Estimating tire cornering stiffness

Abstract

Method for estimating the cornering stiffness of a tire, a pair of tires and / or a set of tires, comprising the following steps: - Estimating (S1) parameters for a tire lateral force, a tire lateral force gradient, a tire contact force, a tire contact force gradient, a tire slip angle rate and a tire slip angle difference of a tire, a pair of tires and / or a set of tires; - Provide (S2) at least one relationship between the estimated parameters and the tire's cornering stiffness by one or more equations; - Evaluate (S3) one or more equations to obtain an estimate for the tire's cornering stiffness.

Description

FIELD OF THE INVENTION

[0001] The present invention relates to a method for estimating the cornering stiffness of a tire, a pair of tires and / or a set of tires during a journey.

[0002] For the technical background of the invention, reference is made to DE 10 2013 219 662 B3, which relates to a method for determining the tread depth of a tire. Reference is also made to EP 3 028 909 A1, which relates to a system for estimating road friction. SUMMARY OF THE INVENTION

[0003] Accordingly, it is provided: - A method for estimating the lean-slip stiffness of a tire, a pair of tires, and / or a set of tires, comprising the following steps: estimating parameters for a tire lateral force, a tire lateral force gradient, a tire contact force, a tire contact force gradient, a tire slip angle rate, and a tire slip angle difference of a tire, a pair of tires, and / or a set of tires; providing at least one relationship between the estimated parameters and the tire lean-slip stiffness by means of an equation; evaluating the equation to obtain an estimate for the tire lean-slip stiffness.

[0004] A sensor, also known as a detector, transducer, or sensor, is a technical component that can qualitatively or quantitatively detect certain physical or chemical properties or conditions, such as temperature, humidity, pressure, speed, brightness, acceleration, pH value, ionic strength, electrochemical potential, and / or the material composition of its environment. These quantities are detected using physical or chemical effects and converted into a processable electrical signal as sensor data.

[0005] Vehicle sensors are either mountable or already mounted on a vehicle. Vehicle sensors include optical sensors, such as cameras, lidar, radar, time-of-flight (TOF), and other sensor technologies, such as acoustic sensors.

[0006] The phrase "a tire, a pair of tires and / or a set of tires" is to be understood as meaning that a statement can refer to a single tire, a pair of tires on an axle, or an entire set of tires comprising at least four tires. This patent application explains, in some sections, estimates and relationships for pairs of tires, namely a front axle, designated by the index "f", and a rear axle, designated by the index "r".

[0007] However, it is understood that the reference to the front and rear axles is purely exemplary and that alternative relationships can be derived for individual wheels, center axles or entire sets of tires, which may be useful for estimating tire lateral stiffness.

[0008] A (linear) tire model is a simplified mathematical model of a vehicle tire that linearly approximates its behavior. It is often based on the assumption that the tire responds linearly to steering and braking inputs, as well as vehicle load, within a specific operating range. This model is frequently used in vehicle dynamics and the design of vehicle control systems to obtain a first approximation of tire behavior. However, a (linear) tire model is always only an approximation of reality, as tire behavior in reality is nonlinear.

[0009] Tire cornering stiffness, also known as tire corner stiffness or lateral tire stiffness, is a property of tires that describes their responsiveness to lateral forces. It influences, for example, driving dynamics, steering behavior, and driving stability.

[0010] Tire lean angle stiffness describes a tire's ability to transmit lateral forces when the vehicle corners or changes direction. When the vehicle corners, lateral forces act on the tires, pulling the vehicle sideways. Tire lean angle stiffness determines how well the tire can resist these lateral forces and how effectively it keeps the vehicle on course.

[0011] Higher tire cornering stiffness means the tire is stiffer and can react better to lateral forces. This usually results in more precise steering and better driving stability.

[0012] Tire contact force, also known as ground contact force or ground reaction force, is the force acting between a tire and the surface (road) on which the vehicle is traveling. This force arises from the deformation of the tire and the reaction of the ground to the vehicle's load.

[0013] When a vehicle travels on a level road, its weight presses the tire against the ground. The tire deforms and simultaneously presses against the road surface. In response to this deformation, the road exerts a force on the tire, which supports the vehicle and allows it to move forward.

[0014] Tire contact force influences driving dynamics. It affects braking, traction, acceleration, and cornering. Sufficient tire contact force is crucial to ensure the tire's grip on the road and to guarantee the vehicle's stability and safety. The required tire contact force depends on various factors, such as the vehicle's weight, the road surface, the tire type and condition, and the vehicle's speed.

[0015] Lateral force is a force generated by a tire when subjected to lateral stress, such as during cornering. When a vehicle turns into a curve, the tires generate a lateral force that steers and stabilizes the vehicle in the desired direction. Lateral force is important for vehicle dynamics and stability, as it influences handling, cornering, and responsiveness.

[0016] A gradient is a mathematical term for the slope or change of one quantity relative to another, such as time. In equations, the gradient of a parameter is indicated by a dot above the parameter symbol.

[0017] Recursion is a concept where a function calls itself or a structure contains its own elements. It refers to the principle of breaking down a task into smaller subproblems that follow the same pattern until they reach a simple basic solution.

[0018] A recursive algorithm is a function that can be used to break down a task into smaller, repetitive steps. Each step calls the function again until a specific termination criterion is met, and the results of each function call are combined to obtain a final solution.

[0019] In this patent application, predetermined thresholds are dimensioned such that they are sufficiently different from zero to avoid numerical singularities. In technical jargon, such thresholds are also referred to as "epsilon".

[0020] Computer program products typically comprise a sequence of instructions that, when the program is loaded, cause the hardware to perform a specific procedure that leads to a particular result.

[0021] The basic idea of ​​the invention is to estimate the tire slip-stiffness based on estimated parameters for a tire lateral force, a tire lateral force gradient, a tire contact force, a tire contact force gradient, a tire slip angle rate and a tire slip angle difference by providing a relationship between these estimated parameters and the tire slip-stiffness through an equation.

[0022] It can be advantageous to couple the evaluation of the equations to certain conditions, whereby the conditions prevent numerical singularities from occurring.

[0023] This patent application is based on several parameters and constants. Some of these are known from sensor data or can be determined from it using numerical differentiation, for example: δ f / r = Wheel steering angle front / rear axle δ̇̇̇ f / r = Wheel steering angle rate front / rear axle ψ̇ = Yaw rate ψ̈ = Yaw acceleration v x = Vehicle longitudinal speed a x / y = Longitudinal / lateral acceleration of the vehicle at its center of gravity (corrected with respect to Nick and roll effects)

[0024] The following parameters can be estimated from this, as described below: F y,f / r = Tire lateral force front / rear axle Ḟ y,f / r = Tire lateral force gradient front / rear axle F z,f / r = Tire contact force front / rear axle Ḟ z,f / r = Tire contact force gradient front / rear axle α f - α r= Tire slip angle difference between front and rear axles α̇ f / r = Tire slip angle rate front / rear axle where the following constants are known: m = vehicle mass l f / r = Distance from center of gravity to front / rear axle I z = moment of inertia g = gravitational constant h = center of gravity height

[0025] The (normalized) tire lateral stiffness to be determined is designated by the letter C.

[0026] Advantageous embodiments and further developments emerge from the further subclaims and from the description with reference to the figures of the drawing.

[0027] Driving dynamics parameters can be estimated, for example, using a so-called sliding mode observer.

[0028] A sliding mode observer on a vehicle is a software-based observer used to estimate the vehicle's condition when certain relevant condition variables cannot be measured directly.

[0029] The Sliding Mode Observer uses data from existing sensors in the vehicle, such as the tachometer, wheel speed sensors, steering angle sensor, inertial measurement unit, and others, to estimate the vehicle's condition. It also uses mathematical models of the vehicle to derive an estimate from this data.

[0030] The tire lateral forces and tire lateral force gradients at the front and rear axles can be determined, for example, by applying a sliding mode observer to the following equations of state: ψ¨=(lfFy,fcos δf−lrFy,rcos δr) / Iz F˙y,f=0 F˙y,r=0 y1=ψ˙ y2=ay=Fy,fcos δf+Fy,r cos δrm

[0031] Suitable estimates for tire contact forces include, for example: Fz,f=m(glr−axh)(lf+lr),Fz,r=m(glf+axh)(lf+lr).

[0032] According to a preferred embodiment of the invention, a multitude of estimates for the tire's cornering stiffness are obtained successively, i.e., one after the other, during a journey, with a recursive algorithm being called for each estimate.

[0033] For example, it is conceivable to use a so-called recursive east-square estimator as a recursive algorithm to recursively determine the tire slant stiffness based on the estimated parameters.

[0034] According to a preferred embodiment of the invention, the slip angle rate of a tire, a pair of tires, and / or a set of tires is estimated, and a relationship between the estimated parameters and the tire slip stiffness is provided. The equation of this relationship is evaluated when the magnitude of the slip angle rate exceeds a predetermined threshold. This prevents numerical singularities by placing the slip angle rate in the denominator of the equation being evaluated.

[0035] For example, it is also useful to estimate the tire slip angle rate for the front axle and / or for the rear axle and to provide a first relationship whose equation is evaluated when the magnitude of the front axle tire slip angle rate exceeds a predetermined threshold and / or to provide a second relationship whose equation is evaluated when the magnitude of the rear axle tire slip angle rate exceeds a predetermined threshold.

[0036] This avoids numerical singularities if the tire slip angle rate of the front axle and / or the rear axle is in the denominator of the equation to be evaluated.

[0037] Examples of equations to be evaluated for a first or second relationship are: C≈(F˙y,fFz,f−Fy,fF˙z,fFz,f2) / α˙f if α˙f≠0 C≈(F˙y,rFz,r−Fy,rF˙z,rFz,r2) / α˙r if α˙r≠0

[0038] The tire slip angle rate and the tire slip angle difference between the front axle and the rear axle can be estimated by: α˙f=δ˙f−ayvx+ψ˙−lfψ¨vx α˙r=δ˙r−ayvx+ψ˙−lrψ¨vx αf−αr=δf−δr−(lf+lr)ψ˙ / vx

[0039] According to a preferred embodiment of the invention, a tire slip angle difference between the front axle and the rear axle is estimated, and a third relationship is provided, the equation of which is evaluated when the magnitude of the tire slip angle difference (α) is determined. f - α r ) exceeds a predetermined threshold. C≈(Fy,fFz,f−Fy,rFz,r) / (αf−αr) if (αf−αr)≠0

[0040] This allows numerical singularities to be avoided if the tire slip angle difference is in the denominator of the equation to be evaluated.

[0041] According to a preferred embodiment of the invention, one or more relationships are provided, the equations of which are evaluated when vehicle dynamics sensor data lie within predetermined ranges.

[0042] Alternatively or additionally, numerical singularities can be prevented from occurring when the equation contains a fraction by monitoring, based on vehicle dynamics or vehicle dynamics sensor data, that the denominator is sufficiently different from zero.

[0043] It goes without saying that this also ensures that the tire slip angle difference and / or the tire slip angle rate exceed a predetermined threshold, i.e., are sufficiently different from zero.

[0044] According to a preferred embodiment of the invention, the method is carried out after a tire model, in particular a linear tire model, has been validated.

[0045] This allows for the identification of relationships based on a tire model or on the assumptions underlying that tire model. In this case, it is advantageous to evaluate the equations only if it is ensured that the underlying tire model is applicable.

[0046] For example, it is conceivable that a linear tire model is not sufficiently accurate in a driving situation dominated by nonlinearities.

[0047] According to a preferred embodiment of the invention, the method is carried out when it is determined that the vehicle is not traveling straight ahead. If the vehicle is traveling straight ahead, it is assumed that the equations to be evaluated contain a denominator that is not sufficiently different from zero.

[0048] It is understood that a method for estimating a slip angle which calls upon the method for estimating a tire slip angle stiffness as described above is advantageous.

[0049] Furthermore, it is understood that a method for estimating a yaw potential, which calls upon the method for estimating a tire slip angle stiffness as described above, is advantageous.

[0050] Furthermore, it is understood that a method for estimating a coefficient of friction between a tire, a pair of tires and / or a set of tires and a road surface, which calls upon the method for estimating a tire slip angle stiffness as described above, is advantageous.

[0051] According to a preferred embodiment of the invention, the tire slip angle stiffness is estimated in order to assess tire wear.

[0052] A computer program product according to a method of an embodiment of the invention performs the steps of a method according to the preceding description when the computer program product runs on a computer, in particular an in-vehicle computer. When the program in question is used on a computer, the computer program product produces an effect, namely the estimation of a parameter, wherein the estimation is based on technical considerations. CONTENT OF THE DRAWINGS

[0053] The present invention will be explained in more detail below with reference to the exemplary embodiments shown in the schematic figures of the drawings. In the drawings: Fig. 1 A schematic block diagram of an embodiment of the invention.

[0054] The accompanying drawings are intended to provide a further understanding of the embodiments of the invention. They illustrate embodiments and, in conjunction with the description, serve to explain the principles and concepts of the invention. Other embodiments and many of the advantages mentioned will become apparent with reference to the drawings. The elements of the drawings are not necessarily shown to scale.

[0055] In the figures of the drawings, identical, functionally equivalent and equally effective elements, features and components - unless otherwise stated - are each provided with the same reference symbols. DESCRIPTION OF EXAMPLES OF EXECUTION

[0056] Fig.Figure 1 shows a method for estimating the slip-angle stiffness of a tire, a pair of tires, and / or a set of tires during a drive, comprising steps S1 to S3. In step S1, a parameter for a tire lateral force, a parameter for a tire lateral force gradient, a parameter for a tire contact force, a parameter for a tire contact force gradient, a parameter for the tire slip angle rate, and a parameter for the tire slip angle difference of a tire, a pair of tires, and / or a set of tires are estimated. In step S2, at least one relationship between the estimated parameters and the tire slip angle stiffness is provided by an equation. In step S3, the equation is evaluated to obtain an estimate for the tire slip angle stiffness. Reference symbol S1-S3 process steps

Claims

[1] A method for estimating a tire slip stiffness of a tire, a pair of tires and / or a set of tires, comprising the following steps: - estimating (S1) parameters for a tire lateral force, a tire lateral force gradient, a tire contact force, a tire contact force gradient, a tire slip angle rate and a tire slip angle difference of a tire, a tire pair and / or a tire set; - providing (S2) at least one relationship between the estimated parameters and the tire slip stiffness by one or more equations; - Evaluate (S3) one or more equations to obtain an estimate of the tire slip stiffness. [2] Method according to claim 1, wherein a plurality of estimates for the tire slip stiffness are successively determined during a trip, a recursive algorithm being called for each estimate. [3] A method according to any preceding claim, wherein a relationship is provided between the estimated parameters and the tire slip angle stiffness, the equation of which is evaluated when the magnitude of the tire slip angle rate exceeds a predetermined threshold. [4] The method of claim 3, wherein a first relationship is provided between the estimated parameters and the tire slip angle stiffness, the equation of which is evaluated when the magnitude of the tire slip angle rate of the front axle exceeds a predetermined threshold and / or a second relationship is provided between the estimated parameters and the tire slip angle stiffness, the equation of which is evaluated when the magnitude of the tire slip angle rate of the rear axle exceeds a predetermined threshold. [5] Method according to one of the preceding claims, wherein a third relationship is provided between the estimated parameters and the tire slip angle stiffness, the equation of which is evaluated when the amount of the tire slip angle difference between the front and rear axles exceeds a predetermined threshold value. [6] Method according to one of the preceding claims, wherein one or more relationships are provided, the equations of which are evaluated when driving dynamics sensor data lie within predetermined ranges. [7] Method according to one of the preceding claims, wherein the method is carried out after a tire model, in particular a linear tire model, has been validated. [8] Method according to one of the preceding claims, wherein the method is carried out when it is determined that the vehicle is not traveling straight ahead. [9] A method for estimating a slip angle based on tire slip angle stiffness, which method calls for the method according to any one of the preceding claims 1-8. [10] A method for estimating a yaw potential based on tire slip angle stiffness, which method calls the method according to any one of the preceding claims 1-8. [11] A method for estimating a coefficient of friction between a tire, a pair of tires and / or a set of tires and a road surface based on the tire slip angle stiffness, which method calls the method according to any one of the preceding claims 1-8. [12] A method according to any preceding claim, wherein the tire slip angle stiffness is estimated to assess tire wear.

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