pressure distribution calculated using FEM analysis . This has the advantage that, as a rule, more data records are available or these can be generated more easily and more cost-effectively.

As an alternative to using an artificial neural network, one or more parameters of the ground pressure distribution function can also be determined using one or more other machine learning methods and / or by storing an associated, fixed parameter value for the respective parameter, in particular in In the form of a characteristic map or the like, the respective associated parameter value is read out, with in particular at least one stored parameter of the soil distribution function having been determined from actually recorded soil pressure distributions, in particular from soil pressure distributions that were actually recorded for different tires as a function of wheel load, tire inflation pressure and / or camber angle are.

Alternatively, one or more parameters of the ground pressure distribution function can also be determined by determining the respective parameter in each case with the aid of an associated, stored regression function, in particular at least one regression function having been determined from actually recorded ground pressure distributions, in particular from ground pressure distributions that are dependent on different tires Wheel load, tire pressure and / or camber angle have actually been recorded.

Alternatively or additionally, one or more parameters of the soil pressure distribution function can also be determined with the aid of one or more interpolations and / or extrapolations, for example with the aid of a stored characteristic map or the like, and / or with the aid of one or more other machine learning methods. An artificial neural network, however, has the greatest flexibility and, in a particularly large number of cases, enables an exact determination of the extent of the ground pressure distribution that occurs.

Particularly preferably, at least one determined ground pressure value can be temporarily stored or stored and / or output as an output value assigned to the selected point, in particular as a characteristic property value of the point. Likewise, the determined soil pressure distribution function can preferably, in particular alternatively or additionally, be temporarily stored or stored and / or output. This enables a simple and resource-saving further use of the result or the information resulting therefrom, in particular, for example, a resource-saving calculation of tire forces acting in the tire contact patch, which are directly dependent on the ground pressure distribution in the tire contact patch.

TO THE SEVENTH ASPECT

1. (a) in einem Schritt, insbesondere bevor für die Gummibürstenelemente, die innerhalb der Reifenaufstandsfläche liegen, die jeweils in der Reifenaufstandsfläche an der jeweiligen Gummibürste infolge der zwischen Reifen und Untergrund wirkenden Reibung anliegenden Kräfte und Momente bestimmt werden, jeweils für jedes Gummibürstenelement mithilfe einer Reifenaufstandsflächen-Umfangskonturfunktion durch erfindungsgemäßes Verfahren gemäß dem dritten oder vierten Aspekt der vorliegenden Erfindung ermittelt wird oder worden ist, ob es sich innerhalb oder außerhalb der Reifenaufstandsfläche befindet, und/oder
2. (b) für alle innerhalb der zugehörigen Reifenaufstandsfläche liegenden Gummibürstenelemente die anliegenden Kräfte und Momente in Abhängigkeit von einer Bodendruckverteilung in der Reifenaufstandsfläche bestimmt werden, wobei die Bodendruckverteilung in der Reifenaufstandsfläche durch ein erfindungsgemäßes Verfahren gemäß dem fünften oder sechsten Aspekt der vorliegenden Erfindung ermittelt wird oder worden ist, wobei insbesondere jeweils für jedes Gummibürstenelement in Abhängigkeit von dem zugehörigen Referenzpunkt ein zugehöriger Bodendruckwert bestimmt wird oder worden ist.

A computer-implemented method according to the seventh aspect of the present invention for calculating at least one resultant tire force and / or at least one resultant tire moment produced by frictional forces in a tire contact patch of a tire, in particular in the case of a tire mounted on a rim and supported on a flat surface a movement is imposed, in particular via the rim, preferably as a function of a load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, the tire force and / or the tire torque being determined numerically with the aid of a tire model that the Properties of the tire, in particular a contact of the tire with a ground, among other things with the help of a large number of massless rubber brush elements in the tread of the tire, and the friction forces arising in the tire contact area Tire force and / or the tire torque is determined by first determining the forces and torques present in the tire contact area on the respective rubber brush as a result of the friction between the tire and the ground for each rubber brush located within the tire contact area Step are summarized over all rubber brushes located within the tire contact area to form the tire force and / or the tire torque, each rubber brush element being assigned a reference point with associated coordinates, by which the position of the rubber brush element is clearly defined, is characterized in that

1. (a) in one step, in particular before for the rubber brush elements that are located within the tire contact area, which are each determined in the tire contact area on the respective rubber brush as a result of the friction acting between the tire and the ground, in each case for each rubber brush element with the aid of a tire contact area - Circumferential contour function is determined or has been determined by the method according to the invention according to the third or fourth aspect of the present invention, whether it is located inside or outside the tire contact patch, and / or
2. (b) for all rubber brush elements lying within the associated tire contact area, the applied forces and moments are determined as a function of a ground pressure distribution in the tire contact area, the ground pressure distribution in the tire contact area being or has been determined by a method according to the invention according to the fifth or sixth aspect of the present invention is, wherein in particular an associated ground pressure value is or has been determined for each rubber brush element as a function of the associated reference point.

In a particularly advantageous embodiment of a method according to the invention according to the seventh aspect of the present invention, the rubber brush elements lying within the tire contact patch are first determined by a method according to the invention according to the third or fourth aspect of the present invention and then by a method according to the invention according to the fifth or sixth aspect of the present invention the respective ground pressure values for these rubber brush elements.

Alternatively, in connection with a method according to the invention according to the third or fourth aspect of the present invention, a different ground pressure distribution model, in particular a different ground pressure distribution function, can also be used to determine the extent of the tire contact patch or a circumferential contour.

It is also possible in connection with a method according to the invention according to the fifth or sixth aspect of the present invention to determine a ground pressure distribution in the tire contact patch to use another method for determining an expansion of the tire contact patch that is established or another circumferential contour function.

auf den Reifen wirken , d.h. wenn gilt ${\overrightarrow{F}}_y=0\text{ und }{\overrightarrow{F}}_x=0$

mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt, und wobei das Latsch-Koordinatensystem insbesondere derart gewählt ist, dass bei einem Sturzwinkel von γ = 0°, bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x - Koordinate eines Punktes der Lauffläche des Reifens ist, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist.In an advantageous embodiment of a method according to the seventh aspect of the present invention, in particular a tire model is used in which at least one of these massless rubber brush elements, in particular each of these massless rubber brush elements, has two translational degrees of freedom in one x _LR y _LR Plane, preferably two translational degrees of freedom in two mutually perpendicular directions, in particular one degree of freedom in x _LR direction and one in y _LR direction, the index LR a right-handed, Cartesian, latsch-proof Laces coordinate system is indicated, the origin of which is in a Laces reference point LR where the Laces reference point LR is preferably selected such that it is at a camber angle of γ = 0 °, with a straight ahead position of the tire, ie with a toe angle of δ _v = 0 °, and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_y=0\text{and}{\overrightarrow{\mathrm{F.}}}_x=0$

coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that with a camber angle of γ = 0 °, with the tire in a straight position and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results, with x _LR one on the tire contact coordinate system LR related x - coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR is.

With such a method, the frictional forces that arise in a tire contact area of a tire, which arise when the tire moves over the rim, can be determined particularly advantageously and precisely, in particular predicted, in particular for steering while stationary and / or when maneuvering.

ON THE EIGHTH ASPECT

auf den Reifen wirken, d.h. wenn gilt ${\overrightarrow{F}}_x=0\text{ und }{\overrightarrow{F}}_y=0$

mit einem auf eine Fahrbahnebene projizierten Reifenmittelpunkt zusammenfällt, und wobei das Latsch-Koordinatensystem insbesondere derart gewählt ist, dass bei einem Sturzwinkel von γ = 0°, bei einer Geradeausstellung des Reifens und wenn keine Seiten- und Längskräfte ${\overrightarrow{F}}_y,{\overrightarrow{F}}_x$

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, insbesondere derart, dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x-Koordinate eines Punktes der Lauffläche des Reifens ist, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist.A computer-implemented method according to the eighth aspect of the present invention for calculating at least one resultant tire force and / or at least one resultant tire moment generated by frictional forces in a tire contact patch of a tire, in particular in the case of a tire mounted on a rim and supported on a flat surface a movement is imposed, in particular via the rim, in particular when steering while stationary and / or when maneuvering, preferably depending on a load on the tire, in particular also depending on a tire condition and / or one or more tire properties, the tire force and / or the tire torque is determined numerically with the help of a tire model, which simulates the properties of the tire, in particular a contact of the tire with a ground, among other things with the help of a large number of massless rubber brush elements in the tread of the tire, and wherein the tire force and / or the Tire torque is determined by first determining, in one step, at least for each rubber brush located within the tire contact area, the forces and moments applied in the tire contact area on the respective rubber brush as a result of the friction acting between the tire and the ground, we In a further step, all rubber brushes located within the tire contact area are combined to form the tire force and / or the tire torque, is characterized in that a tire model is used in which at least one of these massless rubber brush elements, in particular each of these massless rubber brush elements, has two has translational degrees of freedom in an x _LR y _LR plane, preferably two translational degrees of freedom in two mutually perpendicular directions, in particular one degree of freedom in the x _LR direction and one in the y _LR direction, the index LR a right-handed, Cartesian, latsch-proof Laces coordinate system is indicated, the origin of which is in a Laces reference point LR where the Laces reference point LR is preferably selected such that it is at a camber angle of y = 0 °, with a straight ahead position of the tire, ie with a toe angle of δ _v = 0 °, and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_x,{\overrightarrow{\mathrm{F.}}}_y$

act on the tire, ie if applies ${\overrightarrow{\mathrm{F.}}}_x=0\text{and}{\overrightarrow{\mathrm{F.}}}_y=0$

coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that with a camber angle of γ = 0 °, with the tire in a straight position and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, in particular in such a way that a right-handed, Cartesian coordinate system results, with x _LR one on the tire contact coordinate system LR is the related x-coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR is.

In a particularly advantageous embodiment of a method according to the invention according to the seventh or eighth aspect of the present invention, in particular in a further development, the applied forces and moments are preferably determined for all rubber brush elements located within the associated tire contact area as a function of a ground pressure distribution in the tire contact area, wherein the ground pressure distribution in the tire contact patch is preferably determined by a method according to the fifth or sixth aspect of the present invention, each rubber brush element being assigned a reference point with associated coordinates by which the position of the rubber brush element is clearly defined, in particular for each rubber brush element an associated ground pressure value is determined as a function of the associated reference point.

It is also particularly preferred, in particular before for the rubber brush elements that are located within the tire contact area, which are determined in the tire contact area on the respective rubber brush as a result of the friction acting between the tire and the ground, in each case for each rubber brush element, whether it is is located inside or outside the tire contact patch, preferably with the help of a tire contact patch circumferential contour function, in particular by a method according to the third or fourth aspect of the present invention, each rubber brush element being assigned a reference point with associated coordinates by which the position of the rubber brush element is clearly defined.

In other words, in a particularly advantageous embodiment of a method according to the invention according to the eighth aspect of the present invention, likewise and as in a particularly advantageous embodiment of a method according to the seventh aspect of the present invention, initially by a method according to the invention according to the third or fourth aspect According to the present invention, the rubber brush elements lying within the tire contact patch are determined and then by a method according to the invention according to the fifth or sixth aspect of the present invention the respective ground pressure values for these rubber brush elements.

Alternatively, in connection with a method according to the invention according to the third or fourth aspect of the present invention for determining an extension of the tire contact patch or a Circumferential contour but also a different soil pressure distribution model, in particular a different soil pressure distribution function, can be used.

It is also possible in connection with a method according to the invention according to the fifth or sixth aspect of the present invention to determine a ground pressure distribution in the tire contact patch to use another method for determining an expansion of the tire contact patch that is established or another circumferential contour function.

In a further advantageous embodiment of a method according to the seventh or eighth aspect of the present invention, in particular in a further development, in particular a tire model is used in which at least one of these massless rubber brush elements, in particular each of these massless rubber brush elements, each with an associated rigidity and each with one associated damping is simulated in the direction of at least one of the two associated degrees of freedom, preferably in the direction of both degrees of freedom, the associated stiffness and the associated damping in the direction of a degree of freedom, in particular for at least one rubber brush element, preferably for all rubber brush elements, by a simple rheological model for rubber is simulated, preferably by a spring with a, in particular linear, spring stiffness (c _x , c _y ) and a Maxwell body connected in parallel to it, which has a damper with a, esp ondere linear damping (d _x , d _y ) and a spring connected in series with the damper with, in particular linear, spring stiffness (c _{d, x} , c _{d, y} ). In this way, a particularly good and at the same time relatively simple replica of a tire, in particular for the intended purpose, can be achieved.

der die z_LR-Richtung definiert, senkrecht auf zugehörigen Einheitsvektoren ${\overrightarrow{e}}_{x,LR}$

und ${\overrightarrow{e}}_{y,LR}$

des Latsch-Koordinatensystems LR steht. Hierdurch lässt sich eine besonders gute und zugleich relativ einfache Nachbildung eines Reifens, insbesondere für den angestrebten Zweck, erreichen.In a further advantageous embodiment of a method according to the seventh or eighth aspect of the present invention, in particular in a further development, wherein the tire properties are also simulated with the aid of a massless, rigid belt ring element, the connection between the belt ring element and at least all in the area of the tire contact area is , massless rubber brush elements simulated as a connection with a common translational degree of freedom in the z _LR direction, in particular with a common defined rigidity, preferably a linear rigidity, and a common defined damping in the z _LR direction, preferably a linear damping, the connection between Belt ring element and at least all massless rubber brush elements located in the area of the tire contact area, in particular by a spring-damper arrangement with a spring arranged in _{relation to a z LR direction} is simulated with a defined spring stiffness and a damper connected in parallel to this spring with a defined damping, with an associated unit vector ${\overrightarrow{e}}_{z,\mathrm{L.}\mathrm{R.}}$

which defines the z _LR direction, perpendicular to associated unit vectors ${\overrightarrow{e}}_{x,\mathrm{L.}\mathrm{R.}}$

and ${\overrightarrow{e}}_{y,\mathrm{L.}\mathrm{R.}}$

of the Latsch coordinate system LR stands. In this way, a particularly good and at the same time relatively simple replica of a tire, in particular for the intended purpose, can be achieved.

Particularly preferably, the properties of the tire are also simulated with the aid of a rigid rim element, a connection between the rim element and the belt ring element preferably having several degrees of freedom, in particular four degrees of freedom, preferably one translational in the y _LR direction, and three rotational, in particular one around the x _LR axis, one around the y _LR axis and one around the z _LR axis. Particularly preferably, the connection between the rim element and belt ring element is simulated for each of the four degrees of freedom by a simple rheological model for rubber, preferably by a spring with, in particular, a linear, spring stiffness and a damper connected in parallel with an, in particular, linear, Damping and a Maxwell body connected in parallel to it, which comprises a damper with, in particular linear, damping and a spring connected in series with the damper with, in particular linear, spring stiffness. In this way, a particularly good and at the same time relatively simple replica of a tire, in particular for the intended purpose, can be achieved.

In a further advantageous embodiment of a method according to the seventh or eighth aspect of the present invention, in particular in a further development, the applied forces and torques are set to zero for all rubber brush elements lying outside the associated tire contact area. This enables a particularly simple calculation of the tire forces in the tread of the tire.

wobei ei ^LRF_{f,z,q i=1..k} der jeweils normierte Bodendruckwert des jeweiligen Gummibürstenelements ist und q_i=1..k die jeweilige Gummibürste bzw. das jeweilige Gummibürstenelement indiziert und k die Anzahl der Gummibürsten ist, wobei ^LRF_f,z der Bodendruckverteilung zugrundeliegende Radlast ist, und wobei ^IRp_{e,z,q i=1..k} der jeweilige, mittels der Bodendruckverteilungsfunktion bestimmte, zu normierende Bodendruckwert ist, d.h. der jeweilige für das jeweilige Gummibürstenelement q_i=1..k .In a further advantageous embodiment of a method according to the seventh or eighth aspect of the present invention, in particular in a further development, the associated ground pressure value, which is determined for each rubber brush element, is in particular standardized proportionally to a wheel load on which the ground pressure distribution is based, in particular according to the following formula : $${}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,q_{i=\mathrm{1..}k}}=\frac{{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z}}{{\displaystyle \sum _{i=\text{I.}}^k{}^{\mathrm{L.}\mathrm{R.}}{p}_{e,z,q_{i=\mathrm{1..}\text{k}}}}}{\cdot }^{\mathrm{L.}\mathrm{R.}}{p}_{e,z,q_{i=\mathrm{1..}k}},$$

where ei ^LR F _{f, z, q i = 1..k} is the normalized ground pressure value of the respective rubber brush element and q _{i = 1..k} indicates the respective rubber brush or the respective rubber brush element and k is the number of rubber brushes, where ^LR F _{f, e.g.} is the wheel load on which the ground pressure distribution is based, and where ^IR p _{e, z, q i = 1..k} is the respective soil pressure value to be normalized, determined by means of the soil pressure distribution function, ie the respective one for the respective rubber brush element q _{i = 1..k} .

As a result, a total ground pressure in the _vertical direction of the vehicle or in the z LR direction, which results from the sum of all ground pressure values in the wheel contact area, and which is the basis for the tire forces acting in the tire contact area, can be based on a total pressure that actually occurs with a wheel load. Ground pressure can be normalized or scaled, which results in an adaptation and scaling of the calculated tire forces and torques. In particular, the calculation of the tire forces and torques can be independent of the resolution of the tire contact patch or the grid of the tire contact patch or the number of rubber brush elements and an absolute value of the tire forces and torques can be calculated with sufficient accuracy.

In a further advantageous embodiment of a method according to the seventh or eighth aspect of the present invention, in particular in a further development, the forces and moments applied to a rubber brush element are also determined for each rubber brush element as a function of a respective associated ground pressure value or as a function of an associated standardized ground pressure value determines whether static friction or sliding friction acts between the respective rubber brush element and the ground on which the tire is supported.

To calculate a tire force that arises as a function of several influencing variables due to frictional forces in a tire contact patch and / or a tire torque that arises as a function of several influencing variables due to friction forces in a tire contact area, in particular a drilling moment, in particular for calculating one due to friction forces in a tire contact area as a function of at least one Tire property, a wheel load, a tire inflation pressure and / or a camber angle and / or a tire torque, in particular a drilling moment, which arises as a function of at least one tire property, a wheel load, a tire inflation pressure and / or a camber angle, is particularly preferred a corresponding tire contact area circumferential contour function is used, for example a tire contact area circumferential contour function as described in detail above, and / or a corresponding one pending soil pressure distribution function, for example a soil pressure distribution function as described in detail above, in which the respective, aforementioned influencing variables are taken into account.

In this way, the tire forces can be determined reliably and easily in a particularly advantageous manner, above all with good accuracy, even when steering while stationary or when maneuvering.

If a movement is now imposed on the tire via the rim element, this leads to a movement of the belt ring element due to the kinematic coupling of the belt ring element with the rim element in accordance with the coupling, which in turn is transmitted to the tread in accordance with the coupling with the massless rubber brush elements of the tread. Depending on how many of the rubber brush elements are supported on the ground and in what form and with what force, tire forces and moments that counteract the movement are created.

The resulting tire forces are particularly dependent on the extent of the tire contact patch that is being set up or on a circumferential contour of this (this depends on how many of the rubber brush elements are supported on the ground) and on a ground pressure distribution (this depends on whether and which of the Rubber brush elements are supported on the ground by means of static friction and whether and which rubber brush elements are supported on the ground by means of sliding friction and how great the frictional forces are in the tire contact area).

With a method according to the invention according to the seventh or eighth aspect of the invention, the tire forces can be determined reliably and easily in a particularly advantageous manner, especially with good accuracy, even when steering while stationary or when maneuvering.

ON THE NINTH ASPECT

A computer-implemented method according to the ninth aspect of the invention for designing at least one component of a vehicle, preferably for designing a steering arrangement, in particular for designing a rack of a steering gear, whereby for designing the component at least one value of a design variable relevant for designing the component is dependent on a resulting tire force and / or at least one resulting tire torque resulting from frictional forces in a tire contact patch is determined, characterized in that a tire force calculated by a method according to the seventh or eighth aspect of the present invention and / or a tire torque calculated by such a method is used or a method according to the seventh or eighth aspect of the present invention is used, wherein in particular at least one design variable is a function of n a tire force calculated by a method according to the seventh or eighth aspect of the present invention or as a function of a tire torque calculated by such a method is determined.

In this way, for example, a rack of a steering gear can be designed particularly advantageously and / or an actuator device for steering assistance, since the tire force or the tire torque, which is used and significantly influences the design, particularly well reflects the tire forces and torques that actually occur, in particular when maneuvering and / or steering while standing.

FOR THE TENTH ASPECT

A method for operating a driving simulator according to the tenth aspect of the invention, wherein the driving simulator has at least one controllable actuator device, in particular a resistance actuator device for generating a steering resistance, is characterized in that at least one actuator device of the driving simulator as a function of at least one by a method according to the seventh or eighth aspect of the present invention calculated tire force and / or is controlled as a function of at least one tire torque calculated by a method according to the seventh or eighth aspect of the present invention. In this way, a particularly realistic control of the actuator device of the driving simulator can be achieved, since the tire force or the tire torque, which is used, reflects the actually occurring tire forces and torques particularly well, especially when maneuvering and / or steering while stationary.

Particularly preferably, a resulting movement of a rim is recorded or determined as a function of a steering input and a resulting movement imposed on a tire fastened on the rim, with the tire forces and torques arising in the tire contact patch according to the invention being based on this in turn by a method according to the invention the seventh or eighth aspect of the invention. According to the resulting tire forces and torques, the resistance actuator device is controlled in such a way that a corresponding steering resistance through the tire forces and torques, in particular through the frictional forces from the ground, for example a road, is simulated on an associated steering input device.

ON THE ELEVENTH ASPECT

A computer program according to the eleventh aspect of the present invention comprises instructions which cause the computer program to be executed by a computer, a method according to the first aspect of the present invention, a method according to the first aspect of the present invention, a method according to the second aspect of the present invention present Invention, a method according to the third aspect of the present invention, a method according to the fourth aspect of the present invention, a method according to the fifth aspect of the present invention, a method according to the sixth aspect of the present invention, a method according to the seventh aspect of the present invention To carry out the invention and / or a method according to the eighth aspect of the present invention.

TO THE TWELFTH ASPECT

A computer-readable medium, in particular a computer-readable storage medium, according to the twelfth aspect of the present invention comprises instructions which, when executed by a computer, cause the latter, a method according to the first aspect of the present invention, a method according to the first aspect of the present invention according to the second aspect of the present invention, a method according to the third aspect of the present invention, a method according to the fourth aspect of the present invention, a method according to the fifth aspect of the present invention, a method according to the sixth aspect of the present invention, a method according to the seventh aspect of the present invention and / or to carry out a method according to the eighth aspect of the present invention.

ON THE THIRTEENTH ASPECT

A driving simulator according to the invention according to the thirteenth aspect of the present invention is characterized in that the driving simulator is designed to carry out a method according to the tenth aspect of the present invention.

The driving simulator is particularly preferably designed in such a way that a resulting movement of a rim can be detected or determined as a function of a steering input and a resulting movement imposed on a tire attached to the rim, and depending on this, in turn, the movement in the tire contact area resulting tire forces and torques can be determined, wherein the resulting tire forces and torques can be determined according to the invention by a method according to the seventh or eighth aspect of the invention. According to the resulting tire forces and torques, the resistance actuator device can preferably be controlled in such a way that a corresponding steering resistance through the tire forces and torques, in particular the frictional forces from the ground, for example a road, can be simulated on an associated steering input device, in particular with a steering input device if possible high accuracy.

These and other features emerge from the claims and the description also from the drawings, the individual features being implemented individually or in combination in the form of sub-combinations in one embodiment of the invention and representing advantageous and individually protectable designs provided that these are technically feasible.

In order to avoid repetition, many of the above-described features and preferred configurations are each described only once and only in connection with one aspect of the present invention, but also apply to the other aspects of the present invention without explicit reference to this in each case.

The subdivision of the application into individual sections as well as subheadings do not limit the general validity of the statements made under these. Rather, these only serve for better readability and better orientation within the registration. This means that statements made in a section apply, insofar as it is technically sensible, not only for this section, but also for other sections.

BRIEF DESCRIPTION OF THE FIGURES

In the following, the invention will be further explained on the basis of preferred exemplary embodiments for the individual aspects of the present invention, the invention being shown in the accompanying drawings, partly only schematically and partly not to scale. the 1a , 2a and 3a show, by way of example, various tire footprint imprints that result from different loads, tire conditions and tire properties of a tire, the 1b , 2 B and 3b symbolize some of the influencing variables such as the wheel load ( 1a) , the camber angle ( 1b) and the tire pressure ( 1c ). 4th shows a flowchart for an embodiment of a method according to the invention according to the seventh or eighth aspect of the present invention for calculating tire forces and torques arising in a tire contact patch. the 5a until 5c and 6th contain representations to explain the methodical approach of a method according to the invention according to the seventh or eighth aspect of the present invention for calculating the tire forces and torques, which 7th and 8th illustrate the position of the tire contact coordinate system on which the method according to the invention according to the seventh or eighth aspect of the present invention for calculating the tire forces and torques is based, and 9a until 9c as well as the 10 and 11 each illustrate the tire model according to the invention used to calculate the tire forces and torques. 12th shows a flowchart for an embodiment of a method according to the invention according to the first aspect of the invention for determining at least one circumferential contour parameter of a parameterized circumferential contour function for describing the circumferential contour of a tire contact patch, which is suitable for performing a method according to the third and / or fourth aspect of the present invention . the 13th until 19th each show, by way of example, various illustrations for explanation the determination of the circumferential contour parameters by a method according to the first aspect of the present invention. the 20th and 21 illustrate by way of example how an extension of the tire contact patch or its circumferential contour can be determined using the parameters obtained by a method according to the first aspect of the present invention by a method according to the third or fourth aspect of the present invention. 22nd shows a flowchart for an embodiment of a method according to the invention according to the second aspect of the invention for determining at least one ground pressure distribution parameter of a parameterized ground pressure distribution function for describing the ground pressure distribution in a tire contact patch, which is suitable for performing a method according to the fifth and / or sixth aspect of the present invention is. the 23 until 30th each show, by way of example, various representations for explaining the determination of the soil pressure distribution parameters by a method according to the second aspect of the present invention. the 31 and 32 illustrate by way of example how a ground pressure distribution in the tire contact patch can be determined using the parameters obtained by a method according to the second aspect of the present invention by a method according to the fifth or sixth aspect of the present invention. 33 shows a flowchart for an embodiment of a method according to the invention according to the ninth aspect of the present invention for designing at least one component of a vehicle based on tire forces and torques that have been determined by a method according to the seventh or eighth aspect of the present invention. 34 shows a flowchart for an embodiment of a method according to the invention according to the tenth aspect of the present invention for operating a driving simulator as a function of tire forces and torques that have been determined by a method according to the seventh or eighth aspect of the present invention. All features described in more detail or shown in a recognizable manner can be essential to the invention.

Figure list

• the 1a , 2a and 3a show various tire footprints by way of example 10 that are made up of different loads, tire conditions and tire properties on a rim 2 mounted tire 1 result, which deals with its tread 4th , especially with its rubber brushes 5 that along with the grooves 11 of the profile a profile geometry of the tread 4th define on a subsurface S. , for example a street S. or a lane S. supported, with the tire contact patch 10 in each case the developing contact surface between the running surface 4th of the tire 1 and the underground S. is.
• the 1b , 2 B and 3b For example, symbolize some of the influencing variables on the resulting tire contact area 10 , like the wheel load F _Z ( 1a) , the camber angle γ ( 1b) and the tire pressure p _R ( 1c ). Depending on the load on the tire 1 and depending on its tire properties, such as tire width, aspect ratio, load index, profile geometry, rubber compound, etc., as well as its condition, for example depending on its tire inflation pressure p _R , there are different tire footprint imprints 10 .

For example, the difference between the tire footprint results 10 the end 1a and the in 2a from a different angle of fall γ , where is the tire footprint 10 the end 1a was recorded with a camber angle of γ = 0 °, while the tire contact area imprint 10 the end 2a results from a camber angle of γ = + 9 °. The tire contact patch imprint 10 the end 3a was with a significantly lower tire pressure p _R generated than the one out 1a .

How with the 1a , 2a and 3a is recognizable, leads to a different camber angle γ on the one hand to a clearly different geometry, in particular a clearly different circumferential contour of the tire contact patch 10 while another tire pressure p _R essentially the size of the tire contact patch 10 influences, ie their areal expansion.

On the other hand, there is a ground pressure distribution in the tire contact area 10 influences what on the basis of the different light and dark areas in the tire contact patch imprints 10 is recognizable.

4th shows a flowchart for an embodiment of a method according to the invention according to the seventh or eighth aspect of the present invention for calculating in a tire contact patch 10 resulting tire forces and moments.

S0:

Start;

S1:

Definieren und Hinterlegen eines erfindungsgemäßen Reifenmodells, wobei das verwendete Reifenmodell gemäß dem achten Aspekt der Erfindung definiert ist;

S2:

Definieren und Hinterlegen einer Umfangskonturfunktion U zur Ermittlung einer sich einstellenden Ausdehnung der Reifenaufstandsfläche 10, wobei die verwendete Umfangskonturfunktion U eine parametrisierte Umfangskonturfunktion U gemäß dem vierten Aspekt der Erfindung ist, deren Parameter a,b₁₂ ,b₃₄ , n₁₂ ,n₃₄ ,m₁₂ ,m₃₄ , ${}_{LR}{\overrightarrow{r}}_{SE}$

durch ein Verfahren gemäß dem ersten Aspekt der Erfindung ermittelt worden sind;

S3:

Definieren und Hinterlegen einer Bodendruckverteilungsfunktion p zur Ermittlung einer sich einstellenden Bodendruckverteilung in der Reifenaufstandsfläche 10, wobei die verwendete Bodendruckverteilungsfunktion p eine parametrisierte Bodendruckverteilungsfunktion p gemäß dem sechsten Aspekt der Erfindung ist, deren Parameter p_a1...7 , p_b1...3 durch ein Verfahren gemäß dem zweiten Aspekt der Erfindung ermittelt worden sind;

S4:

Aufbringen einer definierten Belastung, d.h. definierter Kräfte und Momente, und/oder einer Bewegung auf einen mittels des hinterlegten, erfindungsgemäßen Reifenmodells nachgebildeten Reifen 1;

S5:

Ermitteln einer Ausdehnung bzw. einer Umfangskontur der aus der auf den Reifen 1 aufgebrachten Belastung und/oder Bewegung resultierenden Reifenaufstandsfläche 10 durch ein erfindungsgemäßes Verfahren gemäß dem dritten bzw. vierten Aspekt der Erfindung basierend auf der in Schritt S2 hinterlegten Umfangskonturfunktion U,

S6:

Ermitteln einer aus der auf den Reifen 1 aufgebrachten Belastung und/oder Bewegung resultierenden Bodendruckverteilung in der resultierenden Reifenaufstandsfläche 10 durch ein erfindungsgemäßes Verfahren gemäß dem fünften bzw. sechsten Aspekt der Erfindung basierend auf der in Schritt S3 hinterlegten Bodendruckverteilungsfunktion p, wobei für jedes einzelne Gummibürstenelement q_i=1..k in der resultierenden Reifenaufstandsfläche 10 ein zugehöriger normierter Bodendruckwert ^LRF_{f,z,q i=1..k} bzw. eine normierte Normalkraft in z_LR-Richtung ermittelt wird;

S7:

Ermitteln der an den jeweiligen einzelnen Gummibürstenelementen q_i=1..k wirkenden resultierenden Kräfte ${}^{LR}{\overrightarrow{F}}_{ƒ,z,q_{i=\mathrm{1..}\text{k}}}$

und Momente ${}^{LR}{\overrightarrow{M}}_{\delta ,z,q_{i=\mathrm{1..}\text{k}}}$

in Abhängigkeit von dem sich jeweils an den jeweiligen einzelnen Gummibürstenelementen q_i=1..k einstellenden normierten Bodendruck ^LRF_{f,z,q i=1...k} ;

S8:

Ermitteln einer Gesamt-Reifenkraft ${}^{LR}{\overrightarrow{F}}_{ƒ},$

insbesondere einer in der Reifenaufstandsfläche wirkenden Gesamt-Reibkraft ${}^{LR}{\overrightarrow{F}}_{ƒ},$

und/oder einem Gesamt-Reifenmoment ${}^{LR}{\overrightarrow{M}}_{\delta }$

insbesondere einem Gesamt-Bohrmoment ${}^{LR}{\overrightarrow{M}}_{\delta }$

insbesondere durch Aufsummieren der einzelnen, an den jeweiligen einzelnen Gummibürstenelementen q_i=1..k wirkenden resultierenden Kräfte ${}^{LR}{\overrightarrow{F}}_{ƒ,z,q_{i=\mathrm{1..}k}}$

und Momente ${}^{LR}{\overrightarrow{M}}_{\delta ,z,q_{i=\mathrm{1..}k}};$

und

S9:

Speichern und/oder Ausgeben der ermittelten Reifenkräfte und - momente, insbesondere der Gesamt-Reifenkraft ${}^{LR}{\overrightarrow{F}}_{ƒ}$

und/oder des Gesamt-Reifenmoments ${}^{LR}{\overrightarrow{M}}_{\delta };$

S10:

Ende.

This exemplary embodiment of a method according to the invention according to the seventh or eighth aspect of the present invention comprises the following steps S0 to S10, which will be explained in more detail in the further course of this application:

S0:

Begin;

S1:

Defining and storing a tire model according to the invention, the tire model used being defined according to the eighth aspect of the invention;

S2:

Define and store a peripheral contour function U to determine a developing expansion of the tire contact area 10 , where the perimeter contour function used U a parameterized perimeter contour function U according to the fourth aspect of the invention, the parameters thereof a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

have been determined by a method according to the first aspect of the invention;

S3:

Define and store a ground pressure distribution function p to determine a ground pressure distribution that is established in the tire contact area 10 , where the ground pressure distribution function used p a parameterized ground pressure distribution function p according to the sixth aspect of the invention is its parameters p _{a1 ... 7} , p _{b1 ... 3} have been determined by a method according to the second aspect of the invention;

S4:

Applying a defined load, ie defined forces and moments, and / or a movement to a tire simulated by means of the stored tire model according to the invention 1 ;

S5:

Determining an extent or a circumferential contour from the on the tire 1 applied load and / or movement resulting tire contact area 10 by a method according to the invention according to the third or fourth aspect of the invention based on the circumferential contour function stored in step S2 U ,

S6:

Determine one from the on the tire 1 applied load and / or movement resulting ground pressure distribution in the resulting tire contact patch 10 by a method according to the invention according to the fifth or sixth aspect of the invention based on the soil pressure distribution function stored in step S3 p , with for each individual rubber brush element q _{i = 1..k} in the resulting tire footprint 10 an associated standardized ground pressure value ^LR F _{f, z, q i = 1..k} or a normalized normal force is determined in the z _LR direction;

S7:

Determine the on the respective individual rubber brush elements q _{i = 1..k} acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,z,q_{i=\mathrm{1..}\text{k}}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta ,z,q_{i=\mathrm{1..}\text{k}}}$

depending on the respective individual rubber brush elements q _{i = 1..k} adjusting normalized ground pressure ^LR F _{f, z, q i = 1 ... k} ;

S8:

Determining a total tire force ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ},$

in particular a total frictional force acting in the tire contact patch ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ},$

and / or a total tire torque ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta }$

in particular a total drilling torque ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta }$

in particular by adding up the individual rubber brush elements on the respective individual rubber brush elements q _{i = 1..k} acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,z,q_{i=\mathrm{1..}k}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta ,z,q_{i=\mathrm{1..}k}};$

and

S9:

Storing and / or outputting the determined tire forces and moments, in particular the total tire force ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ}$

and / or the total tire torque ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta };$

S10:

End.

zugeordnet ist, durch welche die Position des Gummibürstenelementes q_i=1..k eindeutig definiert ist, was anhand der 6 gut erkennbar ist, wobei vorliegend der Referenzpunkt jeweils ein hier nicht näher bezeichneter Mittelpunkt des Gummibürstenelements ist, wie in der Vergrößerung innerhalb der Lupe in der rechten unteren Ecke des Bildes illustriert.The tire model according to the invention stored in step S1, which is defined according to the eighth aspect of the invention, forms the properties of the tire 1 , especially contact with the tire 1 with an underground S. , among other things with the help of a large number of massless rubber brush elements q _{i = 1..k} in the tread 4th of the tire 1 after, with the tread in n _x Rubber brush elements in x _LR direction and in n _y , Rubber brush elements is divided in y _LR direction and each rubber brush element q _{i = 1..k} each a reference point with associated coordinates ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_i=\left(x_{\mathrm{L.}\mathrm{R.},}{y}_{\mathrm{L.}\mathrm{R.}}\right)$

is assigned, through which the position of the rubber brush element q _{i = 1..k} is clearly defined what is based on the 6th is easily recognizable, whereby In the present case, the reference point is in each case a center point of the rubber brush element, not designated here in greater detail, as illustrated in the enlargement within the magnifying glass in the lower right corner of the picture.

und Momente ${}^{LR}{\overrightarrow{M}}_{\delta ,z,q_{i=\mathrm{1..}k}}$

gemäß den in den 5a bis 5c angegebenen Formeln ermittelt werden und zu einer Gesamt-Reifenkraft ${}^{LR}{\overrightarrow{F}}_{ƒ},$

insbesondere einer in der Reifenaufstandsfläche wirkenden Gesamt-Reibkraft ${}^{LR}{\overrightarrow{F}}_{ƒ},$

und/oder einem Gesamt-Reifenmoment ${}^{LR}{\overrightarrow{M}}_{\delta },$

insbesondere einem Gesamt-Bohrmoment ${}^{LR}{\overrightarrow{M}}_{\delta }$

aufsummiert werden.Depending on a proportion of each on a rubber brush element q _{i = 1..k} acting wheel load ^LR F _{f, z, q i} in the z-direction or a ground pressure resulting therefrom or a ground pressure value resulting therefrom on the respective rubber brush element q _{i = 1..k} , how based on the 5a until 5c It is easy to see the forces acting on the individual rubber brush elements q _{i = 1 ... k} ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,z,q_{i=\mathrm{1..}k}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta ,z,q_{i=\mathrm{1..}k}}$

according to the 5a until 5c specified formulas can be determined and a total tire force ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ},$

in particular a total frictional force acting in the tire contact patch ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ},$

and / or a total tire torque ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta },$

in particular a total drilling torque ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta }$

be summed up.

und über den Untergrund S gleitend bleibt, wenn gilt: $$\frac{1}{{}^{LR}{F}_{ƒ,z,q_{i=\mathrm{1..}k}}}\left|\left|\left[\begin{array}{cc}{}^{LR}{\mu }_{G,x}& 0\\ 0& {}^{LR}{\mu }_{G,y}\end{array}\right]\left[\begin{array}{c}{}^{LR}{F}_{ƒ,x,q_{i=\mathrm{1..}k}}\\ {}^{LR}{F}_{ƒ,y,q_{i=\mathrm{1..}k}}\end{array}\right]\right|\right|=\mathrm{1,}$$

wobei ^LRF_{f,x,q i=1..k} und ^LRF_{f,y,q i=1..k} jeweils die x- und y-Komponente von ${}^{LR}{\overrightarrow{F}}_{ƒ,q_{i=\mathrm{1..}k}}$

sind, wobei ^LRµ_H,x ein zugehöriger Haftreibungskoeffizient in x-Richtung ist, ^LRµ_H,y ein zugehöriger Haftreibungskoeffizient in y-Richtung, ^LR µ_G,x ein zugehöriger Gleitreibungskoeffizient in x-Richtung und ^LRµ_G,y ein zugehöriger Gleitreibungskoeffizient in y -Richtung.For a particularly advantageous determination of the tire contact patch 10 In this exemplary embodiment of a method according to the invention for calculating the tire forces, the resulting tire forces and torques are taken into account, whether as a function of the prevailing ground pressure on a rubber brush element q _{i = 1..k} the rubber brush element q _{i = 1..k} on the underground S. adheres like the rubber brush elements q _{i = 1..k} in the fields of A1 and A2 or already over the ground S. slides like the rubber brush elements q _{i = 1..k} , in the fields of B1 and B2 , with a rubber brush element on the ground S. remains liable if: $$\frac{1}{{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,q_{i=\mathrm{1..}k}}}\left|\left|\left[\begin{array}{cc}{}^{\mathrm{L.}\mathrm{R.}}{\mu }_{H,x}& 0\\ 0& {}^{\mathrm{L.}\mathrm{R.}}{\mu }_{H,y}\end{array}\right]\left[\begin{array}{c}{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,x,q_{i=\mathrm{1..}k}}\\ {}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,y,q_{i=\mathrm{1..}k}}\end{array}\right]\right|\right|\le 1$$

and over the underground S. remains floating if the following applies: $$\frac{1}{{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,q_{i=\mathrm{1..}k}}}\left|\left|\left[\begin{array}{cc}{}^{\mathrm{L.}\mathrm{R.}}{\mu }_{G,x}& 0\\ 0& {}^{\mathrm{L.}\mathrm{R.}}{\mu }_{G,y}\end{array}\right]\left[\begin{array}{c}{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,x,q_{i=\mathrm{1..}k}}\\ {}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,y,q_{i=\mathrm{1..}k}}\end{array}\right]\right|\right|=\mathrm{1,}$$

where ^LR F _{f, x, q i = 1..k} and ^LR F _{f, y, q i = 1..k} the x and y components of ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,q_{i=\mathrm{1..}k}}$

are, where ^LR µ _{H, x} is an associated coefficient of static friction in the x-direction, ^LR µ _{H, y} an associated coefficient of static friction in the y direction, ^LR µ _{G, x} an associated coefficient of sliding friction in the x direction and ^LR µ _{G, y} an associated coefficient of sliding friction in the y direction.

${\overrightarrow{F}}_x$

auf den Reifen wirken mit einem auf eine Fahrbahnebene S projizierten Reifenmittelpunkt C zusammenfällt, wobei die Lage des Latsch-Koordinatensystems aus den 7 und 8 deutlich wird, welche verschiedene, übliche Reifenkoordinatensystem zeigen, wobei 7 eine leicht modifizierte Darstellung von 2.9 aus „Vo D.Q., Marzbani H., Fard M., Jazar R.N. (2016) Caster-Camber Relationship in Vehicles. In: Jazar R., Dai L. (eds) Nonlinear Approaches in Engineering Applications. Springer, Cham, https://doi.org/10.1007/978-3-319-27055-5_2“ ist. Der Index C bezieht sich dabei jeweils auf ein Reifenlatsch-Koordinatensystem, der Index H auf ein Horizontal-Koordinatensystem, mit welchem das Reifenlatsch-Koordinatensystem LR bei einem Sturzwinkel von γ=0° zusammenfällt. Der Index S kennzeichnet ein Untergrund- bzw. Straßen- Koordinatensystem und der Index G ein Gürtelring-Koordinatensystem. Sämtliche Größen bzw. Koordinaten können dabei mittels den entsprechenden, grundsätzlich aus dem Stand der Technik bekannten Koordinatentransformationsgleichungen ineinander umgerechnet werden.The index LR indicates a right-handed, Cartesian, latsch-proof Laces coordinate system, the origin of which is in a Laces reference point LR where the Laces reference point LR in this case is chosen such that it is at a camber angle of γ = 0 °, with a straight ahead position of the tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,$

${\overrightarrow{\mathrm{F.}}}_x$

act on the tire with one on a road surface S. projected tire center C. coincides with the position of the Latsch coordinate system from the 7th and 8th it becomes clear which different, common tire coordinate systems show, wherein 7th a slightly modified representation of 2 .9 from “Vo DQ, Marzbani H., Fard M. ., Jazar R. .N. (2016) Caster-Camber Relationship in Vehicles. In: Jazar R. ., Dai L. (eds) Nonlinear Approaches in Engineering Applications. Springer, Cham, https://doi.org/10.1007/978-3-319-27055-5_2 “is. The index C. In each case, refers to a tire contact coordinate system, the index H to a horizontal coordinate system with which the tire contact coordinate system LR with a camber angle of γ = 0 ° coincides. The index S. identifies an underground or road coordinate system and the index G a belt ring coordinate system. All variables or coordinates can be converted into one another by means of the corresponding coordinate transformation equations known in principle from the prior art.

auf den Reifen wirken, eine Abszisse x_LR des Latsch-Koordinatensystems in Fahrzeuglängsrichtung nach fahrzeugvorne zeigt und eine zugehörige Applikate z_LR in Fahrzeughochrichtung nach oben und eine zugehörige Ordinate y_LR jeweils senkrecht auf der Abszisse x_LR und der Applikate z_LR steht, so dass sich ein rechtshändiges, kartesisches Koordinatensystem ergibt, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x-Koordinate eines Punktes der Lauffläche 4 des Reifens 1 ist, für den ein Bodendruck p bestimmt werden soll, und wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist.In the exemplary embodiment described here, the Latsch coordinate system is used LR chosen such that with a camber angle of γ = 0 °, when the tire is straight ahead and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _LR of the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _{LR in the vertical direction of the} vehicle upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the applicate z _LR stands, so that a right-handed, Cartesian coordinate system results, where x _LR one on the tire contact coordinate system LR related x-coordinate of a point on the tread 4th of the tire 1 is for which a ground pressure p should be determined, and where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR is.

und Momenten ${}^{LR}\overrightarrow{M}{}_{\delta ,q_{i=\mathrm{1..}k}}$

ergibt sich die Gesamt-Reifenkraft ${}^{LR}\overrightarrow{F}{}_{ƒ}$

durch Aufsummieren der an den jeweiligen Gummibürstenelemente q_i=1..k wirkenden resultierenden Kräfte ${}^{LR}\overrightarrow{F}{}_{ƒ,q_{i=\mathrm{1..}k}}$

wie folgt: $${}^{LR}\overrightarrow{F}{}_{ƒ}={\displaystyle \sum _{i=1}^k{}^{LR}\overrightarrow{F}{}_{ƒ,q_i}}={\displaystyle \sum _{i=1}^k{}^{LR}\left[F_{ƒ,x,q_i},F_{ƒ,y,q_i},F_{ƒ,z,q_i}\right]},$$

wobei bei den resultierenden Kräften ${}^{LR}\overrightarrow{F}{}_{ƒ,q_{i=\mathrm{1..}k}}$

noch unterschieden wird, ob es sich um eine Gleit-Reibungskraft oder eine Haft-Reibungskraft handelt (vgl. 5a bis 5c), wobei für ${}^{LR}\overrightarrow{F}{}_{ƒ,q_{i=\mathrm{1..}k}}$

entweder gilt ${}^{LR}\overrightarrow{F}{}_{ƒ,q_{i=\mathrm{1..}k}}={}^{LR}\overrightarrow{F}{}_{ƒ,G,q_{i=\mathrm{1..}k}}$

oder ${}^{LR}\overrightarrow{F}{}_{ƒ,q_{i=\mathrm{1..}k}}={}^{LR}\overrightarrow{F}{}_{ƒ,H,q_{i=\mathrm{1..}k}},$

je nachdem, ob wie vorbeschrieben die Haftreibungs- oder die Gleitreibungsbedingung erfüllt ist.Based on the individual rubber brush elements q _{i = 1..k} acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta ,q_{i=\mathrm{1..}k}}$

results in the total tire force ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}$

by adding up the amounts on the respective rubber brush elements q _{i = 1..k} acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}$

as follows: $${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}={\displaystyle \sum _{i=1}^k{}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_i}}={\displaystyle \sum _{i=1}^k{}^{\mathrm{L.}\mathrm{R.}}\left[{\mathrm{F.}}_{ƒ,x,q_i},{\mathrm{F.}}_{ƒ,y,q_i},{\mathrm{F.}}_{ƒ,z,q_i}\right]},$$

where at the resulting forces ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}$

A distinction is still made as to whether it is a sliding frictional force or an adhesive frictional force (cf. 5a until 5c ), where for ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}$

either applies ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}={}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,G,q_{i=\mathrm{1..}k}}$

or ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}={}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,H,q_{i=\mathrm{1..}k}},$

depending on whether the static or sliding friction condition is met as described above.

ergibt sich durch Aufsummieren der an den jeweiligen Gummibürstenelementen q_i=1..k anliegenden resultierenden Reifenmomente ${}^{LR}\overrightarrow{M}{}_{\delta ,q_{i=\mathrm{1..}k}}$

gemäß: $${}^{LR}\overrightarrow{M}{}_{\delta }={\displaystyle \sum _{i=1}^k{}^{LR}\overrightarrow{M}{}_{\delta ,q_i}}.$$

The total tire moment ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }$

is obtained by adding up the amounts on the respective rubber brush elements q _{i = 1..k} applied resulting tire torques ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta ,q_{i=\mathrm{1..}k}}$

according to: $${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }={\displaystyle \sum _{i=1}^k{}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta ,q_i}}.$$

und/oder des Gesamt-Reifenmoments ${}^{LR}\overrightarrow{M}{}_{\delta },$

kann dabei in Bezug auf das Reifenlatsch-Koordinatensystem LR erfolgen. Alternativ oder zusätzlich können die jeweils mit Bezug auf das Reifenlatsch-Koordinatensystem LR ermittelte Gesamt-Reifenkraft ${}^{LR}\overrightarrow{F}{}_{ƒ}$

und/oder das Gesamt-Reifenmoment ${}^{LR}\overrightarrow{M}{}_{\delta }$

aber auch mithilfe einer Koordinatentransformation, wie sie allgemein bekannt ist, auf ein (beliebiges) anderes Koordinatensystem umgerechnet werden und dann entsprechend mit Bezug auf dieses Koordinatensystem ausgegeben werden, je nach Schnittstelle bzw. Weiterverwendung der ermittelten Gesamt-Reifenkraft ${}^{LR}\overrightarrow{F}{}_{ƒ}$

und/oder des ermittelten Gesamt-Reifenmoments ${}^{LR}\overrightarrow{M}{}_{\delta }.$

Für viele Simulationsmodelle und eine Weiterverwendung der ermittelten Gesamt-Reifenkraft ${}^{LR}\overrightarrow{F}{}_{ƒ}$

und/oder des Gesamt-Reifenmoments ${}^{LR}\overrightarrow{M}{}_{\delta }$

kann beispielsweise eine Umrechnung (mittels Koordinatentransformation) in das C- oder H-Koordinatensystem aus 7 vorteilhaft sein.The output of the determined tire forces and torques, in particular the total tire force ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}$

and / or the total tire torque ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta },$

can be in relation to the tire contact coordinate system LR take place. As an alternative or in addition, they can each with reference to the tire contact coordinate system LR determined total tire force ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}$

and / or the total tire torque ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }$

but can also be converted to (any) other coordinate system using a coordinate transformation, as is generally known, and then output accordingly with reference to this coordinate system, depending on the interface or further use of the total tire force determined ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}$

and / or the total tire torque determined ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }.$

For many simulation models and further use of the determined total tire force ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}$

and / or the total tire torque ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }$

can, for example, perform a conversion (by means of coordinate transformation) into the C or H coordinate system 7th be beneficial.

The following is based on the 9a until 9c as well as the 10 and 11 the tire model according to the invention used to calculate the tire forces and torques is explained in more detail.

In the exemplary embodiment described here for calculating the tire forces, each of the massless rubber brush elements q _{i = 1..k} to replicate the rubber brushes 5 in the tread 4th of the tire 1 two translational degrees of freedom in an x _LR y _LR plane, as based on 9c (upper illustration) and 11 is recognizable.

Each of these massless rubber brush elements is here q _{i = 1..k} , each with an associated rigidity and an associated damping in the direction of the two associated degrees of freedom simulated, the associated stiffness and the associated damping in the direction of a degree of freedom in this case for all rubber brush elements q _{i = 1..k} are simulated by a simple rheological model for rubber by a spring with a linear spring stiffness c _x , c _y and a Maxwell body connected in parallel to it, one damper with a linear damping d _x , d _y and one with the damper in series includes switched spring with a linear spring stiffness.

The mature 1 is also used in this embodiment with the help of a massless, rigid belt ring element 3 simulated, the connection between the belt ring element 3 and at least everyone is in the area of the tire contact patch 10 located, massless rubber brush elements q _{i = 1..k} is simulated as a connection with a common translational degree of freedom in the z _LR direction with a common defined stiffness and a jointly defined linear damping in the z _LR direction (see Sect. 9c lower illustration).

der die z_LR-Richtung definiert, senkrecht auf zugehörigen Einheitsvektoren ${\overrightarrow{e}}_{x,LR}\text{ und }{\overrightarrow{e}}_{y,LR}$

des Latsch-Koordinatensystems LR steht.The connection between belt ring element 3 and at least everyone in the area of the tire contact patch 10 located massless rubber brush elements q _{i = 1..k} is simulated by an unspecified spring-damper arrangement with a _{spring arranged in the z LR} direction with a defined spring stiffness and a damper connected in parallel to this spring with a defined damping, with an associated unit vector ${\overrightarrow{e}}_{z,\mathrm{L.}\mathrm{R.}},$

which defines the z _LR direction, perpendicular to associated unit vectors ${\overrightarrow{e}}_{x,\mathrm{L.}\mathrm{R.}}\text{and}{\overrightarrow{e}}_{y,\mathrm{L.}\mathrm{R.}}$

of the Latsch coordinate system LR stands.

As mentioned above, the rim 2 as a rigid element 2 replicated. The connection between the rigid rim element 2 and the belt ring element 3 is simulated in this example with four degrees of freedom: one translatory in the y _LR direction, and three rotatory, in particular one around the x _LR axis, one around the y _LR axis and one around the z _LR axis. The connection between the rim element 2 and belt ring element 3 is simulated for each of the four degrees of freedom by a simple rheological model for rubber by a spring with a linear spring stiffness and a damper connected in parallel with linear damping and a Maxwell body connected in parallel, which has a damper with a linear, Includes damping and a spring connected in series with the damper with a linear spring stiffness (cf. 9a , 9b and 10 ).

mit a,b₁₂,b_34. ∈ □ ^>0 und n₁₂ ,n₃₄,m₁₂,m₃₄ ∈ □ ^>1
mit $$\left(\begin{array}{c}{x}_{SE}\\ y_{SE}\end{array}\right)=\left(\begin{array}{c}-x_{LR}\\ y_{LR}\end{array}\right){+}_{LR}{\overrightarrow{r}}_{SE}=\left(\begin{array}{c}-x_{LR}{+}_{LR}r{x}_{SE}\\ y_{LR}{+}_{LR}r{y}_{SE}\end{array}\right),$$

und mit ${}_{LR}r{x}_{SE}=0$

wobei die Indizes 12 die erste Teilfunktion indizieren, welche die Umfangskontur in einem ersten Quadranten und in einem zweiten Quadranten des Superellipsen-Koordinatensystems SE sowie des Latsch-Koordinatensystems LR definiert, während die Indizes 34 die zweite Teilfunktion indizieren, welche die Umfangskontur im dritten und vierten Quadranten des Superellipsen-Koordinatensystems SE sowie des Latsch-Koordinatensystems LR definiert. D.h. es gilt: $$U\left(x_{SE},y_{SE}\right):\{\begin{array}{c}{U}_{12}\left(x_{SE},y_{SE}\right):\text{für }{y}_{SE}\ge 0\text{ bzw}.\text{ für }{y}_{LR}\ge {-}_{LR}r{y}_{SE}\\ U_{34}\left(x_{SE},y_{SE}\right):\text{für }{y}_{SE}<0\text{ bzw}.\text{ für }{y}_{LR}<{-}_{LR}r{y}_{SE}\end{array}$$

Durch Auflösen der Gleichungen ergibt sich jeweils $$y_{SE12}=ƒ\left(x_{SE}\right)=b_{12}\cdot {\left[1-{\left|\frac{x_{SE}}{a}\right|}^{n_{12}}\right]}^{\frac{1}{m_{12}}}$$

$$y_{SE34}=ƒ\left(x_{SE}\right)=-b_{34}\cdot {\left[1-{\left|\frac{x_{SE}}{a}\right|}^{n_{34}}\right]}^{\frac{1}{m_{34}}}$$

bzw. $$x_{SE12}=ƒ\left(y_{SE}\right)=\pm a\cdot {\left[1-{\left(\frac{y_{SE}}{b_{12}}\right)}^{m_{12}}\right]}^{\frac{1}{n_{12}}}.$$

$$x_{SE34}=ƒ\left(y_{SE}\right)=\pm a\cdot {\left[1-{\left|\frac{y_{SE}}{b_{34}}\right|}^{m_{34}}\right]}^{\frac{1}{n_{34}}}$$

The peripheral contour function U , which is stored in step S2, in this embodiment is composed of a first sub-function and a second sub-function, the first sub-function and the second sub-function each being defined by one half of a 4-parametric superellipse, the tire contact area used in this example. Perimeter contour function U is defined by: $$U\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):\{\begin{array}{c}{U}_{\mathrm{12th}}\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{\mathrm{12th}}}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{\mathrm{12th}}}\right)}^{m_{\mathrm{12th}}}=1\text{for}{y}_{\mathrm{S.}\mathrm{E.}}\ge 0\\ U_{34}\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right):{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{34}}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{34}}\right)}^{m_{34}}=1\text{for}{y}_{\mathrm{S.}\mathrm{E.}}<0\end{array}$$

with a, b ₁₂ , b _34. ∈ □ ^{> 0} and n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ ∈ □ ^{> 1}
with $$\left(\begin{array}{c}{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{S.}\mathrm{E.}}\end{array}\right)=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}\\ y_{\mathrm{L.}\mathrm{R.}}\end{array}\right){+}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}=\left(\begin{array}{c}-x_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{x}_{\mathrm{S.}\mathrm{E.}}\\ y_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}\right),$$

and with ${}_{\mathrm{L.}\mathrm{R.}}r{x}_{\mathrm{S.}\mathrm{E.}}=0$

wherein the indices 12 indicate the first partial function which the circumferential contour in a first quadrant and in a second quadrant of the superellipse coordinate system SE as well as the Latsch coordinate system LR defines, while the indices 34 indicate the second partial function, which the circumferential contour in the third and fourth quadrants of the superellipse coordinate system SE as well as the Latsch coordinate system LR Are defined. That means: $$U\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\{\begin{array}{c}{U}_{\mathrm{12th}}\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\text{for}{y}_{\mathrm{S.}\mathrm{E.}}\ge 0\text{respectively}.\text{for}{y}_{\mathrm{L.}\mathrm{R.}}\ge {-}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\\ U_{34}\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):\text{for}{y}_{\mathrm{S.}\mathrm{E.}}<0\text{respectively}.\text{for}{y}_{\mathrm{L.}\mathrm{R.}}<{-}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\end{array}$$

Solving the equations results in each case $$y_{\mathrm{S.}\mathrm{E.}\mathrm{12th}}=ƒ\left(x_{\mathrm{S.}\mathrm{E.}}\right)=b_{\mathrm{12th}}\cdot {\left[1-{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{\mathrm{12th}}}\right]}^{\frac{1}{m_{\mathrm{12th}}}}$$

$$y_{\mathrm{S.}\mathrm{E.}34}=ƒ\left(x_{\mathrm{S.}\mathrm{E.}}\right)=-b_{34}\cdot {\left[1-{\left|\frac{x_{\mathrm{S.}\mathrm{E.}}}{a}\right|}^{n_{34}}\right]}^{\frac{1}{m_{34}}}$$

respectively. $$x_{\mathrm{S.}\mathrm{E.}\mathrm{12th}}=ƒ\left(y_{\mathrm{S.}\mathrm{E.}}\right)=\pm a\cdot {\left[1-{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{\mathrm{12th}}}\right)}^{m_{\mathrm{12th}}}\right]}^{\frac{1}{n_{\mathrm{12th}}}}.$$

$$x_{\mathrm{S.}\mathrm{E.}34}=ƒ\left(y_{\mathrm{S.}\mathrm{E.}}\right)=\pm a\cdot {\left[1-{\left|\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_{34}}\right|}^{m_{34}}\right]}^{\frac{1}{n_{34}}}$$

jeweils als von den vier Reifeneigenschaften C₁ ,...,C₄ , von der aufgebrachten Radlast ^LRF_f,z dem Reifenfülldruck p_R und dem Sturzwinkel γ hinterlegt sind beziehungsweise mithilfe eines entsprechend trainierten künstlichen neuronalen Netzes KNN-U (vgl. 22 und 23) in Abhängigkeit von den vier Reifeneigenschaften C₁ , ...,C₄ , von der aufgebrachten Radlast ^LRF_f,z ,dem Reifenfülldruck p_R und dem Sturzwinkel γ bestimmt werden können. D.h. es gilt: $$\begin{array}{l}{U}_i\left(x_{LR},y_{LR},C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right):{\left(\frac{x_{SE}}{a_i}\right)}^{n_i}+{\left(\frac{y_{SE}}{b_i}\right)}^{m_i}=1\hfill \\ \text{mit }{a}_i=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right),b_i=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right)\in {\text{R}}^{>0}\hfill \\ \text{und }{n}_i=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right),m_i=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right)\in {\text{R}}^{>1}\hfill \\ \text{und mit }{x}_{SE}=-x_{LR}\text{ und }{y}_{SE}=y_{LR}{+}_{LR}r{y}_{SE}\hfill \end{array}$$

The tire footprint perimeter contour function used U is also of four tire properties in this embodiment C ₁ , ..., C ₄ depending, in particular on a tire width C ₁ , an aspect ratio C ₂ , a load index C ₃ and a speed index C ₄ , as well as an applied wheel load ^LR F _{f, e.g.} , a tire pressure p _R and a camber angle γ , with all of the circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

each than of the four tire properties C ₁ , ..., C ₄ , from the applied wheel load ^LR F _{f, e.g.} the tire pressure p _R and the camber angle γ are stored or with the help of a suitably trained artificial neural network KNN-U (see. 22nd and 23 ) depending on the four tire properties C ₁ , ..., C ₄ , from the applied wheel load ^LR F _{f, e.g.} , the tire pressure p _R and the camber angle γ can be determined. That means: $$\begin{array}{l}{U}_i\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1\hfill \\ \text{with}{a}_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right),b_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>0}\hfill \\ \text{and}{n}_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right),m_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>1}\hfill \\ \text{and with}{x}_{\mathrm{S.}\mathrm{E.}}=-x_{\mathrm{L.}\mathrm{R.}}\text{and}{y}_{\mathrm{S.}\mathrm{E.}}=y_{\mathrm{L.}\mathrm{R.}}{+}_{\mathrm{L.}\mathrm{R.}}r{y}_{\mathrm{S.}\mathrm{E.}}\hfill \end{array}$$

wobei die Bodendruckverteilungsfunktion p ebenfalls in Bezug auf das Latsch-Koordinatensystem LR definiert ist, wobei x_LR eine auf das Reifenlatsch-Koordinatensystem LR bezogene x -Koordinate eines Punktes der Lauffläche des Reifens ist, für den ein Bodendruck p bestimmt werden soll, wobei y_LR die y-Koordinate dieses Punktes bezogen auf das Reifenlatsch-Koordinatensystem LR ist, wobei N_x(y_LR ) eine Normierungsfunktion ist zur Normierung des Koordinatenwertes von x_LR auf eine Länge einer Erstreckung der Reifenaufstandsfläche in x-Richtung, wobei N_y(x_LR , y_LR ) eine Abbildungsfunktion ist zur Abbildung des Koordinatenwertes von y_LR auf einen definierten Wertebereich in Abhängigkeit von einer Länge einer Erstreckung der Reifenaufstandsfläche in y-Richtung, wobei A(ŷ_LR) eine Skalierungsfunktion ist, die insbesondere mit Hilfe eines ersten (Regressions-)Parametersatzes p_a1...7 einen ersten Bodendruckverteilungs-Parameter in Form eines Skalierungsparameters in Abhängigkeit von ŷ_LR definiert, und wobei B(ŷ_LR) eine Krümmungsfunktion ist, die insbesondere mithilfe eines zweiten (Regressions-)Parametersatzes p_b1...3 einen zweiten Bodendruckverteilungsparameter in Form eines Krümmungsparameters in Abhängigkeit von γ̂_LR definiert.The soil pressure distribution function p which is stored in step S3 in this exemplary embodiment is defined by: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right]\hfill \\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \end{array},$$

where the ground pressure distribution function p also in relation to the Laces coordinate system LR is defined, where x _LR one on the tire contact coordinate system LR is the related x -coordinate of a point on the tread of the tire for which a ground pressure p should be determined, where y _LR the y-coordinate of this point in relation to the tire contact coordinate system LR where N _x ( y _LR ) a normalization function is used to normalize the coordinate value of x _LR over a length of an extension of the tire contact patch in x-direction, where N _y ( x _LR , y _LR ) a mapping function is used to map the coordinate value of y _LR to a defined range of values as a function of a length of an extension of the tire contact patch in the y-direction, where A (ŷ _LR ) is a scaling function, which is determined in particular with the aid of a first (regression) parameter set p _{a1 ... 7} defines a first soil pressure distribution parameter in the form of a scaling parameter as a function of ŷ _LR , and where B (ŷ _LR ) is a curvature function, which in particular with the aid of a second (regression) parameter set p _{b1 ... 3} defines a second soil pressure distribution parameter in the form of a curvature parameter as a function of γ̂ _LR.

durch y_LR verlaufenden Sekante einer zugehörigen Reifenaufstandsfläche 10 sein, wobei die Sekante eine Umfangskontur der Reifenaufstandsfläche in zwei Schnittpunkten S₃ und S₄ schneidet, wobei die Normierungsfunktion N_x(y_LR ) in diesem Fall definiert ist durch: $$N_x\left(y_{LR}\right)=\left|\left({\overrightarrow{S}}_3\left(y_{LR}\right)-{\overrightarrow{S}}_4\left(y_{LR}\right)\right)\right|.$$

N_y(x_LR ,y_LR ) kann beispielsweise eine Abbildungsfunktion zur linearen Abbildung des Koordinatenwertes y_LR auf einen definierten Wertebereich von [L₁=-1,L₂=1] in Abhängigkeit von einer Länge einer parallel zum Einheitsvektor ${\overrightarrow{e}}_{y,LR}$

durch y_LR verlaufenden Sekante einer zugehörigen Reifenaufstandsfläche sein, wobei die Sekante eine Umfangskontur der Reifenaufstandsfläche in zwei Schnittpunkten S₁ und S₂ schneidet, wobei die Abbildungsfunktion N_y(x_LR ,y_LR ) in diesem Fall definiert ist durch: $$\begin{array}{l}{N}_y\left(x_{LR},y_{LR}\right)={\widehat{y}}_{LR}\hfill \\ =ƒ\left(S_1\left(x_{LR}\right),S_2\left(x_{LR}\right),L_1,L_2,y_{LR}\right)\hfill \\ =N_y\left(S_1\left(x_{LR}\right),S_2\left(x_{LR}\right),L_1,L_2,y_{LR}\right)\hfill \\ =\frac{1}{2}\left[\left(L_1+L_2\right)+\left(L_2-L_1\right)\cdot \left[\frac{2\cdot y_{LR}+\left(S_1\left(x_{LR}\right)+S_2\left(x_{LR}\right)\right)}{\left(S_2\left(x_{LR}\right)-S_1\left(x_{LR}\right)\right)}\right]\right]\hfill \end{array}.$$

For example, N _x ( y _LR ) a normalization function for normalizing the coordinate value of x _LR to a length one parallel to the unit vector ${\overrightarrow{e}}_{x,\mathrm{L.}\mathrm{R.}}$

by y _LR running secant of an associated tire contact patch 10 where the secant intersects a circumferential contour of the tire contact patch at two points of intersection S ₃ and S ₄ , where the normalization function N _x ( y _LR ) in this case is defined by: $$N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)=\left|\left({\overrightarrow{\mathrm{S.}}}_3\left(y_{\mathrm{L.}\mathrm{R.}}\right)-{\overrightarrow{\mathrm{S.}}}_{\mathrm{4th}}\left(y_{\mathrm{L.}\mathrm{R.}}\right)\right)\right|.$$

N _y ( x _LR , y _LR ) can, for example, be a mapping function for linear mapping of the coordinate value y _LR to a defined range of values of [L ₁ = -1, L ₂ = 1] depending on a length of a parallel to the unit vector ${\overrightarrow{e}}_{y,\mathrm{L.}\mathrm{R.}}$

by y _LR running secant of an associated tire contact patch, the secant intersecting a circumferential contour of the tire contact patch at two points of intersection S ₁ and S ₂ , where the mapping function N _y ( x _LR , y _LR ) in this case is defined by: $$\begin{array}{l}{N}_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)={\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\hfill \\ =ƒ\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{L.}}_1,{\mathrm{L.}}_2,y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \\ =N_y\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right),{\mathrm{L.}}_1,{\mathrm{L.}}_2,y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \\ =\frac{1}{2}\left[\left({\mathrm{L.}}_1+{\mathrm{L.}}_2\right)+\left({\mathrm{L.}}_2-{\mathrm{L.}}_1\right)\cdot \left[\frac{2\cdot y_{\mathrm{L.}\mathrm{R.}}+\left({\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right)+{\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right)\right)}{\left({\mathrm{S.}}_2\left(x_{\mathrm{L.}\mathrm{R.}}\right)-{\mathrm{S.}}_1\left(x_{\mathrm{L.}\mathrm{R.}}\right)\right)}\right]\right]\hfill \end{array}.$$

The length of the extension of the tire contact patch in the x-direction and in the y-direction as well as the intersection points S ₁ , S ₂ , S ₃ , S ₄ are determined with the aid of the tire contact patch circumferential contour function described above and stored in step S2 U determined.

By choosing the parameter functions A (ŷ _LR ) and B (ŷ _LR ), different load cases and the resulting soil pressure distributions can be mapped, in particular different dependencies of the soil pressure distribution in the y-direction. In particular, this approach enables the influence of the camber angle to be mapped γ , which in particular has a significant influence when maneuvering and steering while standing.

$$\begin{array}{l}B\left({\widehat{y}}_{LR}\right)=p_{b1}{\left({\widehat{y}}_{LR}\right)}^2+p_{b2}\cdot {\widehat{y}}_{LR}+p_{b3}\hfill \\ \text{mit }{p}_{b\mathrm{1..3}}\in \square \hfill \\ \text{und }{\widehat{y}}_{LR}=N_y\left(x_{LR},y_{LR}\right)\hfill \end{array}.$$

The soil pressure distribution parameters A (ŷ _LR ) and B (ŷ _LR ) or the scaling function A (ŷ _LR ) and the curvature function B (ŷ _LR ) are each a polynomial function, with the scaling function A (ŷ _LR ) being a sixth degree polynomial and the curvature function B (ŷ _LR ) is a polynomial of the second degree with: $$\begin{array}{l}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{a1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{6th}}+p_{a2}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^5+p_{a3}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^{\mathrm{4th}}+p_{a\mathrm{4th}}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^3+p_{a5}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+p_{a\mathrm{6th}}\cdot {\widehat{y}}_{\mathrm{L.}\mathrm{R.}}+p_{a\mathrm{7th}}\hfill \\ \text{with}{p}_{a\mathrm{1..7}}\in \square \hfill \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \end{array}$$

$$\begin{array}{l}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=p_{b1}{\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\cdot {\widehat{y}}_{\mathrm{L.}\mathrm{R.}}+{\mathrm{<figure-callout\; id="3"\; label="p\; b"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\hfill \\ \text{with}{\mathrm{<figure-callout\; id="1"\; label="p\; b"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">p</figure-callout>}}_b\in \square \hfill \\ \text{and}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \end{array}.$$

mit $$\begin{array}{l}A\left({\widehat{y}}_{LR}\right)=ƒ\left(x_{LR},y_{LR},C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right){\text{ mit p}}_{a\mathrm{1..7}}=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right)\\ B\left({\widehat{y}}_{LR}\right)=ƒ\left(x_{LR},y_{LR},C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right){\text{ mit p}}_{b\mathrm{1..3}}=ƒ\left(C_1,C_2,C_3,C_4,{}^{LR}F{}_{ƒ,z},p_R,\gamma \right)\end{array}$$

The ground pressure distribution function used p is also in this exemplary embodiment, in particular like the previously described circumferential contour function U , of the four tire properties C ₁ , ..., C ₄ depending, especially on the tire width C ₁ , the aspect ratio C ₂ , the load index C ₃ and the speed index C ₄ , as well as the applied wheel load ^LR F _{f, e.g.} the tire pressure p _R and the camber angle γ , with all of the ground pressure distribution parameter parameters p _{a1 ... 7} , p _{b1 ... 3} each than of the four tire properties C ₁ , ..., C ₄ , from the applied wheel load F _z , the tire inflation pressure p _R and the camber angle γ are stored or with the help of a suitably trained artificial neural network KNN-p (see. 34 and 35 ) depending on the four tire properties C ₁ , ..., C ₄ , from the applied wheel load ^LR F _{f, e.g.} , the tire pressure p _R and the camber angle γ can be determined. That means: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},{\widehat{y}}_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right]\hfill \\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\text{and}\hfill \\ \text{with}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right),\hfill \\ \text{and}\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\hfill \end{array}$$

with $$\begin{array}{l}\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right){\text{with p}}_{a\mathrm{1..7}}=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\\ \mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=ƒ\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}},{\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right){\text{with <figure-callout id="1" label="p b" filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png" state="{{state}}">p</figure-callout>}}_b=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}},{}^{\mathrm{L.}\mathrm{R.}}\mathrm{F.}{}_{ƒ,z},p_{\mathrm{R.}},\gamma \right)\end{array}$$

die innerhalb der für den jeweiligen Lastfall resultierenden Reifenaufstandsfläche 10 liegen und die jeweils durch einen Ortsvektor definiert sind, am Untergrund S abgestützt werden, insbesondere durch die im Reifenlatsch 10 wirkenden Reibkräfte.If now, in step S4, a defined load and / or movement is exerted on the rim 2 can be applied via the kinematic coupling of the rubber brush elements q _{i = 1..k} with the rim 2 as reproduced by the tire model used, which is inserted into the rubber brush elements q _{i = 1..k} Introduced forces and moments can be determined, which via the rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in},$

the tire contact area resulting for the respective load case 10 and which are each defined by a position vector, on the subsurface S. be supported, especially by those in the tire contact 10 acting frictional forces.

ab (der in diesem Fall ein Vektor ist, welcher jeweils einen zugehörigen Haft- und Gleit-Reibungskoeffizienten ^LRµ_G,H,x für die x-Richtung und einen zugehörigen Haft- und Gleit-Reibungskoeffizienten ^LRµ_G.H.y für die y-Richtung aufweist), sondern maßgeblich vor allem von der Ausdehnung der sich einstellenden Reifenaufstandsfläche 10 und damit von der Anzahl der innerhalb der Reifenaufstandsfläche 10 liegenden Gummibürstenelementen ${}^{LR}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

sowie vom dem jeweils an den einzelnen, innerhalb der Reifenaufstandsfläche 10 liegenden Gummibürstenelementen ${}^{LR}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

anliegenden Bodendruck ^LRp_e,z,qi=1...k, von welchem insbesondere abhängt, ob ein Gummibürstenelement ${}^{LR}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

am Untergrund S haftet oder über diesen gleitet.As is easy to imagine, they hang between tires 1 and underground S. resulting frictional forces not only from the associated coefficient of friction of the subsurface ${}^{\mathrm{L.}\mathrm{R.}}\overline{\mu }{}_{G,H,xy}$

ab (which in this case is a vector that has an associated coefficient of static friction and sliding friction ^LR µ _{G, H, x} for the x direction and an associated coefficient of _static ^{friction and sliding friction LR} µ GHy for the y direction ), but mainly on the extent of the tire contact area that is established 10 and thus on the number of within the tire contact area 10 lying rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

as well as from each to the individual, within the tire contact area 10 lying rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

applied ground pressure ^LR p _{e, z, qi = 1 ... k} , on which in particular depends whether a rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}$

on the ground S. adheres or slides over it.

With a circumferential contour function as described above and stored in step S2 U In step S5, the extent or the circumferential contour of the on the tire 1 applied load and / or movement resulting tire contact area 10 determine particularly precisely, the determination in this exemplary embodiment by a method according to the invention according to the third or fourth aspect of the invention based on the circumferential contour function stored in step S2 U he follows.

das sich innerhalb der resultierenden Reifenaufstandsfläche 10 befindet, ein zugehöriger normierter Bodendruckwert ^LRF_f,z,qi=1...k ermittelt wird.With a ground pressure distribution function as described above and stored in step S3 p In step S6, the ground pressure distribution can be derived from the on the tires 1 applied load and / or movement resulting tire contact area 10 determine particularly precisely, the determination in this exemplary embodiment by a method according to the invention according to the fifth or sixth aspect of the invention based on the circumferential contour function stored in step S3 p takes place, for each individual rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in},$

that is within the resulting tire footprint 10 is located, an associated standardized ground pressure value ^LR F _{f, z, qi = 1 ... k} is determined.

ermittelte Bodendruckwert ^LRp_{e,z,q i=1..k} jeweils anteilig gemäß der folgenden Formel $${}^{LR}{F}_{ƒ,z,q_{i=i\mathrm{..}k}}=\frac{{}^{LR}{F}_{ƒ,z}}{{\displaystyle \sum _{i=1}^k{}^{LR}{p}_{e,z,q_{i=\mathrm{1..}k}}}}{\cdot }^{LR}{p}_{e,z,q_{i=\mathrm{1..}k}},$$

auf eine der Bodendruckverteilung zugrundeliegende Radlast ^LRF_f,z normiert,
wobei ^LRF_{f,z,q i=1..k} der jeweils normierte Bodendruckwert des jeweiligen Gummibürstenelements ist und q_l=1..k die jeweilige Gummibürste bzw. das jeweilige Gummibürstenelement indiziert und k die Anzahl der Gummibürsten ist, wobei ^LRF_f,z der Bodendruckverteilung zugrundeliegende Radlast ist,
und wobei ^LRp_f,z,qi=1..k der jeweilige, mittels der Bodendruckverteilungsfunktion bestimmte, zu normierende Bodendruckwert ist, d.h. der jeweilige für das jeweilige Gummibürstenelement q_l=1..k.This is done by means of the ground pressure distribution function p for each rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

determined ground pressure value ^LR p _{e, z, q i = 1..k} in each case proportionally according to the following formula $${}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,q_{i=i\mathrm{..}k}}=\frac{{}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z}}{{\displaystyle \sum _{i=1}^k{}^{\mathrm{L.}\mathrm{R.}}{p}_{e,z,q_{i=\mathrm{1..}k}}}}{\cdot }^{\mathrm{L.}\mathrm{R.}}{p}_{e,z,q_{i=\mathrm{1..}k}},$$

on a wheel load on which the ground pressure distribution is based ^LR F _{f, e.g.} normalized,
where ^LR F _{f, z, q i = 1..k} is the normalized ground pressure value of the respective rubber brush element and q _{l = 1..k indicates} the respective rubber brush or the respective rubber brush element and k is the number of rubber brushes, where ^LR F _{f, e.g.} is the wheel load underlying the ground pressure distribution,
and where ^LR p _{f, z, qi = 1..k is} the respective soil pressure value to be normalized, determined by means of the soil pressure distribution function, ie the respective one for the respective rubber brush element q _{l = 1..k} .

wird der zugehörige normierte Bodendruckwert ^LRF_{f,z,q i=1..k} auf null gesetzt, d.h. es gilt für diese Gummibürstenelemente ${}^{LR}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{out}:$

^LRF_{f,z,q i=1..k} =0.
Ist für jedes, sich innerhalb der resultierenden Reifenaufstandsfläche 10 befindende Gummibürstenelement ${}^{LR}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

ein zugehöriger normierter Bodendruckwert ^LRF_{f,z,q i=1..k} ermittelt worden, werden in Schritt S7 an den jeweiligen einzelnen Gummibürstenelementen ${}^{LR}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

die wirkenden resultierenden Kräfte ${}^{LR}{\overrightarrow{F}}_{ƒ,q_{i-\mathrm{1..}k}}$

und Momente ${}^{LR}{\overrightarrow{M}}_{\delta ,q_{i-\mathrm{1..}k}}$

in Abhängigkeit von dem sich jeweils an den jeweiligen einzelnen Gummibürstenelementen ${}^{LR}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

einstellenden normierten Bodendruck ^LRF_{f,z,q i=1..k} unter Berücksichtigung, ob Haftreibung oder Gleitreibung vorliegt, ermittelt.For yourself outside the tire contact area 10 located rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{Out}$

the associated normalized ground pressure value ^LR F _{f, z, q i = 1..k} set to zero, i.e. it applies to these rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{Out}:$

^LR F _{f, z, q i = 1..k} = 0.
Is for everyone to be within the resulting tire footprint 10 located rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

an associated standardized ground pressure value ^LR F _{f, z, q i = 1..k} are determined in step S7 on the respective individual rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

the acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,q_{i-\mathrm{1..}k}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta ,q_{i-\mathrm{1..}k}}$

depending on the respective individual rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

adjusting normalized ground pressure ^LR F _{f, z, q i = 1..k} taking into account whether there is static friction or sliding friction.

wirkenden resultierenden Kräfte ${}^{LR}{\overrightarrow{F}}_{ƒ,q_{i-\mathrm{1..}k}}$

und Momente ${}^{LR}{\overrightarrow{M}}_{\delta ,q_{i-\mathrm{1..}k}}$

, welche in Schritt S9 gespeichert und/oder ausgegeben werden.Based on this, the resulting total tire force, in particular the total frictional force acting in the tire contact patch, and the total tire torque, in particular the total drilling torque, are determined in step S8, in particular by adding up the individual rubber brush elements ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

acting resulting forces ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{F.}}}_{ƒ,q_{i-\mathrm{1..}k}}$

and moments ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{\mathrm{M.}}}_{\delta ,q_{i-\mathrm{1..}k}}$

which are stored and / or output in step S9.

der parametrisierten Umfangskonturfunktion U bestimmt worden sind, wobei dieses Ausführungsbeispiel eines erfindungsgemäßen Verfahrens gemäß dem ersten Aspekt die folgenden Schritte umfasst:

S2-1:

Auswählen der Umfangskonturfunktion U, für welche die Parameter ermittelt werden sollen, wobei bei diesem Beispiel die wie vorstehend beschriebene Umfangskonturfunktion U ausgewählt wird;

S2-1A:

Erzeugen von einer Vielzahl von ReifenaufstandsflächenAbdrücken 10 durch Messungen für verschiedene definierte Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen;

S2-1B:

Ermitteln der jeweiligen Umfangskontur-Parameter a, b₁₂ , b₃₄ , n₁₂ , n₃₄ , m₁₂ , m₃₄ , ${}_{LR}{\overrightarrow{r}}_{SE}$

aus den einzelnen Reifenaufstandsflächen-Abdrücken 10, und Ermitteln von Umfangskontur-Parameter-Datensätzen aus den jeweils aus den einzelnen Reifenaufstandsflächen-Abdrücken 10 ermittelten Umfangskonturparametern a, b₁₂ , b₃₄ , n₁₂ , n₃₄ , m₁₂ , m₃₄ , ${}_{LR}{\overrightarrow{r}}_{SE}$

für die verschiedenen definierten Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen; und

S2-2:

Trainieren eines künstlichen neuronalen Netzes KNN-U zur Ermittlung von an verschiedene definierte Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen angepassten Umfangskontur-Parametern

$$a_i=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right),$$

$$b_i=ƒ\left({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">C</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0259.png"\; state="\{\{state\}\}">C</figure-callout>}}_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)\in {\text{R}}^{>0}$$

$$n_i=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right),$$

$$m_i=ƒ\left({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">C</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0259.png"\; state="\{\{state\}\}">C</figure-callout>}}_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)\in {\text{R}}^{>1}$$

$${}_{LR}{\overrightarrow{r}}_{SE}$$

mit zumindest einem Teil der Umfangskontur-Parameter-Datensätze und Hinterlegen des trainierten, künstlichen neuronalen Netzes zusammen mit der Umfangskonturfunktion,
wobei das Ermitteln der jeweiligen Umfangskontur-Parameter a, b₁₂ , b₃₄ , n₁₂ , n₃₄ , m₁₂ , m₃₄ , ${}_{LR}{\overrightarrow{r}}_{SE}$

aus den einzelnen Reifenaufstandsflächen-Abdrücken 10 durch ein erfindungsgemäßes Verfahren gemäß dem ersten Aspekt der vorliegenden Erfindung in diesem Fall mit den später noch näher erläuterten Schritten S2-1B1 bis S2-1B6 erfolgt. 12th shows a flowchart for an embodiment of a method according to the invention according to the first aspect of the invention with the circumferential contour parameters in this example a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

the parameterized perimeter contour function U have been determined, this embodiment of a method according to the invention according to the first aspect comprising the following steps:

S2-1:

Selecting the perimeter contour function U , for which the parameters are to be determined, whereby in this example the circumferential contour function as described above U is selected;

S2-1A:

Generate a variety of tire footprints 10 by measurements for different defined loads and / or movements with different tires with different tire properties and tire conditions;

S2-1B:

Determination of the respective circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

from the individual tire footprints 10 , and determining circumferential contour parameter data sets from the individual tire contact patch imprints 10 determined circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

for the different defined loads and / or movements with different tires with different tire properties and tire conditions; and

S2-2:

Training an artificial neural network KNN-U to determine circumferential contour parameters adapted to different defined loads and / or movements with different tires with different tire properties and tire conditions

$$a_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right),$$

$$b_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>0}$$

$$n_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right),$$

$$m_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>1}$$

$${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$$

with at least some of the circumferential contour parameter data sets and storing the trained, artificial neural network together with the circumferential contour function,
whereby the determination of the respective circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

from the individual tire footprints 10 is carried out by a method according to the invention according to the first aspect of the present invention in this case with the steps S2-1B1 to S2-1B6 explained in more detail below.

The creation of a variety of tire footprints 10 by measurements for different defined loads and / or movements with different tires 1 with different tire properties and tire conditions in step S2-1 was carried out in the example described here, in the tire 1 with different tire properties such as tire width C ₁ , Aspect ratio C ₂ , Load index C ₃ and speed index C ₄ , with different tire conditions, in particular different tire inflation pressures p _R , with different wheel loads ^LR F _{f, e.g.} at different camber angles γ were supported on a tire test bench (FlatTrack) on a pressure measuring plate (Tekscan VersaTek TireScan TVR8406) and the determined pressure readings were graphically displayed.

bzw. die Lage des Latsch-Referenzpunktes LR bekannt, können die Sensorkoordinaten x_s ,y_s bzw. die Koordinaten der Punkte P der Umfangskontur in die Koordinaten mit Bezug auf das Latsch-Koordinatensystem LR umgerechnet werden und die ermittelten Bodendruckwerte in Bezug auf das Latsch-Koordinatensystem LR angegeben werden. 13th shows an example of a tire footprint 10 as it has been recorded with a pressure measuring plate, for the area within the tire contact patch 10 , which is limited by the points P of a circumferential contour, each with the help of corresponding pressure sensors depending on the sensor coordinates x _s , y _s , in each case a ground pressure has been recorded, which is shown by means of a false color plot. The sensor coordinates x _s , y _s are in relation to a sensor coordinate system with a coordinate origin S. defines which of the 13th is in the upper left corner of the pressure measuring plate. Is a coordinate transformation vector $\mathrm{L.}{\mathrm{R.}}^{\overrightarrow{r}}\mathrm{S.}\mathrm{E.}$

or the position of the Latsch reference point LR known, the sensor coordinates x _s , y _s or the coordinates of the points P of the circumferential contour in the coordinates with reference to the Latsch coordinate system LR are converted and the determined ground pressure values in relation to the Latsch coordinate system LR can be specified.

aus den einzelnen Reifenaufstandsflächen-Abdrücken 10 in Schritt S2-1B wurden diese zunächst aufbereitet (insbesondere mittels Bildbearbeitung und Bilddatenanalyse, gefiltert, ausgerichtet etc.), bevor die Umfangskontur-Parameter a, b₁₂ , b₃₄ , n₁₂ , n₃₄ , m₁₂, m₃₄ , ${}_{LR}{\overrightarrow{r}}_{SE}$

mit den Schritten S2-1B1 bis S2-1B6 wie nachfolgend anhand der 14 bis 19 erläutert wird, bestimmt worden sind.For determining the respective circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

from the individual tire footprints 10 In step S2-1B, these were first prepared (in particular by means of image processing and image data analysis, filtered, aligned, etc.) before the circumferential contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

with steps S2-1B1 to S2-1B6 as follows using the 14th until 19th is explained, have been determined.

S2-1B1:

Bestimmen einer maximalen Erstreckung 2a des Reifenaufstandsflächen-Abdrucks 10 in x_LR-Richtung, insbesondere mithilfe einer mittels Bilddatenanalyse ermittelten Hüllkurve, (siehe 14),

S2-1B2:

Bestimmen einer maximalen Erstreckung b₁₂ +b₃₄ des Reifenaufstandsflächenabdrucks in y_LR-Richtung, insbesondere mithilfe einer mittels Bilddatenanalyse ermittelten Hüllkurve, (siehe 14),

S2-1B3:

Ermitteln des Umfangskonturfunktion-Koordinatenursprungs SE in Abhängigkeit von der maximalen Erstreckung 2a des Reifenaufstandsflächen-Abdrucks 10 in x_LR-Richtung und in Abhängigkeit von der maximalen Erstreckung b₁₂ +b₁₄ des Reifenaufstandsflächen-Abdrucks 10 in y_LR-Richtung (siehe 14),

S2-1B4:

Ermitteln der Umfangskontur-Parameter a, b₁₂ , b₃₄ der parametrisierten Reifenaufstandsflächen-Umfangskonturfunktion U in Abhängigkeit von einem Abstand a, b₁₂ , b₃₄ eines Umfangskonturpunktes des ReifenaufstandsflächenAbdrucks 10 zum Umfangskonturfunktion-Koordinatenursprung SE in x_LR-Richtung und y_LR-Richtung (siehe 14),

S2-1B5:

Ermitteln der weiteren Umfangskontur-Parameter n₁₂ , n₃₄ , m₁₂ , m₃₄ der parametrisierten Reifenaufstandsflächen-Umfangskonturfunktion U mithilfe eines Optimierungsverfahrens (siehe 15 und 16), und

S2-1B6:

Ermitteln eines Koordinatentransformationsvektors $L{R}^{\overrightarrow{r}}SE,$

welcher eine zugehörige Koordinatentransformation für eine Verschiebung des Umfangskonturfunktion-Koordinatenursprungs SE des Umfangskonturfunktion-Koordinatensystems SE in einen Reifenlatsch- Koordinatenursprung LR eines Reifenlatsch-Koordinatensystems LR definiert (siehe 14 und 16).

The steps S2-1B1 to S2-1B6 are:

S2-1B1:

Determining a maximum extent 2a of the tire contact patch imprint 10 in the x _LR direction, in particular with the help of an envelope curve determined by means of image data analysis (see 14th ),

S2-1B2:

Determining a maximum extension b ₁₂ + b ₃₄ of the tire contact area imprint in y _LR direction, in particular with the help of an envelope curve determined by means of image data analysis (see 14th ),

S2-1B3:

Determining the circumferential contour function coordinate origin SE as a function of the maximum extent 2a of the tire contact patch imprint 10 in x _LR direction and depending on the maximum extension b ₁₂ + b ₁₄ of the tire contact patch imprint 10 in y _LR direction (see 14th ),

S2-1B4:

Determination of the circumferential contour parameters a , b ₁₂ , b ₃₄ the parameterized tire contact patch circumferential contour function U depending on a distance a , b ₁₂ , b ₃₄ of a circumferential contour point of the tire footprint 10 to the circumferential contour function coordinate origin SE in x _LR direction and y _LR direction (see 14th ),

S2-1B5:

Determination of the further circumferential contour parameters n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ the parameterized tire contact patch circumferential contour function U using an optimization procedure (see 15th and 16 ), and

S2-1B6:

Find a coordinate transformation vector $\mathrm{L.}{\mathrm{R.}}^{\overrightarrow{r}}\mathrm{S.}\mathrm{E.},$

which is an associated coordinate transformation for a displacement of the circumferential contour function coordinate origin SE of the circumferential contour function coordinate system SE into a tire contact coordinate origin LR a tire contact coordinate system LR defined (see 14th and 16 ).

The perimeter contour parameters a , b ₁₂ , b ₃₄ as well as the circumferential contour function coordinate origin SE can be done directly by means of an image data analysis from the individual, determined tire contact patch imprints 10 are recorded.

The other circumferential contour parameters n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , the parameterized tire contact patch circumferential contour function U however, cannot simply be read or measured and have been determined with the aid of a mathematical optimization method based on a minimization of the distance squares between a circumferential contour initially determined with defined starting parameters and the determined envelope curve.

ist mithilfe mehrerer Profilgeometrieinformationen ermittelt worden, insbesondere mithilfe mehrerer Rilleninformationen, die sich aus den Rillen 11 ermitteln lassen, insbesondere mithilfe mehrerer Rillenabstandswerte r_1...8 , welche ein Profil des jeweiligen Reifens charakterisieren und mit deren Hilfe zunächst jeweils der Latsch-Referenzpunkt LR ermittelt worden ist, siehe 17 und 18. In Abhängigkeit von dem ermittelten Latsch-Referenzpunkt LR wurde dann in Verbindung mit dem Koordinatenursprung SE der Koordinatentransformationsvektor ${}_{LR}{\overrightarrow{r}}_{SE}$

bestimmt.The coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

has been determined with the aid of a number of profile geometry information items, in particular with the aid of a number of groove information items that result from the grooves 11 can be determined, in particular with the help of several groove spacing values r _{1 ... 8} which characterize a profile of the respective tire and with their help initially the contact point reference point LR has been determined, see 17th and 18th . Depending on the determined Latsch reference point LR was then associated with the origin of coordinates SE the coordinate transformation vector ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

certainly.

Since there is a tire contact area for a camber angle of γ = 0 ° 10 adjusts whose center of gravity M. with the Latsch reference point LR coincides, the Latsch reference point could be LR for camber angles of γ = 0 °, alternatively also independently of a groove information by determining the center of the area as a function of the determined circumferential contour function U be determined. A determination with the help of one or more profile geometry information and / or with the help of a stamp pattern is, however, possible in all cases, in particular also with a camber angle of γ ≠ 0 ° (provided the stamp pattern is introduced into the tire in such a way that it is always within the tire contact area) , and therefore particularly advantageous.

insbesondere des hierfür erforderlichen Latsch-Referenzpunktes LR, nur mithilfe von Profilgeometrieinformationen wie beispielweise einer oder mehrerer Rilleninformationen und/oder einer Markierung und/oder eines Stempelmusters oder dergleichen möglich.With camber angles of y ≠ 0 °, the contact point reference point is determined LR by means of the center of gravity M. not possible because of the center of gravity M. the tire contact patch 10 not with that of the Latsch reference point LR coincides. In this case the determination of the coordinate transformation vector is ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

in particular the Latsch reference point required for this LR , only possible with the help of profile geometry information such as one or more groove information and / or a marking and / or a stamp pattern or the like.

ermittelt, die mehrere Umfangskontur-Parameter-Datensätze bilden, die jeweils für die verschiedenen definierten Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen eine jeweilige sich einstellende Umfangskontur definieren, was durch die vier verschieden Umfangskonturen in 19 symbolisiert sein soll.With steps S2-1B1 to S2-1B6, the individual tire contact patches became imprints 10 the respective circumferential contour parameters for the different defined loads and / or movements with different tires with different tire properties and tire conditions a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

determined, which form several circumferential contour parameter data sets, each of which defines a circumferential contour that is established for the various defined loads and / or movements with different tires with different tire properties and tire conditions, which is indicated by the four different circumferential contours in 19th should be symbolized.

$$b_i=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)\in {\text{R}}^{>0}$$

$$n_i=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right),$$

$$m_i=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)\in {\text{R}}^{>1}$$

$${}_{LR}{\overrightarrow{r}}_{SE}$$

trainiert worden und zusammen mit der Umfangskonturfunktion U hinterlegt worden. Das vorliegend verwendete künstliche neuronale Netzt KNN-U weist dabei zwei Schichten auf, insbesondere eine verdeckte Schicht und eine Ausgabeschicht.With some of these data sets, an artificial neural network is then created in step S2-2 KNN-U (see. ( 20th ) to determine circumferential contour parameters adapted to different defined loads and / or movements with different tires with different tire properties and tire conditions $$a_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right),$$

$$b_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>0}$$

$$n_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right),$$

$$m_i=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)\in {\text{R.}}^{>1}$$

$${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$$

been trained and together with the circumferential contour function U been deposited. The artificial neural network used here KNN-U has two layers, in particular a hidden layer and an output layer.

in Abhängigkeit von den Eingangsgrößen bestimmt werden. Dies ermöglicht eine besonders genaue Ermittlung der Ausdehnung bzw. der Umfangskontur der sich in Abhängigkeit von den Eingangsgrößen einstellenden Reifenaufstandsfläche 10 und damit auch eine besonders genaue Berechnung der Reifenkräfte und -momente im Reifenlatsch in Schritt S5, wobei insbesondere, wie schematisch in 21 dargestellt, für jedes Gummibürstenelement ${}^{LR}{\overrightarrow{q}}_{i=\mathrm{1..}k}$

ermittelt worden ist, ob es sich innerhalb oder außerhalb der Reifenaufstandsfläche 10 befindet.With the help of the artificial neural network KNN-U can depending on the input variables ^LR _{Fj, z} , p _R, γ , C ₁ , C ₂ , C ₃ , C ₄ the perimeter contour parameters a , b ₁₂ , b ₃₄ , n ₁₂ , n ₃₄ , m ₁₂ , m ₃₄ , ${}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}$

can be determined depending on the input variables. This enables a particularly precise determination of the extent or the circumferential contour of the tire contact area that is established as a function of the input variables 10 and thus also a particularly precise calculation of the tire forces and torques in the tire contact in step S5, in particular, as shown schematically in FIG 21 shown for each rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}$

it has been determined whether it is inside or outside the tire contact patch 10 is located.

S3-1:

Auswählen der Bodendruckverteilungsfunktion p, für welche die Parameter ermittelt werden sollen, wobei bei diesem Beispiel die wie vorstehend beschriebene Bodendruckverteilungsfunktion p ausgewählt wird;

S3-1A:

Erzeugen von einer Vielzahl von Bodendruckverteilungen mit jeweils einer Vielzahl von Bodendruckwerten durch Messungen für verschiedene definierte Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen;

S3-1B:

Ermitteln der jeweiligen Bodendruckverteilungs-Parameter p_{a1... 7} , p_b1...3 aus den einzelnen Bodendruckverteilungen und Ermitteln von Umfangskontur-Parameter-Datensätzen aus den jeweils aus den einzelnen Bodendruckverteilungen ermittelten Bodendruckverteilungs-Parametern p_a1...7 , p_b1...3 für die verschiedenen definierten Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen; und

S3-2:

Trainieren eines künstlichen neuronalen Netzes KNN-p zur Ermittlung von an verschiedene definierte Belastungen und/oder Bewegungen mit verschiedenen Reifen mit verschiedenen Reifeneigenschaften und Reifenzuständen angepassten Bodendruckverteilungs-Parametern $$p_{a\mathrm{1..7}}=ƒ\left({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">C</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0259.png"\; state="\{\{state\}\}">C</figure-callout>}}_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)$$

$${\mathrm{<figure-callout\; id="1"\; label="p\; b"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">p</figure-callout>}}_b=ƒ\left({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">C</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0251.png"\; state="\{\{state\}\}">C</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="DE102020112487A1\_0247.png,DE102020112487A1\_0259.png"\; state="\{\{state\}\}">C</figure-callout>}}_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)$$

mit zumindest einem Teil der Bodendruckverteilungs-Parameter-Datensätze und Hinterlegen des trainierten, künstlichen neuronalen Netzes zusammen mit der Bodendruckverteilungsfunktion,

wobei das Ermitteln der jeweiligen Bodendruckverteilungs-Parameter p_a1...7 , p_b1...3 aus den einzelnen Bodendruckverteilungen durch ein erfindungsgemäßes Verfahren gemäß dem zweiten Aspekt der vorliegenden Erfindung in diesem Fall mit den später noch näher erläuterten Schritten S3-1B1 bis S3-1B3 erfolgt ist. 22nd shows a flowchart for an embodiment of a method according to the invention according to the second aspect of the invention with the soil pressure distribution parameters in this example p _{a1 ... 7} , p _{b1 ... 3} the parameterized ground pressure distribution function p have been determined, this embodiment of a method according to the invention according to the second aspect comprising the following steps:

S3-1:

Select the ground pressure distribution function p , for which the parameters are to be determined, whereby in this example the soil pressure distribution function as described above p is selected;

S3-1A:

Generating a multiplicity of ground pressure distributions, each with a multiplicity of ground pressure values, by measurements for different defined loads and / or movements with different tires with different tire properties and tire conditions;

S3-1B:

Determination of the respective soil pressure distribution parameters p _{a1 ... 7} , p _{b1 ... 3} from the individual soil pressure distributions and determination of circumferential contour parameter data sets the soil pressure distribution parameters determined from the individual soil pressure distributions p _{a1 ... 7} , p _{b1 ... 3} for the different defined loads and / or movements with different tires with different tire properties and tire conditions; and

S3-2:

Training an artificial neural network KNN-p to determine ground pressure distribution parameters adapted to different defined loads and / or movements with different tires with different tire properties and tire conditions $$p_{a\mathrm{1..7}}=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)$$

$$p_{b\mathrm{1..3}}=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)$$

with at least some of the soil pressure distribution parameter data sets and storing the trained, artificial neural network together with the soil pressure distribution function,

wherein the determination of the respective soil pressure distribution parameters p _{a1 ... 7} , p _{b1 ... 3} from the individual soil pressure distributions by a method according to the invention according to the second aspect of the present invention in this case with the steps S3-1B1 to S3-1B3 explained in more detail below.

The generation of a large number of ground pressure distributions through measurements for different defined loads and / or movements with different tires 1 with different tire properties and tire conditions in step S3-1 was also carried out in the example described here, in the tire 1 with different tire properties such as tire width C ₁ , Aspect ratio C ₂ , Load index C ₃ and speed index C ₄ , with different tire conditions, in particular different tire inflation pressures p _R , with different wheel loads ^LR F _fz at different camber angles γ were supported on a tire test bench on a pressure measuring plate (Tekscan VersaTek TireScan TVR8406) and the determined pressure readings were recorded.

23 shows an example of a corresponding, recorded soil pressure distribution.

For determining the respective soil pressure distribution parameters p _{a1 ... 7} , p _{b1 ... 3} From the individual soil pressure distributions in step S3-1B, these were first processed (filtered, aligned, etc.) before the soil pressure distribution parameters p _{a1 ... 7} , p _{b1 ... 3} with steps S3-1B1 to S3-1B3 as follows using the 24 until 30th is explained by way of example, have been determined.

S3-1B1:

Unterteilen der Reifenaufstandsfläche in y_LR-Richtung, hier beispielhalber in mehrere annähernd äquidistante Abschnitte 1 bis 10, und Ermitteln eines statistisch repräsentativen Bodendruckwertes, insbesondere eines mittleren Bodendruckwertes, für wenigstens einen der Abschnitte aus wenigstens zwei definierten Punkten der Reifenaufstandsfläche, die innerhalb dieses Abschnitts liegen und jeweils einen gleichen Koordinatenwert in x_LR-Richtung aufweisen,

S3-1B2:

wobei Schritt S3-1B1 für jeden Abschnitt und für alle Koordinatenwerte, in x_LR-Richtung wiederholt wird, zu denen jeweils ein definierter Punkt innerhalb der Reifenaufstandfläche 10 mit jeweils einem zugehörigen Bodendruckwert existiert,

S3-1B3:

Ermitteln der Regressionsparameter p_a1...7 und p_b1..3 der Bodendruckverteilungs-Parameter A(ŷ_LR) und B(ŷ_LR), d.h. der Regressionsparameter p_a1...7 der Skalierungsfunktion A(ŷ_LR) und der Regressionsparameter p_b1..3 von der Krümmungsfunktion B(ŷ_LR) der Bodendruckverteilungsfunktion, die jeweils durch eine parametrisierte Regressionsfunktion wie vorstehend definiert sind, durch ein mathematisches Optimierungsverfahren.

The steps S3-1B1 to S3-1B3 are:

S3-1B1:

Subdivide the tire contact area in y _LR direction, here for example into several approximately equidistant sections 1 until 10 , and determining a statistically representative ground pressure value, in particular a mean ground pressure value, for at least one of the sections from at least two defined points of the tire contact area that lie within this section and each have the same coordinate _{value in the x LR} direction,

S3-1B2:

Step S3-1B1 being repeated for each section and for all coordinate values in the x _LR direction, for each of which a defined point within the tire contact area 10 each with an associated ground pressure value exists,

S3-1B3:

Determine the regression parameters p _{a1 ... 7} and p _b1..3 the soil pressure distribution parameters A (ŷ _LR ) and B (ŷ _LR ), ie the regression parameter p _{a1 ... 7} the scaling function A (ŷ _LR ) and the regression parameters p _b1..3 from the curvature function B (ŷ _LR ) of the soil pressure distribution function, each of which is defined by a parameterized regression function as above, by a mathematical optimization method.

Instead of 10 sections, it is also possible to subdivide it into more or fewer sections. Likewise, the tire contact area 10 can also be subdivided into non-equidistant or exactly equidistant sections.

25th shows the result of steps S3-1B1 and S3-1B2, where for each coordinate value x _LR in each case a mean ground pressure value according to 26th results, where 26th by way of example, the mean ground pressure values determined in the manner described above and a ground pressure value curve for section calculated using the ground pressure distribution function according to the invention 6th normalized to a maximum compressive force. 27 shows the corresponding mean and standardized soil pressure values as well as the calculated soil pressure value curves for the sections 1 , 4th , 6th and 10 .

28 illustrates the influence of the soil pressure distribution parameters A (ŷ _LR ) and B (ŷ _LR ), i.e. the scaling function A (ŷ _LR ) and the curvature function B (ŷ _LR ), on the soil pressure value, which is dependent on the soil pressure distribution function p is obtained, with this illustration clearly showing that the soil pressure distribution parameter A (ŷ _LR ) has or is a scaling function and the soil pressure distribution parameter B (ŷ _LR) a curvature function.

29 shows, by way of example, a course of the soil pressure distribution parameter A (ŷ _LR ), ie the scaling function A (ŷ _LR ), which is based on a sixth degree polynomial as described above, depending on ŷ _LR , ie in this case depending on the defined range of values [-1, 1] as a function of a length of the extension of the tire contact patch in the y _LR -direction mapped y -coordinate value y _LR compared to the real recorded soil pressure measurements after their preparation.

30th shows, by way of example, a course of the soil pressure distribution parameter B (ŷ _LR ), ie the curvature function B (ŷ _LR ), which is based on a polynomial of the second degree as described above, also as a function of ŷ _LR and in comparison to the real recorded soil pressure measurements according to their Processing.

With steps S3-1B1 to S3-1B3, the respective soil pressure distribution parameters were determined from the individually determined, in particular measured, soil pressure distributions for the various defined loads and / or movements with different tires with different tire properties and tire conditions p _{a1 ... 7} and p _b1..3 determined, which form a plurality of soil pressure distribution parameter data sets, each defining a ground pressure distribution for the different defined loads and / or movements with different tires with different tire properties and tire conditions.

$$p_{b\mathrm{1..3}}=ƒ\left(C_1,C_2,C_3,C_4{,}^{LR}{F}_{ƒ,z,}{p}_R,\gamma \right)$$

trainiert worden und zusammen mit der Bodendruckverteilungsfunktion p hinterlegt worden. Das vorliegend verwendete künstliche neuronale Netz KNN-p weist dabei ebenfalls zwei Schichten auf, insbesondere eine verdeckte Schicht und eine Ausgabeschicht.With some of these data sets, an artificial neural network is then created in step S3-2 KNN-p (see. ( 31 ) to determine ground pressure distribution parameters adapted to different defined loads and / or movements with different tires with different tire properties and tire conditions $$p_{a\mathrm{1..7}}=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)$$

$${\mathrm{<figure-callout\; id="1"\; label="p\; b"\; filenames="DE102020112487A1\_0255.png,DE102020112487A1\_0256.png"\; state="\{\{state\}\}">p</figure-callout>}}_b=ƒ\left({\mathrm{C.}}_1,{\mathrm{C.}}_2,{\mathrm{C.}}_3,{\mathrm{C.}}_{\mathrm{4th}}{,}^{\mathrm{L.}\mathrm{R.}}{\mathrm{F.}}_{ƒ,z,}{p}_{\mathrm{R.}},\gamma \right)$$

trained and together with the ground pressure distribution function p been deposited. The artificial neural network used here KNN-p also has two layers, in particular a hidden layer and an output layer.

innerhalb der Reifenaufstandsfläche ein zugehöriger Bodendruckwert bzw. eine zugehörige Bodendruckkraft bzw. ein zugehöriger Kraftanteil ^LRF_f,z,qi=1...k an der Radlast ermittelt wird.With the help of the artificial neural network KNN-p can depending on the input variables ^LR F _{f, e.g.} , p _R , γ , C ₁ , C ₂ , C ₃ , C ₄ the soil pressure distribution parameters p _{a1 ... 7} and p _b1..3 can be determined depending on the input variables. This enables a particularly precise determination of the ground pressure distribution that is established as a function of the input variables in the tire contact area and thus also a particularly precise calculation of the tire forces and torques in the tire contact area in step S6, with in particular, as shown schematically in FIG 32 shown for each rubber brush element ${}^{\mathrm{L.}\mathrm{R.}}{\overrightarrow{q}}_{i=\mathrm{1..}k}^{in}$

an associated ground pressure value or an associated ground pressure force or an associated force component within the tire contact area ^LR F _{f, z, qi = 1 ... k} is determined on the wheel load.

S11:

Start;

S12:

Definieren auslegungsrelevanter Belastungen/Bewegungen;

S0-S10:

Ermitteln der infolgedessen entstehenden Reifenkräfte und -momente durch ein erfindungsgemäßes Verfahren wie vorbeschrieben mit den Schritten S0-S10;

S13:

Ermitteln der hieraus resultierenden Belastungen der Komponente;

S14:

Vergleichen mit den zulässigen Belastungen der Komponente;

S15:

Prüfen, ob die ermittelte resultierende Belastung unter der zulässigen Belastung liegt; falls nein weiter mit Schritt S16; falls ja, weiter mit Schritt S17.

S16:

Anpassen der Komponente und Wiederholen der Schritte S13 bis S15;

S17:

Ende

33 shows a flowchart for an embodiment of a method according to the invention according to the ninth aspect of the present invention for designing at least one component of a vehicle based on tire forces and torques that have been determined by a method according to the seventh or eighth aspect of the present invention, this embodiment includes the following steps:

S11:

Begin;

S12:

Define design-relevant loads / movements;

S0-S10:

Determination of the tire forces and torques arising as a result by a method according to the invention as described above with steps S0-S10;

S13:

Determining the resulting loads on the component;

S14:

Comparing with the permissible loads of the component;

S15:

Check whether the resulting load determined is below the permissible load; if not, continue with step S16; if so, continue with step S17.

S16:

Adapting the component and repeating steps S13 to S15;

S17:

end

If the resulting load determined is very far below the permissible load, in some cases it can also be advantageous to adapt the component and repeat steps S13 to S15 in accordance with step S16 in order to avoid oversizing.

S18:

Start;

S19:

Aufbringen einer Lenkeingabe auf den Fahrsimulator

S0-S10:

Ermitteln der infolgedessen entstehenden Reifenkräfte und -momente durch ein erfindungsgemäßes Verfahren wie vorbeschrieben mit den Schritten S0-S10;

S20:

Ermitteln einer oder mehrerer Stellgrößenwerte zur Ansteuerung einer Widerstands-Aktuatorvorrichtung des Fahrsimulators; und

S21:

Ansteuern der Widerstands-Aktuatorvorrichtung des Fahrsimulators gemäß der ermittelten Stellgrößenwerte, um an der Lenkeingabevorrichtung einen den ermittelten Reifenkräften- und -momenten entsprechenden Lenkwiderstand zu erzeugen;

S22:

Ende

34 shows a flowchart for an embodiment of a method according to the invention according to the tenth aspect of the present invention for operating a driving simulator according to the invention as a function of tire forces and torques that have been determined by a method according to the seventh or eighth aspect of the present invention, this embodiment the includes the following steps:

S18:

Begin;

S19:

Applying a steering input to the driving simulator

S0-S10:

Determination of the tire forces and torques arising as a result by a method according to the invention as described above with steps S0-S10;

S20:

Determining one or more manipulated variable values for controlling a resistance actuator device of the driving simulator; and

S21:

Controlling the resistance actuator device of the driving simulator according to the determined manipulated variable values in order to generate a steering resistance corresponding to the determined tire forces and torques on the steering input device;

S22:

end

With the described method according to the invention, the tire forces and torques arising between the tire and the ground (road) in the individual driving states can also be used for low speeds and high camber values, in particular as they occur when steering while stationary and when maneuvering, with one for one improved, in particular suitable steering design, sufficient, in particular sufficient accuracy can be determined, in particular predicted.

In particular, an extension of the tire contact patch that is established or its circumferential contour, as well as an established soil pressure distribution, can be determined with improved accuracy. Likewise, with the proposed tire model, an improved simulation of a tire and thus a more precise determination of the tire forces and torques can be achieved.

Furthermore, the described methods according to the invention have a high degree of flexibility and can be easily adapted to different tires and / or tire loads and / or driving conditions, for example to different camber values or different tire inflation pressures, due to their parameterization, especially through the advantageously selected parameters. This allows the influence of various variables, such as wheel load, tire pressure, camber and, for example, the tire dimension, to be more reliably forecast. especially at an early stage of development when this is particularly desirable. This enables an improved design of vehicle components, including an improved steering design.

Of course, a large number of modifications, in particular structural modifications, to the illustrated embodiment are possible without departing from the content of the claims.

List of reference symbols

1

tires

2

Rim / wheel carrier

3

Sidewall / belt ring

4th

Tread

5

Rubber brushes

6th

Tire plane / radial center plane of the tire

7th

Ground level / street level / road level / horizontal level

8th

Laces symmetry axis

9

Vertical plane

10

Tire contact patch / tire contact / tire contact patch imprint

11

(Profile) groove

A1, A2

Static friction area

B1, B2

Sliding friction area

b

Index to identify the reference to a rubber brush element

C.

Spring stiffness

C.

Tire center

C1

Tire width

C2

Aspect ratio

C3

Load index

C4

Speed index

d

Attenuation / index to identify the reference to a damper

Δr

Groove spacing (distance between two grooves)

ΔrLR

Distance of a groove to the tire contact coordinate system origin LR

e

Index to identify the reference to a corner of a rubber brush element

eGy

Unit vector of the belt ring coordinate system in the y-direction

eLRx, eLRy, eLRz

Unit vectors of the tire contact coordinate system

eSz

Unit vector of the street coordinate system in the z-direction

f, F

Index to identify the reference to the rim

LRFf, z, q i = 1 ... k

normalized ground pressure value / normalized normal force in Z _LR direction on the rubber brush element q _i

Frictional force on the rubber brush element q _i

Total tire force, in particular total frictional force

Sliding friction force on the rubber brush element q _i

Static friction force on the rubber brush element q _i

Wheel load share / ground pressure force on the rubber brush element q _i

LRFf, e.g.

Wheel load (scalar value)

g, G

Index to identify the reference to the belt ring or sliding friction

γ

Camber angle

i

Run variable

k

Number of rubber brush elements

LR

Coordinate origin of the tire contact coordinate system / contact point reference point

K1, K2

curvature

KNN-p

artificial neural network for determining ground pressure distribution parameters

KNN-U

artificial neural network for determining circumferential contour parameters

L1, L2

Limits of a defined mapping value range

M.

Center of gravity of the resulting tire contact area

Drilling torque on rubber brush element q _i

Total tire torque, total drilling torque

nx

Number of rubber brush elements in x _LR direction

ny

Number of rubber brush elements in y _LR direction

p

Ground pressure distribution function

A (ŷLR)

Scaling parameters of the ground pressure distribution function

B (ŷLR)

Curvature parameters of the ground pressure distribution function

pa1 ... 7, pb1 ... 3

Ground pressure distribution function parameters

LRpf, z, q i = 1 ... k-

Ground pressure value on the rubber brush element q _i

PR

Tire pressure

qi = 1..k

Rubber brush element

Position vector of the rubber brush element q _i in the tire contact coordinate system

rubber brush elements located within the resulting tire contact area (defined by the associated position vector)

rubber brush elements located outside the resulting tire contact area (defined by the associated position vector)

Vector with the coefficient of friction of the subsurface

LRµH, x

Static friction coefficient in the x-direction

LRµH, y

Static friction coefficient in y-direction

LRµG, x

Coefficient of sliding friction in the x direction

LRµG, y

Coefficient of sliding friction in y-direction

R, rstat

static tire radius

RT

Index to identify the reference to the rim

Coordinate transformation vector

LR rxSE

x-coordinate of the coordinate transformation vector

LR rySE

y coordinate of the coordinate transformation vector

r1 ... 8

Distance to the Laces reference point LR

S.

Underground / road / road

S0..S22

Procedural steps

SE

Origin of coordinates of the superellipse coordinate system or the circumferential contour function

Position vectors of the points of intersection with the circumferential contour

U

Perimeter contour function

a, b12, b34, n12, n34 m12, m34

Parameters of the perimeter contour function

ySE12

Functional section of the perimeter contour function U in the first quadrant I. and in the second quadrant II

ySE34

Functional section of the perimeter contour function U in the third quadrant III and in the fourth quadrant IV

xc

Abscissa or x coordinate of the tire center point coordinate system

yc

Ordinate or y-coordinate of the tire center point coordinate system

zc

Applicates or z-coordinates of the tire center point coordinate system

xH

Abscissa or x coordinate of the horizontal coordinate system

yH

Ordinate or y-coordinate of the horizontal coordinate system

zH

Applicates or or z-coordinates of the horizontal coordinate system

xLR

Abscissa or x-coordinate of the tire contact coordinate system

yLR

Ordinate or y-coordinate of the tire contact coordinate system

zLR

Applicates or z-coordinates of the tire contact coordinate system

xs

Abscissa or x coordinate of a pressure measuring plate coordinate system

ys

Ordinate or y-coordinate of the pressure measuring plate coordinate system

XSE

Abscissa or x coordinate of the superellipse coordinate system

ySE

Ordinate or y-coordinate of the superellipse coordinate system

zSE

Applicates or or z-coordinates of the superellipse coordinate system

xLR

resulting direction of movement of a component of the tire in the tire contact coordinate system

ẋLR

resulting speed of movement of a component of the tire in the tire contact coordinate system

xF

resulting direction of movement of a component of the tire in the rim coordinate system

ẋF

resulting speed of movement of a component of the tire in the rim coordinate system

I, II, III, IV

Quadrants in the superellipse coordinate system

Claims (13)

Method for determining at least one circumferential contour parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

a parameterized tire contact area circumferential contour function (U), by means of which a circumferential contour of a tire contact area (10) that occurs under a defined load for a tire (1) can be described, in particular a circumferential contour of a tire contact area (10), which changes when steering while stationary and / or adjusts during maneuvering, preferably depending on the load on the tire ( ^LR F _{f, z} ), in particular also depending on a tire condition (p _R ) and / or one or more tire properties (C _1.4 ), wherein the parameterized tire contact patch circumferential contour function (U) in relation to a circumferential contour function coordinate system with a circumferential contour function coordinate origin (SE) and by at least one independent variable (x _LR , y _LR ) and at least one parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

is defined, with at least one circumferential contour parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

is determined from a tire contact area imprint (10) of a tire contact area (10) of a tire (1), which is determined as a function of a defined load ( ^LR F _{f, z} ) of the tire, in particular also as a function of a tire condition (p _R ) and / or one or more tire properties (C _1,4 ), has been set or is to be expected, characterized in that at least one circumferential contour parameter that is determined is a coordinate transformation vector $\left({}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

which defines an associated coordinate transformation for a shift of the circumferential contour function coordinate origin (SE) of the circumferential contour function coordinate system into a tire contact coordinate origin (LR) of a tire contact coordinate system. Method for determining at least one ground pressure distribution parameter (A (ŷ _LR ), B (ŷ _LR )) of a parameterized ground pressure distribution function (p) by means of a ground pressure distribution that occurs under a defined load for a tire (1) in an associated, under the defined load-adjusting tire contact area (10) can be mathematically described, in particular a ground pressure distribution that occurs when steering while stationary and / or when maneuvering, preferably as a function of a load on the tire ( ^LR F _{f, z} ), in particular also as a function of a Tire condition (p _R ) and / or one or more tire properties (C _1..4 ), the parameterized ground pressure distribution function (p) in relation to a tire contact coordinate system with a tire contact coordinate origin (LR) and by at least one independent Variable (x _LR , y _LR ) and at least one soil pressure distribution parameter (A (ŷ _LR ), B (ŷ _LR )) is defined, with at least one soil pressure distribution parameter (A (ŷ _LR ), B (ŷ _LR )) a ground pressure distribution in a tire contact patch (10) of a tire (1) is determined, which has set or is expected as a function of a defined load on the tire, in particular also as a function of a tire condition and / or one or more tire properties, wherein for Defined points of the tire contact patch, which are each clearly defined by their coordinates in relation to the tire contact coordinate system (LR), each having an associated ground pressure value, characterized by the following steps: (a) Subdivide the tire contact patch in a first ground pressure distribution direction (y _LR ) in several sections (1..10), preferably in several, at least partially equidistant sections (1..10), the first soil pressure distribution ungs-direction (y _LR ) preferably based on a functional installation state of the tire in a vehicle corresponds to a transverse direction of the vehicle, and (b) determining a statistically representative ground pressure value, in particular a mean ground pressure value, for at least one of the sections from at least two defined points of the tire contact area ( 10), which lie within this section (1..10) and each have the same coordinate value (x _LR ) in a second soil pressure distribution direction (x _LR ), the second soil pressure distribution direction (x _LR ) preferably based on a functional The installed state of the tire in a vehicle corresponds to a vehicle longitudinal direction. Computer-implemented method, in particular simulation method, for determining, in particular for predicting, an expansion of a tire contact area (10) of a tire (1) subject to a defined load, in particular for determining an expansion of the tire contact area (10) that occurs when steering while stationary and / or when maneuvering ), preferably as a function of a load ( ^LR F _{f, z} ) on the tire (1), in particular also as a function of a tire condition (p ₁ ) and / or one or more tire properties (C _1..4 ), the expansion is determined with the help of a parameterized tire contact area circumferential contour function (U), which describes a circumferential contour of the tire contact area (10) in particular mathematically, preferably as a function of a load ( ^LR F _{f, z} ) on the tire and in particular also as a function of a tire condition (p _R ) and / or one or more tire properties (C _1..4 ), where the Re ifen contact area circumferential contour function (U) in relation to a circumferential contour function coordinate system with a circumferential contour function coordinate origin (SE) and by at least one independent variable (x _LR , y _LR ) and at least one circumferential contour parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

is defined, characterized in that at least one circumferential contour parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

by a procedure according to Claim 1 is determined or has been determined. Computer-implemented method, in particular simulation method, for determining, in particular for predicting, an expansion of a tire contact area (10) of a tire (1) subject to a defined load, in particular for determining a tire contact area (10) that occurs when steering while stationary and / or when maneuvering, preferably as a function of a tire load, in particular also as a function of a tire condition and / or one or more tire properties, the extent being determined with the aid of a parameterized tire contact area circumferential contour function (U), which describes a circumferential contour of the tire contact area mathematically, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, the tire contact patch circumferential contour function in relation to a circumferential contour function coordinate system em with a circumferential contour function coordinate origin (SE) and by at least one independent variable (x _LR , y _LR ) and at least one circumferential contour parameter $\left(a,b_{\mathrm{12th}},b_{34},n_{\mathrm{12th}},n_{34},m_{\mathrm{12th}},m_{34}{,}_{\mathrm{L.}\mathrm{R.}}{\overrightarrow{r}}_{\mathrm{S.}\mathrm{E.}}\right)$

is defined, characterized in that the tire contact patch circumferential contour function (U) that is used, at least in sections, in particular in a function section i, is defined by a 4-parametric superellipse according to the following formula: $$U_i\left(x_{\mathrm{S.}\mathrm{E.}},y_{\mathrm{S.}\mathrm{E.}}\right):{\left(\frac{x_{\mathrm{S.}\mathrm{E.}}}{a_i}\right)}^{n_i}+{\left(\frac{y_{\mathrm{S.}\mathrm{E.}}}{b_i}\right)}^{m_i}=1{\text{with a}}_i,b_i\in {\text{R.}}^{>0}\text{and}{n}_i,m_i\in {\text{R.}}^{>0},$$

The index i indicates an associated functional section, the index SE indicating the circumferential contour function coordinate system with its circumferential contour function coordinate origin (SE), the circumferential contour function coordinate system being a Cartesian, right-handed superellipse coordinate system, the origin of which is at the intersection of the semiaxes of the associated superellipse is, where an abscissa x _{SE of} the right-handed superellipse coordinate system in the vehicle's longitudinal direction points to the rear of the _{vehicle, an associated application z SE} in the vehicle vertical direction downwards and an associated ordinate y _{SE each perpendicular to the abscissa x SE} and the application z _SE , in particular in such a way that a right-handed, Cartesian coordinate system results, and the parameter a _i defines a first semiaxis length in the x _SE direction of the associated superellipse, the parameter b _i a second semiaxis length in the y _SE direction of the associated superellipse and d The two remaining parameters n _i , m _{i are} each curvature parameters for parameterizing a curvature of the superellipse. Computer-implemented method, in particular simulation method, for determining, in particular for predicting, a ground pressure distribution that is established in a tire contact area of a tire with a defined load, in particular for determining a soil pressure distribution that is established in the tire contact area when steering while stationary and / or when maneuvering, preferably as a function of a Tire condition and / or one or more tire properties, the ground pressure distribution being determined using a defined ground pressure distribution function (p), which describes the ground pressure distribution in the tire contact area (10) of the tire (1), preferably as a function of a load ( ^LR F _{f, e.g.} ) of the tire (1) and in particular also as a function of a tire condition (p _R ) and / or one or more tire properties (C _1,4 ), the method comprising the following steps: Selecting defined points $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right),$

which lie within the tire contact patch (10), - determining the coordinates of the selected points $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

in a defined coordinate system, if necessary, converting the coordinates of the selected points $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

into the coordinate system to which the defined soil pressure distribution function (p) relates, which is used to determine the soil pressure distribution, and - determining an associated soil pressure value (p (x _LR , y _LR )) for each of the selected points $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

using the defined ground pressure distribution function (p), where the ground pressure distribution function (p), which is used to determine the ground pressure distribution in the tire contact patch, is a parameterized ground pressure distribution function (p) that relates to a tire contact coordinate system with a tire contact coordinate origin (LR) and is defined by at least one independent variable (x _LR , y _LR ) and at least one soil pressure distribution parameter (A (ŷ _LR ), B (ŷ _LR )), characterized in that at least one soil pressure distribution parameter (A (ŷ _LR ) , B (ŷ _LR )) by a procedure Claim 2 is determined or has been determined. Computer-implemented method, in particular simulation method, for determining, in particular for predicting, a ground pressure distribution that occurs in a tire contact area (10) of a tire (1) subject to a defined load, in particular for determining a pressure distribution in the tire contact area (10 ) setting ground pressure distribution, preferably as a function of a tire condition and / or one or more tire properties, the ground pressure distribution in the tire contact area being determined with the aid of a defined ground pressure distribution function (p), which describes the ground pressure distribution (p) in a tire contact area of the tire, preferably as a function of a load on the tire and in particular also as a function of a tire condition and / or one or more tire properties, the method comprising the following steps: selecting defined points $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right),$

which lie within the tire contact area, - determining the coordinates of the selected points in a defined coordinate system, - if necessary, converting the coordinates of the selected points into the coordinate system to which the defined ground pressure distribution function refers, which is used to determine the ground pressure distribution, and - determining a associated ground pressure value (p (x _LR , y _LR )) for each of the selected points using the defined ground pressure distribution function (p), where the ground pressure distribution function (p), which is used to determine the ground pressure distribution in the tire contact patch, is a parameterized ground pressure distribution function (p) which, in relation to a tire contact coordinate system with a tire contact coordinate origin (LR) and by at least one independent variable (x _LR , y _LR ) and at least one soil pressure distribution parameter (A (ŷ _LR ), B (ŷ _LR )) is defined, characterized in that d ass the ground pressure distribution function (p), which is used to determine the ground pressure distribution in the tire contact patch, is defined by: $$\begin{array}{l}p\left(x_{\mathrm{L.}\mathrm{R.}},{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)=\mathrm{A.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)\cdot \left[1-{\left|\frac{x_{\mathrm{L.}\mathrm{R.}}}{N_x\left(y_{\mathrm{L.}\mathrm{R.}}\right)}\right|}^{\mathrm{B.}\left({\widehat{y}}_{\mathrm{L.}\mathrm{R.}}\right)}\right]\hfill \\ \text{with}{\widehat{y}}_{\mathrm{L.}\mathrm{R.}}=N_y\left(x_{\mathrm{L.}\mathrm{R.}},y_{\mathrm{L.}\mathrm{R.}}\right)\hfill \end{array},$$

The ground pressure distribution function (p) is defined in relation to the Laces coordinate system, which is a defined, right-handed, Cartesian, non-slip coordinate system, the origin of which lies in a Laces reference point (LR), the Laces reference point (LR) preferably of this type is selected that it is at a camber angle of γ = 0 ° and with a straight ahead position of the Tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, coincides with a tire center point projected onto a roadway plane, and the contact surface coordinate system being selected in particular such that with a camber angle of γ = 0 °, with a straight-ahead position of the tire and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _{LR of} the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the application z _LR , in particular in this way that the result is a right-handed, Cartesian coordinate system, where x _{LR is} an x-coordinate of a point on the tire's tread, for which a ground pressure p is to be determined, with _{respect to the tire contact coordinate system, where y LR is} the y-coordinate of this point on the tire contact coordinate system, where N _x (y _LR ) is a normalization function for normalizing the coordinate value of x _LR to a length of an extension of the tire contact patch in the x direction, where N _y (x _LR , y _LR ) is a mapping function for Mapping of the coordinate _{value of y LR} to a defined range of values depending on a length of an extension of the tire contact area in the y-direction, where A (ŷ _{LR) is} a scaling function that defines a first ground pressure distribution parameter, in particular a scaling parameter, depending on ŷ _LR , and where B (ŷ _{LR) is} a curvature function that defines a second ground pressure distribution parameter , in particular a curvature parameter, is defined as a _{function of ŷ LR.} Computer-implemented method for calculating at least one resulting tire force resulting from frictional forces in a tire contact patch of a tire $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or at least one resulting tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right),$

in particular in the case of a tire (1) which is supported on a level surface and is mounted on a rim (2) and is forced to move, in particular via the rim, in particular when steering while standing and / or when maneuvering, preferably depending on a load on the Tire, in particular also as a function of a tire condition and / or one or more tire properties, wherein the tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is determined numerically with the help of a tire model, which the properties of the tire (1), in particular a contact of the tire (1) with a substrate (S), among other things with the help of a large number of massless rubber brush elements (q _{i = 1..k} ) in the tread of the tire (1), the tire force arising in the tire contact area (10) due to frictional forces $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is determined by initially at least for each rubber brush lying within the tire contact patch in one step $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

_{the forces applied to the respective rubber brush (q i = 1..k} ) in the tire contact area (10) as a result of the friction between the tire and the ground $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}\right)$

and moments $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta ,q_{i=\mathrm{1..}k}}\right)$

can be determined which in a further step each over all rubber brushes located within the tire contact area $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

to the resulting tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the resulting tire torque ( ${}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }$

), with each rubber brush element (q _{i = 1..k} ) each having a reference point $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{}\right)$

is assigned with associated coordinates by which the position of the rubber brush element (q _{i = 1..k} ) is clearly defined, characterized in that (a) in one step, in particular before for the rubber brush elements $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right),$

which lie within the tire contact area (10), which are determined in the tire contact area (10) on the respective rubber brush (q _{i = 1..k} ) as a result of the friction between the tire and the ground, for each rubber brush element ( q _{i = 1..k} ) with the help of a tire contact area circumferential contour function (U) by a method according to Claim 3 or 4th it is determined or has been determined whether it is located inside or outside the tire contact patch, and / or (b) for all rubber brush elements lying within the associated tire contact area (10) $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

the applied forces and moments are determined as a function of a soil pressure distribution in the tire contact patch, the soil pressure distribution in the tire contact patch by a method according to FIG Claim 5 or 6th is determined, or has been, in particular in each case for each of the rubber brush element (q _{i = 1..K)} in response to the associated reference point, an associated ground pressure value ^(LR _{e p, z, q i = 1 ... k} ) is or has been determined. Computer-implemented method for calculating at least one resulting tire force resulting from frictional forces in a tire contact patch of a tire $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or at least one resulting tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right),$

in particular in the case of a tire (1) which is supported on a level surface and is mounted on a rim (2) and is forced to move, in particular via the rim, in particular when steering while standing and / or when maneuvering, preferably depending on a load on the Tire, in particular also as a function of a tire condition and / or one or more tire properties, wherein the tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is determined numerically with the help of a tire model, which the properties of the tire (1), in particular a contact of the tire with a ground, among other things with the help of a large number of massless rubber brush elements (q _{i = 1..k} ) in the tread (4) of the tire ( 1), whereby the tire force generated in the tire contact area (10) by frictional forces $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is determined by initially at least for each rubber brush lying within the tire contact patch in one step $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{in}\right)$

the forces applied to the respective rubber brush in the tire contact area (10) as a result of the friction acting between the tire and the ground $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ,q_{i=\mathrm{1..}k}}\right)$

and moments $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta ,q_{i=\mathrm{1..}k}}\right)$

can be determined, which in a further step each over all rubber brushes (q _{i = 1..k} ) located within the tire contact area (10) to the resulting tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or the resulting tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

can be summarized, with each rubber brush element (q _{i = 1..k} ) each having a reference point $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{q}{}_{i=\mathrm{1..}k}^{}\right)$

is assigned with associated coordinates, by which the position of the rubber brush element is clearly defined, characterized in that a tire model is used in which at least one of these massless rubber brush elements (q _{i = l..k)} , in particular each of these massless rubber brush elements, two translational Has degrees of freedom in an x _LR y _LR plane, with the index LR indicating a right-handed, Cartesian, non-slip coordinate system, the origin of which lies in a slip reference point (LR), the land reference point (LR) preferably being selected in this way that it is at a camber angle of γ = 0 °, when the tire is in a straight position and when there are no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire with a tire center point (C) projected onto a roadway plane (S) coincides, and the contact surface coordinate system being selected in such a way that with a camber angle of γ = 0 °, with a straight-ahead position of the tire and when no lateral and longitudinal forces ${\overrightarrow{\mathrm{F.}}}_y,{\overrightarrow{\mathrm{F.}}}_x$

act on the tire, an abscissa x _{LR of} the Latsch coordinate system in the longitudinal direction of the vehicle points to the front of the vehicle and an associated application z _LR in the vehicle vertical direction upwards and an associated ordinate y _LR each perpendicular to the abscissa x _LR and the application z _LR , in particular in this way that a right-handed, Cartesian coordinate system results, where x _{LR is} an x -coordinate, related to the tire contact coordinate system, of a point on the tread of the tire for which a ground pressure ( ^LR p _{e, z, q i = 1 ... k} ) is to be determined, where y _{LR is} the y-coordinate of this point in relation to the tire contact coordinate system. Computer-implemented method for designing at least one component of a vehicle, preferably for designing a steering arrangement, in particular for designing a rack of a steering gear, whereby for designing the component at least one value of a design variable relevant for designing the component as a function of a value caused by frictional forces in a tire contact area The resulting tire force arising from the tire and / or at least one resulting tire torque is determined, characterized in that, for the design of the component, a method according to Claim 7 or 8th calculated tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

and / or a tire torque calculated by such a method $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is used or a method according to Claim 7 or 8th is used, with in particular at least one design variable depending on one by a method according to Claim 7 or calculated tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

or a tire torque calculated by such a method $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is determined. A method for operating a driving simulator, the driving simulator having at least one controllable actuator device, characterized in that at least one actuator device of the driving simulator is carried out as a function of at least one by a method according to Claim 7 or 8th calculated tire force $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{F.}}{}_{ƒ}\right)$

) and / or as a function of at least one by a method according to Claim 7 or 8th calculated tire torque $\left({}^{\mathrm{L.}\mathrm{R.}}\overrightarrow{\mathrm{M.}}{}_{\delta }\right)$

is controlled. Computer program, comprising instructions which, when the computer program is executed by a computer, cause the computer to carry out a method according to one of the preceding claims. Computer-readable medium, in particular computer-readable storage medium, comprising instructions which, when executed by a computer, cause the computer to carry out a method according to one of the preceding claims. Driving simulator, characterized in that the driving simulator to carry out a method according to Claim 10 is trained.

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