Tire cornering stiffness identification method

Abstract

The invention provides a tire cornering stiffness identification method, and relates to the technical field of vehicle parameter identification. Comprising the following steps: S1, establishing a lateral force tire model; s2, designing a tire lateral force estimator; s3, designing a slip angle feedback estimator based on the lateral force estimated in the step S2; and S4, designing a cornering stiffness online identification algorithm based on the lateral force estimated in the step S2 and the slip angle estimated in the step S3. According to the identification method, the real-time lateral force and the slip angle of the tire are considered, the tire cornering stiffness can be estimated in real time, the steps are simple and clear, the accuracy of a calculation result is high, and the problems that most existing tire cornering stiffness obtaining methods are tedious in steps, complex in calculation, low in accuracy and the like are solved.

Description

Technical Field

[0001] The invention relates to the technical field of vehicle parameter identification, and in particular to a tire cornering stiffness identification method. Background Art

[0002] In order to reduce the frequency of vehicle traffic accidents, researchers in the prior art have developed a series of vehicle control systems and methods, among which active safety control systems have been widely used. The vehicle motion state and parameters are crucial to the active safety control system, especially the tire, which is the only part of the vehicle that is in direct contact with the ground. Its cornering stiffness is an important parameter to characterize the nonlinear characteristics of the tire and will directly affect the stability of the vehicle. Therefore, the tire cornering stiffness is closely related to the vehicle's handling characteristics and is an important parameter in the active safety control system. Real-time and accurate estimation of the tire cornering stiffness is of great significance to improving the vehicle's handling characteristics.

[0003] However, most of the current methods for obtaining tire cornering stiffness have limitations such as cumbersome steps, complex calculations, and low accuracy. For example, the Chinese patent with publication number CN115219247A provides a method for testing and identifying tire cornering stiffness, including: testing the tire on the tire six-component force test bench; collecting test data according to the set sampling frequency; collecting multiple periodic data, drawing the lateral force-side slip angle curve based on the periodic data, and performing curve fitting on it, taking the first-order coefficient as the first cornering stiffness value; evaluating the difference in multiple periodic side stiffness values ​​and optimizing them; obtaining output side slip characteristic test data through side slip characteristic test preparation and side slip characteristic test, and thereby obtaining the second side slip stiffness value and the return stiffness value; performing model identification on the model parameters according to the output side slip angle characteristic test data; and correcting the model identification through the first side slip stiffness. Although the method provided by the patent can eventually complete the identification of tire cornering stiffness, it is necessary to establish a model based on the test of a certain tire, which requires many steps, complex calculations, and the results are easily interfered with.

[0004] Therefore, the present invention provides a tire cornering stiffness identification method, which can estimate the tire cornering stiffness efficiently and accurately in real time. Summary of the invention

[0005] The purpose of the present invention is to provide a tire cornering stiffness identification method to solve the problem mentioned in the above background technology that real-time and accurate estimation of tire cornering stiffness is of great significance to improving vehicle handling characteristics, but most of the current tire cornering stiffness acquisition methods have limitations such as cumbersome steps, complex calculations, and low accuracy.

[0006] The present invention is achieved by adopting the following technical solutions:

[0007] A method for identifying tire cornering stiffness comprises the following steps:

[0008] Step S1: establishing a lateral force tire model;

[0009] Step S2: designing a tire lateral force estimator;

[0010] Step S3: designing a side slip angle feedback estimator based on the lateral force estimated in step S2;

[0011] Step S4: Based on the lateral force estimated in step S2 and the slip angle estimated in step S3, an online identification algorithm for the cornering stiffness is designed.

[0012] Furthermore, the method further comprises the following steps:

[0013] Step S5: Building a joint simulation experimental platform to verify the online identification algorithm of the lateral stiffness.

[0014] Furthermore, the step S2 includes the following sub-steps:

[0015] Step S2-1: designing a lateral force sliding mode observer based on sliding mode theory;

[0016] Step S2-2: obtaining a rear axle lateral force estimator based on the lateral force sliding mode observer;

[0017] Step S2-3: Based on the lateral force sliding mode observer, a front axle lateral force estimator is obtained.

[0018] Furthermore, the step S2-3 includes the following sub-steps:

[0019] Step S2-3-1: designing a front axle longitudinal force estimator to obtain the front axle longitudinal force;

[0020] Step S2-3-2: Based on the calculated front axle longitudinal force, obtain the front axle lateral force estimator.

[0021] Furthermore, the step S4 includes the following sub-steps:

[0022] Step S4-1: Based on the limited memory recursive least square method, the real-time estimated lateral force and sideslip angle are used as input to obtain a lateral force expression approximated by the quadratic expression of the tire sideslip angle;

[0023] Step S4-2: Analyze the lateral force expression expressed by the quadratic approximation of the tire slip angle to obtain an online identification algorithm for the cornering stiffness.

[0024] Furthermore, the cornering stiffness online identification algorithm comprises the following steps:

[0025] Step A-1: ​​using a lateral force expression expressed by a quadratic approximation of the tire slip angle as a nonlinear tire lateral force model;

[0026] Step A-2: Substitute the expressions of the tire lateral force estimator and the sideslip angle feedback estimator into the nonlinear tire lateral force model to estimate the tire cornering stiffness.

[0027] Furthermore, in step S1:

[0028] The established lateral force tire model is used to express the relationship between the lateral force, the road adhesion coefficient, and the vertical load. The expression of the lateral force tire model is as follows:

[0029]

[0030] Where C = 4a 2 bk e is the tire cornering stiffness, σ m =3μF z / C is the slip limit, a and b are the length and width of the tire contact, respectively, k e is the unit stiffness of the contact area, μ is the road adhesion coefficient, F z is the vertical load and σ is the lateral slip rate.

[0031] Furthermore, in step S2:

[0032] The expression of the lateral force sliding mode observer is as follows:

[0033]

[0034]

[0035] In the formula, x is the current system state, u is the system input variable, d is a bounded unknown variable, d is the disturbance to the system, E and P are real constants, P is the system output, L is the feedback coefficient, and ζ1 is the boundary layer thickness;

[0036] The expression of the rear axle lateral force estimator is as follows:

[0037]

[0038] Where m is the vehicle mass, is the yaw angle of the vehicle, l f , l r are the distances from the front axle and rear axle to the center of mass, respectively, and F yr is the total lateral force on the rear axle tire, is the estimated total lateral force on the rear axle tire, I z is the moment of inertia around the Z axis;

[0039] The expression of the front axle lateral force estimator is as follows:

[0040]

[0041] In the formula, F xf is the longitudinal force on the front axle tire.

[0042] Furthermore, in step S3:

[0043] The expression of the sideslip angle feedback estimator is as follows:

[0044]

[0045] In the formula, α f , α r are the sideslip angles of the front and rear wheels respectively.

[0046] Furthermore, in step S4:

[0047] The lateral force expression expressed by the quadratic approximation of the tire slip angle is as follows:

[0048]

[0049] In the formula, C f , C r are the total cornering stiffness of the front and rear wheels respectively.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] A tire cornering stiffness identification method is provided, which takes into account the real-time lateral force and slip angle of the tire. By executing steps S1 to S4, an online cornering stiffness identification algorithm can be designed to estimate the tire cornering stiffness in real time. The steps in the identification method provided by the present invention are concise and clear, and the calculation results are highly accurate, which helps to improve the performance of the vehicle active safety control system, thereby effectively improving the vehicle's handling stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the identification method according to an embodiment of the present invention;

[0053] Figure 2 is a schematic diagram of the effect of the road adhesion coefficient on the cornering stiffness according to an embodiment of the present invention;

[0054] Figure 3 is a schematic diagram of the effect of vertical load on lateral stiffness according to an embodiment of the present invention;

[0055] Figure 4 is an estimation diagram of the lateral forces of the high-adhesion front and rear axles according to an embodiment of the present invention;

[0056] Figure 5 is an estimation diagram of the high adhesion front and rear axle slip angles according to an embodiment of the present invention;

[0057] Figure 6 is an identification diagram of the high-adhesion front axle cornering stiffness according to an embodiment of the present invention;

[0058] Figure 7 is an identification diagram of the high-adhesion rear axle lateral stiffness according to an embodiment of the present invention;

[0059] Figure 8 is an estimation diagram of the low adhesion front and rear axle lateral forces according to an embodiment of the present invention;

[0060] Fig. 9 is an estimation diagram of the low adhesion front and rear axle slip angles according to an embodiment of the present invention;

[0061] Fig.10 is an identification diagram of the low-adhesion front axle cornering stiffness according to an embodiment of the present invention;

[0062] Fig.11 It is an identification diagram of the low-adhesion rear axle lateral stiffness described in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0064] Example 1

[0065] This embodiment provides a tire cornering stiffness identification method. Figure 1 , including the following steps:

[0066] Step S1: Establish a lateral force tire model and analyze the factors affecting the tire cornering stiffness.

[0067] Specifically:

[0068] During vehicle driving, the tires will generate lateral force and slip angle due to their own operating conditions such as turning and changing lanes, or external interference factors such as slopes and side winds. When the vehicle speed is low or the intensity of lane changes is low, the tire's motion state remains in the linear region, and the relationship between the lateral force and the slip angle remains linear, so the cornering stiffness is a constant; as the intensity of vehicle driving increases, the relationship between the lateral force and the slip angle is no longer linear, so the cornering stiffness is no longer a constant.

[0069] In order to analyze the influencing factors of tire cornering stiffness more intuitively and clearly, a lateral force tire model is established in Simulink; the relationship between lateral force, road adhesion coefficient and vertical load is expressed through the established lateral force tire model. The lateral force tire model is a brush tire model, and the specific expression is as follows:

[0070]

[0071] Where C = 4a 2 bk e is the tire cornering stiffness, σ m =3μF z / C is the slip limit, a and b are the length and width of the tire contact, respectively, k e is the unit stiffness of the contact area, μ is the road adhesion coefficient, F z is the vertical load and σ is the lateral slip rate.

[0072] like Figure 2 As shown in the figure, the tire cornering stiffness under different road adhesion coefficients, and the slopes of the four curves in the figure represent the respective tire cornering stiffnesses; when the vertical load is constant, as the road adhesion coefficient decreases, the tire will reach the tire sideslip limit under smaller lateral forces and sideslip angles, and the tire cornering stiffness reaches the minimum value at this time; the lower the road adhesion coefficient, the greater the difference between the linear cornering stiffness and the actual cornering stiffness of the tire, the greater the calculation error, and the greater the possibility of reducing vehicle tracking accuracy and stability.

[0073] like Figure 3 As shown in the figure, the tire cornering stiffness under different vertical load conditions, the slopes of the four curves in the figure represent their respective tire cornering stiffness; within a certain vertical load range, with the increase of vertical load, the tire cornering stiffness will also increase to a certain extent; when the vertical load is 1500N, the actual tire cornering stiffness is less than the linear cornering stiffness, and when the vertical load is 5500N, the actual tire cornering stiffness exceeds the linear cornering stiffness, but with the increase of slip angle and lateral force, the tire cornering stiffness will gradually decrease.

[0074] Step S2: Design a tire lateral force estimator based on the dynamic model and sliding mode observation algorithm.

[0075] Specifically, the method includes the following sub-steps:

[0076] Step S2-1: Design a lateral force sliding mode observer based on sliding mode theory.

[0077] For nonlinear model parameters and unknown external disturbances, sliding mode control has the advantages of strong real-time performance and high robustness. However, as a nonlinear system, the motion state of the tire will be disturbed by factors such as lateral wind and road roughness during vehicle driving. Therefore, in this identification method, the lateral force sliding mode observer is designed based on the sliding mode theory, and its expression is as follows:

[0078]

[0079]

[0080] Where x is the current system state, u is the system input variable, d is a bounded unknown variable, d is the disturbance to the system, E and P are real constants, P is the system output, L is the feedback coefficient, and ζ1 is the boundary layer thickness.

[0081] Step S2-2: Based on the lateral force sliding mode observer, a rear axle lateral force estimator is obtained.

[0082] The specific expression is as follows:

[0083]

[0084] Where m is the vehicle mass, is the yaw angle of the vehicle, l f , l r are the distances from the front axle and rear axle to the center of mass, F yr is the total lateral force on the rear axle tire, is the estimated total lateral force on the rear axle tire, I z is the moment of inertia about the Z axis.

[0085] Step S2-3: Based on the lateral force sliding mode observer, a front axle lateral force estimator is obtained.

[0086] In the front axle lateral force estimator, since the front axle longitudinal force is unknown, the front axle longitudinal force required by the front axle lateral force estimator should be estimated first, that is, step S2-3 includes the following sub-steps:

[0087] Step S2-3-1: Design a front axle longitudinal force estimator to obtain the front axle longitudinal force.

[0088] In order to avoid directly differentiating the angular velocity of the front wheel and reduce the impact of sensor measurement error, let ρ = -R w Γ1 / I w , Then the expression of the front axle longitudinal force estimator is as follows:

[0089]

[0090] In the formula, F xf is the longitudinal force on the front axle tire, I w is the tire moment of inertia, R w is the tire rolling radius, w f is the angular velocity of the front wheel rolling, T w It is the vector sum of the front wheel driving torque and the braking torque.

[0091] Step S2-3-2: Based on the calculated front axle longitudinal force, obtain the front axle lateral force estimator.

[0092] The specific expression is as follows:

[0093]

[0094] Step S3: Based on the lateral force estimated in step S2 and according to the lateral force estimation error, a sideslip angle feedback estimator is designed.

[0095] In this identification method, according to Newton's second law, the force analysis of the two-degree-of-freedom model is carried out, and the differential equation of the two-degree-of-freedom model is obtained as follows:

[0096]

[0097]

[0098] Based on this, the expressions of the front and rear wheel slip angles are as follows:

[0099]

[0100] Based on the differential equation of the two-degree-of-freedom model and the expressions of the front and rear wheel slip angles, the following expressions are obtained:

[0101]

[0102] Substituting the lateral force estimated in step S2, considering that direct integration may lead to error accumulation, the lateral force estimation error is used as the feedback of the sideslip angle estimator, and the expression of the sideslip angle feedback estimator is as follows:

[0103]

[0104] In the formula, α f , α r are the sideslip angles of the front and rear wheels respectively.

[0105] Step S4: Based on the lateral force estimated in step S2 and the slip angle estimated in step S3, an online identification algorithm for the cornering stiffness using a recursive least squares method with limited memory is designed.

[0106] Specifically, the method includes the following sub-steps:

[0107] Step S4-1: Based on the recursive least square method with limited memory, the real-time estimated lateral force and sideslip angle are used as input to obtain a lateral force expression approximated by the quadratic equation of the tire sideslip angle.

[0108] According to the Fiala tire cornering characteristic formula, it can be assumed that the tire lateral force is saturated with the ground adhesion, and the lateral force expression that can be approximated by the quadratic expression of the tire side slip angle is as follows:

[0109]

[0110] In the formula, C f , C r are the total cornering stiffness of the front and rear wheels respectively.

[0111] Step S4-2: Analyze the lateral force expression expressed by the quadratic approximation of the tire slip angle to obtain an online identification algorithm for the cornering stiffness.

[0112] It can be seen from the lateral force expression expressed by the quadratic approximation of the tire slip angle that the lateral force, slip angle and cornering stiffness of the front and rear axles of the tire are nonlinearly related. Based on this, the obtained cornering stiffness online identification algorithm includes the following steps:

[0113] Step A-1: ​​using a lateral force expression expressed by a quadratic approximation of the tire slip angle as a nonlinear tire lateral force model;

[0114] Step A-2: Substitute the expressions of the tire lateral force estimator and the sideslip angle feedback estimator into the nonlinear tire lateral force model to estimate the tire cornering stiffness.

[0115] In this identification method, the tire cornering stiffness fitting model is obtained based on the recursive least squares method to achieve the effect of real-time online estimation of the tire cornering stiffness by the nonlinear tire lateral force model. The equation of the recursive least squares method is as follows:

[0116]

[0117] Theoretically, in the process of online identification using the recursive least squares method, as the observation time increases, the estimation accuracy of the parameters to be estimated will become higher and higher; however, when the recursive least squares method processes a large amount of data, due to information overload or limited data processing speed, the performance of the algorithm will decline, which will in turn reduce the amount of information obtained from excessive data sampling, thereby increasing the estimation error, i.e., forming a data saturation problem. To solve this problem, the recursive least squares method with limited memory is used in this identification method to avoid overfitting by limiting the effective memory length L of the observed data, especially when the input signal or data has cyclic characteristics, which can effectively prevent the data saturation problem. Specifically:

[0118] When introducing a new k+Lth data sequence, it is necessary to remove the old data of the original kth data sequence to maintain the consistency of the sequence's timing characteristics and dynamic changes. After removing the old data, the information contained between the k+1th measurement period and the k+Lth measurement period is: (k+1, k+L), P(k+1, k+L), K(k+1, k+L). Therefore, the formula of the limited memory recursive least squares identification algorithm is expressed as follows:

[0119]

[0120] Each time a group of new information is added to the k+Lth data sequence, the parameter estimate (k, k+L), the gain matrix P(k, k+L) and the covariance matrix K(k, k+L) of the data sequence between k and k+L are calculated through formulas I, II and III; then, the old information provided by the kth data sequence is removed through formulas IV, V and VI, and the parameter estimate (k+1, k+L), the gain matrix P(k+1, k+L) and the covariance matrix K(k+1, k+L) of the data sequence between k+1 and k+L are calculated; through continuous iteration, it can be ensured that only the latest group of L observation equation data are effective each time the parameters are estimated, thereby overcoming the adverse effects of the data saturation problem in the recursive least squares method and improving the accuracy of parameter estimation.

[0121] Step S5: Build a joint simulation experimental platform to verify the online identification algorithm of the lateral stiffness under various extreme working conditions.

[0122] Specifically:

[0123] A joint simulation experimental platform based on CarSim and Simulink was built to verify that the online identification algorithm of cornering stiffness can more accurately characterize the relationship between tire lateral force, slip angle and cornering stiffness based on the nonlinear tire lateral force model. Figure 4 The relationship between the estimated and true values ​​of the lateral forces on the front and rear axles under high adhesion conditions is shown. Figure 5 The relationship between the estimated and true values ​​of the front and rear axle slip angles under high adhesion conditions is shown, from which it can be seen that the error between the estimated and true values ​​is small; Figure 6 The identification results of the front axle cornering stiffness under high adhesion conditions are shown. Figure 7 The identification results of the rear axle cornering stiffness under high adhesion conditions are shown, from which it can be seen that the identified cornering stiffness value can accurately track the actual cornering stiffness value; Figure 8 The relationship between the estimated and true values ​​of the lateral forces on the front and rear axles under low adhesion conditions is shown. Fig. 9 The relationship between the estimated and true values ​​of the front and rear axle slip angles under low adhesion conditions is shown, from which it can be seen that the error between the estimated and true values ​​is small; Fig.10 The identification results of the front axle cornering stiffness under low adhesion conditions are shown. Fig.11 The identification results of the rear axle cornering stiffness under low adhesion conditions are shown, from which it can be seen that the identified cornering stiffness value can accurately track the actual cornering stiffness value.

[0124] Through simulation verification, it can be seen that this identification method is robust to changes in road conditions and has good tracking accuracy and stability under both high and low adhesion conditions, so it effectively improves the real-time, accuracy and applicability of cornering stiffness identification.

[0125] In summary, the tire cornering stiffness identification method provided in this embodiment takes into account the real-time lateral force and slip angle of the tire. By executing steps S1 to S4, an online cornering stiffness identification algorithm can be designed to estimate the tire cornering stiffness in real time. The steps in the identification method provided by the present invention are concise and clear, and the calculation results are highly accurate, which helps to improve the performance of the vehicle's active safety control system, thereby effectively improving the vehicle's handling stability.

[0126] It should be noted that the parts not described in detail or expanded in the above scheme are all existing technologies, which do not belong to the improvements made by the present invention on the existing technologies, nor do they belong to the protection scope of the technical scheme of the present invention. Therefore, they will not be described in detail in this article.

[0127] Of course, the above contents are only preferred embodiments of the present invention and cannot be considered to limit the scope of the embodiments of the present invention. The present invention is not limited to the above examples, and equal changes and improvements made by ordinary technicians in the technical field within the essential scope of the present invention should all fall within the scope of the patent coverage of the present invention.

Claims

1. A tire cornering stiffness identification method, characterized in that: The steps include: Step S1: establishing a lateral force tire model; Step S2: designing a tire lateral force estimator; Step S3: designing a side slip angle feedback estimator based on the lateral force estimated in step S2; Step S4: Based on the lateral force estimated in step S2 and the slip angle estimated in step S3, an online identification algorithm for the cornering stiffness is designed.

2. The tire cornering stiffness identification method according to claim 1, characterized in that: The following steps are also included: Step S5: Building a joint simulation experimental platform to verify the online identification algorithm of the lateral stiffness.

3. The tire cornering stiffness identification method according to claim 1, characterized in that: The step S2 includes the following sub-steps: Step S2-1: designing a lateral force sliding mode observer according to sliding mode theory; Step S2-2: obtaining a rear axle lateral force estimator based on the lateral force sliding mode observer; Step S2-3: Based on the lateral force sliding mode observer, a front axle lateral force estimator is obtained.

4. The tire cornering stiffness identification method according to claim 3, characterized in that: The step S2-3 includes the following sub-steps: Step S2-3-1: designing a front axle longitudinal force estimator to obtain the front axle longitudinal force; Step S2-3-2: Based on the calculated front axle longitudinal force, obtain the front axle lateral force estimator.

5. The tire cornering stiffness identification method according to claim 3, characterized in that: The step S4 includes the following sub-steps: Step S4-1: Based on the limited memory recursive least square method, the real-time estimated lateral force and sideslip angle are used as input to obtain a lateral force expression approximated by the quadratic expression of the tire sideslip angle; Step S4-2: Analyze the lateral force expression expressed by the quadratic approximation of the tire slip angle to obtain an online identification algorithm for the cornering stiffness.

6. The tire cornering stiffness identification method according to claim 5, characterized in that: The cornering stiffness online identification algorithm comprises the following steps: Step A-1: ​​using a lateral force expression expressed by a quadratic approximation of the tire slip angle as a nonlinear tire lateral force model; Step A-2: Substitute the expressions of the tire lateral force estimator and the sideslip angle feedback estimator into the nonlinear tire lateral force model to estimate the tire cornering stiffness.

7. The tire cornering stiffness identification method according to claim 6, characterized in that: In step S1: The established lateral force tire model is used to express the relationship between the lateral force, the road adhesion coefficient, and the vertical load. The expression of the lateral force tire model is as follows: Where C = 4a 2 bk e is the tire cornering stiffness, σ m =3μF z / C is the slip limit, a and b are the length and width of the tire contact, respectively, k e is the unit stiffness of the contact area, μ is the road adhesion coefficient, F z is the vertical load and σ is the lateral slip rate.

8. The tire cornering stiffness identification method according to claim 7, characterized in that: In step S2: The expression of the lateral force sliding mode observer is as follows: In the formula, x is the current system state, u is the system input variable, d is a bounded unknown variable, d is the disturbance to the system, E and P are real constants, P is the system output, L is the feedback coefficient, and ζ1 is the boundary layer thickness; The expression of the rear axle lateral force estimator is as follows: Where m is the vehicle mass, is the yaw angle of the vehicle, l f , l r are the distances from the front axle and rear axle to the center of mass, F yr is the total lateral force on the rear axle tire, is the estimated total lateral force on the rear axle tire, I z is the moment of inertia around the Z axis; The expression of the front axle lateral force estimator is as follows: In the formula, F xf is the longitudinal force on the front axle tire.

9. The tire cornering stiffness identification method according to claim 8, characterized in that: In step S3: The expression of the sideslip angle feedback estimator is as follows: In the formula, α f , α r are the sideslip angles of the front and rear wheels respectively.

10. The tire cornering stiffness identification method according to claim 9, characterized in that: In step S4: The lateral force expression expressed by the quadratic approximation of the tire slip angle is as follows: In the formula, C f , C r are the total cornering stiffness of the front and rear wheels respectively.

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