A method for predicting steady-state lateral force of tires based on finite element transient simulation

Abstract

This invention discloses a method for predicting steady-state lateral force of a tire based on finite element transient simulation. The method includes performing transient pure sideslip simulation in finite element simulation software and extracting the simulation results; extracting the simulation results at small sideslip angles and identifying the relaxation length and tire lateral stiffness at small sideslip angles using a first-order transfer function; extracting the transient sideslip angle and randomly setting the magic formula model parameters to calculate the steady-state lateral force and the nonlinear relaxation length at large sideslip angles; extracting the sideslip angle from the simulation results at large sideslip angles and calculating the effective sideslip angle and transient lateral force; extracting the transient lateral force from the simulation results and calculating the error value, iterating until the error is minimized, and outputting the steady-state magic formula model parameters and steady-state lateral force. This invention is based on a first-order inertial transfer model, derives the expression method, and establishes an identification process for predicting steady-state lateral force from transient lateral force, thus predicting high-precision steady-state lateral force.

Description

Technical Field

[0001] This invention relates to the field of tire design technology, and in particular to a method for predicting the steady-state lateral force of a tire based on finite element transient simulation. Background Technology

[0002] Tire models play a crucial role in vehicle development. With increasingly shorter automotive development cycles, finite element simulation (FEM) methods are needed to obtain tire mechanical property data and build tire models—essentially, virtual modeling. While explicit FEM can acquire tire mechanical property data, its efficiency is severely hampered by limitations in computer hardware, requiring significant time and server resources.

[0003] Currently, there are two methods for obtaining tire lateral force in finite element simulation:

[0004] Method 1: Simulation using a quasi-steady-state sweeping approach. In the simulation, the tire slip angle sweeps from 0°, is applied up to a large slip angle, and then reaches a steady state. The slip angle loading rate is relatively slow throughout the process.

[0005] Method 2: Simulation is performed by calculating each sideslip angle individually. In the simulation task, the tire is sequentially loaded to each sideslip angle and moves for a period of time until it reaches a steady state.

[0006] The shortcomings of existing technology are:

[0007] In Method 1, the tire's movement speed is relatively slow under each simulation task, the simulation time is long, and the simulation results are prone to vibration instability.

[0008] Method 2 involves a large number of simulation tasks, resulting in a long overall simulation time and high simulation resource requirements. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the existing technology. To achieve the above objective, a method for predicting the steady-state lateral force of a tire based on finite element transient simulation is adopted to solve the problems mentioned in the background technology.

[0010] A method for predicting the steady-state lateral force of a tire based on finite element transient simulation includes the following steps:

[0011] Step S1: Perform transient pure sideslip simulations under small and large sideslip angles in finite element simulation software, and extract the simulation results;

[0012] Step S2: Based on the simulation results extracted under the small sideslip angle, the relaxation length and tire lateral stiffness of the small sideslip angle are obtained by using the first-order transfer function identification.

[0013] Step S3: Based on the sideslip angle extracted from the simulation results under large sideslip angle, and randomly set a set of initial steady-state magic formula model parameters, calculate the steady-state lateral force and the nonlinear relaxation length of the large sideslip angle.

[0014] Step S4: Calculate the effective sideslip angle based on the calculated nonlinear relaxation length, and substitute it into the formula for calculating steady-state lateral force to obtain the transient lateral force.

[0015] Step S5: Calculate the error value based on the calculated transient lateral force, and output the steady-state magic formula model parameters and steady-state lateral force by iterating the steady-state magic formula model parameters until the error is minimized.

[0016] As a further aspect of the present invention, the specific steps in step S1 include:

[0017] In the finite element simulation software, transient pure sideslip simulation tasks with one small sideslip angle and two large sideslip angles are performed, and simulation data is acquired in real time. Simultaneously, simulation conditions parameters are set, including tire pressure, load, roll angle, rolling speed, and sampling frequency.

[0018] Extract the simulation results, which include simulation time t, sideslip angle α, and lateral force.

[0019] As a further aspect of the present invention: the first-order transfer function in step S2, and the tire lateral stiffness c y The calculation formula is:

[0020]

[0021]

[0022] Where α is the sideslip angle and t is the simulation time.

[0023] As a further aspect of the present invention: the steady-state lateral force F in step S3 y and the nonlinear relaxation length r of large sideslip angle y The calculation formula is:

[0024] F y =D y sin[C y arctan{B y α-E y (B y α-arctan(B y α))}]+S Vy ;

[0025]

[0026] Among them, B y C y D y E y , and S Vy The parameters to be identified.

[0027] As a further aspect of the present invention: the transient lateral force in step S4 The calculation formula is:

[0028]

[0029]

[0030] Where τ is the effective sideslip angle, ω is the tire rolling angular velocity, and B y C y D y E y , and S Vy The parameters to be identified.

[0031] As a further aspect of the present invention: the formula for calculating the error value ε in step S5 is as follows:

[0032]

[0033] in, It is a transient lateral force. It is a lateral force.

[0034] Compared with the prior art, the present invention has the following technical advantages:

[0035] Using the aforementioned technical solution, based on a first-order inertial transmission model, and considering the relationship between tire relaxation characteristics and sideslip angle, the predicted steady-state lateral force is highly accurate, starting from the transient mechanical characteristics of the tire. A corresponding tire transient model and parameter identification process were established. Furthermore, the steady-state lateral force of the tire is predicted based on finite element transient simulation. By simulating three sideslip conditions, transient lateral force curves under large sideslip angles are obtained, thus enabling the prediction of steady-state lateral forces at various sideslip angles, significantly reducing simulation time and resources. Moreover, it is applicable to both lateral and longitudinal forces and can be used for related research on tire transient characteristics. Attached Figure Description

[0036] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings:

[0037] Figure 1 This is a schematic diagram illustrating the steps of the prediction method according to an embodiment of this application;

[0038] Figure 2 This is a schematic diagram of tire deformation during transient lateral slip according to an embodiment of this application;

[0039] Figure 3 This is a flowchart illustrating the parameter identification process of an embodiment disclosed in this application.

[0040] Figure 4 This is a schematic diagram of the fitting results of the 1° transient sideslip lateral force according to an embodiment of this application;

[0041] Figure 5 This is a schematic diagram showing the nonlinear relaxation length calculation results of an embodiment disclosed in this application;

[0042] Figure 6 This is a fitting diagram of the transient lateral force during 12° yaw in an embodiment of this application;

[0043] Figure 7 This is a schematic diagram comparing the steady-state lateral force prediction results with the simulation results of the embodiments disclosed in this application. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] Please refer to Figure 1 In this embodiment of the invention, a method for predicting the steady-state lateral force of a tire based on finite element transient simulation includes the following steps:

[0046] Step S1: Perform transient pure sideslip simulations under small and large sideslip angles in finite element simulation software, and extract the simulation results. In this embodiment, transient pure sideslip simulations under one small sideslip angle and two large sideslip angles are performed simultaneously, and the simulation results are extracted. The specific steps include:

[0047] A pure sideslip simulation task is performed in finite element simulation software, and simulation data is acquired in real time. Simultaneously, simulation working condition parameters are set, including tire pressure, load, roll angle, rolling speed, and sampling frequency.

[0048] Extract the simulation results, which include simulation time t, sideslip angle α, and lateral force.

[0049] Step S2: Based on the simulation results extracted at the small sideslip angle, the relaxation length and tire lateral stiffness at the small sideslip angle are identified using the first-order transfer function, including the first-order transfer function and the tire lateral stiffness c. y The calculation formula is:

[0050]

[0051]

[0052] Where α is the sideslip angle and t is the simulation time.

[0053] Step S3: Based on the sideslip angles extracted from the simulation results under the two large sideslip angles, and by randomly setting a set of initial steady-state magic formula model parameters, calculate the steady-state lateral force F. y and the nonlinear relaxation length r of large sideslip angle y The calculation formula is:

[0054] F y =D y sin[C y arctan{B y α-E y (B y α-arctan(B y α))}]+S Vy ;

[0055]

[0056] Among them, B y C y D y E y , and S Vy The parameters to be identified;

[0057] Step S4: Based on the calculated nonlinear relaxation length, calculate the effective sideslip angle τ, and substitute it into the steady-state lateral force calculation formula to obtain the transient lateral force. Transient lateral force The calculation formula is:

[0058]

[0059]

[0060] Where τ is the effective sideslip angle, ω is the tire rolling angular velocity, and B y C y D y E y , and S Vy The parameters to be identified.

[0061] Step S5: Based on the calculated transient lateral force, calculate the error value ε. Iterate the steady-state magic formula model parameters until the error is minimized, then output the steady-state magic formula model parameters and the steady-state lateral force. The formula for calculating the error value ε is:

[0062]

[0063] in, It is a transient lateral force. It is a lateral force.

[0064] In this embodiment, the simulation time t, sideslip angle α, and lateral force F are... yFEA All of these can be obtained directly from the simulation results. B can be obtained by using the formulas for calculating transient lateral forces and employing parameter identification methods. y C y D y E y S Vy S Hy The value of the formula is given, and the steady-state lateral force is calculated. The derivation of the formula is as follows:

[0065] like Figure 2 As shown, when the tire is in transient lateral deflection, the lateral force F acting on the contact patch is... y This causes the tire to deform laterally. At this point, the actual slip speed of the tire is different from the nominal slip speed. The lateral force on the tire can be approximated as:

[0066]

[0067] v y =V x tanα (2)

[0068] in, For transient lateral force, v is the steady-state lateral force corresponding to the nominal slip velocity. y V is the nominal slip velocity. x Let be the tire's longitudinal velocity. Due to the nonlinearity of the tire's lateral force, this calculation results in... The result is smaller than the actual result.

[0069] For such a spring-damped system, the transient lateral force on the tire can also be expressed as:

[0070]

[0071] Among them, c y d represents the lateral stiffness of the tire carcass. y This refers to the lateral damping of the tire carcass.

[0072] From formulas (1) to (3), we can obtain:

[0073]

[0074] The typical form of a first-order transfer differential equation is as follows:

[0075]

[0076] Therefore, the relaxation length of tire lateral deviation is:

[0077]

[0078] Where ω is the tire rolling angular velocity, R e Tire rolling radius, T y is the time constant.

[0079] The transient lateral force characteristic of the tire is defined as a first-order response, which is expressed as:

[0080]

[0081] Where τ is the effective sideslip angle during transient sideslip.

[0082] As shown in Table 1 below:

[0083] Table 1

[0084]

[0085] Given the steady-state lateral force and the simulated transient lateral force, identify and calculate c in the expression for the relaxation length. y and d y After fitting and verification, due to the previous approximation, The value is too large, which makes the identified d y The values ​​are negative and all are near zero; their values ​​are much smaller than... The value of d contributes very little to the relaxation length and is difficult to obtain, therefore the tire body damping d can be ignored. y The effect of this. Meanwhile, when the tire is laterally biased, no longitudinal slippage occurs, and the V-shape at this time... x =|ωR e Therefore, the formula for calculating the lateral relaxation length can be simplified to:

[0086]

[0087] like Figure 3 As shown, Figure 3 The relaxation length identification result is for a 1° lateral slip. When the tire has a 1° lateral slip, the entire process is within the linear region of the lateral force curve. Based on the output of the lateral force, the actual effective lateral slip angle τ can be calculated using the following formula:

[0088]

[0089] Among them, F ymax α represents the peak value of the lateral force. max The sideslip angle is the angle at which the lateral force reaches its peak.

[0090] Since the lateral force changes approximately linearly with the sideslip angle within 1°, we assume a relaxation length r here. y It remains constant within 1°. Input the sideslip angle α, the effective sideslip angle τ, and the rolling speed V. x Substituting the transfer function into the least squares fit, we can obtain the relaxation length at 1° lateral deviation.

[0091]

[0092] The lateral stiffness c of the tire carcass y for:

[0093]

[0094] Because the lateral force during steady-state tire lateral tilt cannot be determined, such as Figure 4 As shown, the steady-state lateral force F is predicted here using an iterative solution method. y The specific process is as follows:

[0095] Step 1: Randomly generate a set of magic formula model parameters (B) y C y D y E y S Vy Combining the sideslip angle sequence extracted by sideslip sweep under large sideslip angles, the lateral nonlinear relaxation length r is calculated using formulas (8) and (12). y ;

[0096] F y =D y sin[C y arctan{B y α-E y (B y α-arctan(B y α))}]+S Vy (12)

[0097] Step 2: Using the first-order transfer function formula (7) and the nonlinear relaxation length r y The time series and side slip angle series extracted by the side slip sweep under large side slip angles are used to calculate the effective side slip angle τ, and then the magic formula model parameters (B) are used. y C y D y E y S Vy ), calculate the transient lateral force

[0098]

[0099] Step 3: Calculate the transient lateral force The fitting error is used for iteration;

[0100]

[0101] Step 4: Determine if the objective is met (minimum error between calculated transient lateral force and simulated transient lateral force), and output the magic formula model parameters (B) at this point. y C y D y E y S Vy ), calculate the steady-state lateral force F y .

[0102] Table 2

[0103]

[0104] Depend on Figure 5 , Figure 6 , Figure 7 As shown in Table 2 above, the calculation method of the present invention can express the change of tire slack length with slip angle, while transient lateral force... The fitting error and steady-state lateral force F y The prediction errors are all less than 2%, which can be used for virtual tire modeling to replace a large number of finite element simulations, reduce the consumption of simulation resources and time, and improve simulation efficiency.

[0105] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention. The scope of the invention is defined by the appended claims and their equivalents, all of which should be included within the scope of protection of the invention.

Claims

1. A method for predicting the steady-state lateral force of a tire based on finite element transient simulation, characterized in that, Includes the following steps: Step S1: Perform transient pure sideslip simulations under small and large sideslip angles in finite element simulation software, and extract the simulation results; Step S2: Based on the simulation results extracted under the small sideslip angle, the relaxation length and tire lateral stiffness of the small sideslip angle are obtained by using the first-order transfer function identification. Step S3: Based on the sideslip angle extracted from the simulation results under large sideslip angle, and randomly set a set of initial steady-state magic formula model parameters, calculate the steady-state lateral force and the nonlinear relaxation length of the large sideslip angle. Step S4: Calculate the effective sideslip angle based on the calculated nonlinear relaxation length, and substitute it into the formula for calculating steady-state lateral force to obtain the transient lateral force. Step S5: Calculate the error value based on the calculated transient lateral force, and output the steady-state magic formula model parameters and steady-state lateral force by iterating the steady-state magic formula model parameters until the error is minimized.

2. The method for predicting tire steady-state lateral force based on finite element transient simulation according to claim 1, characterized in that, The specific steps in step S1 include: In the finite element simulation software, transient pure sideslip simulation tasks with one small sideslip angle and two large sideslip angles are performed, and simulation data is acquired in real time. Simultaneously, simulation conditions parameters are set, including tire pressure, load, roll angle, rolling speed, and sampling frequency. Extract the simulation results, which include simulation time t, sideslip angle α, and lateral force.

3. The method for predicting tire steady-state lateral force based on finite element transient simulation according to claim 1, characterized in that, The first-order transfer function in step S2, and the tire lateral stiffness c y The calculation formula is: Where α is the sideslip angle and t is the simulation time.

4. The method for predicting tire steady-state lateral force based on finite element transient simulation according to claim 1, characterized in that, The steady-state lateral force F in step S3 y and the nonlinear relaxation length r of large sideslip angle y The calculation formula is: Among them, B y C y D y E y ,as well as The parameters to be identified.

5. The method for predicting tire steady-state lateral force based on finite element transient simulation according to claim 1, characterized in that, The transient lateral force in step S4 The calculation formula is: Where τ is the effective sideslip angle, ω is the tire rolling angular velocity, and B y C y D y E y ,as well as The parameters to be identified.

6. The method for predicting tire steady-state lateral force based on finite element transient simulation according to claim 1, characterized in that, The formula for calculating the error value ε in step S5 is as follows: in, It is a transient lateral force. This is a lateral force.

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