Method for predicting longitudinal force of tire based on finite element transient simulation

Abstract

The invention discloses a method for predicting the longitudinal force of a tire based on finite element transient simulation. The method comprises the following steps: carrying out pure longitudinal slip simulation in finite element simulation software to obtain finite element simulation data, respectively carrying out steady-state simulation under a small slip rate and transient simulation under a large slip rate, and extracting a simulation calculation result; randomly generating a group of magic formula model parameters, and calculating an effective slip rate in combination with a slip rate sequence extracted by longitudinal slip scanning under a large slip rate; calculating a transient longitudinal force, an error between the transient longitudinal force and a simulation transient longitudinal force, and an error between the longitudinal force under a small slip rate and the simulation longitudinal force; optimizing and outputting the error between the transient longitudinal force and the simulated transient longitudinal force and the optimal parameter of the magic formula model when the error between the longitudinal force and the simulated longitudinal force under the small slip rate is minimum; and substituting the initial slip rate sequence into the optimized model, and calculating a steady-state longitudinal force. According to the prediction method, the longitudinal force of the tire can be predicted by using a small amount of simulation data, and the precision is high.

Description

Technical Field

[0001] The invention belongs to the technical field of tire modeling and data simulation, and relates to a method for predicting tire longitudinal force based on finite element transient simulation. Background Art

[0002] Tire models play an important role in vehicle development. As the automobile development cycle continues to shorten, vehicle manufacturers need tire manufacturers to use finite element simulation to obtain tire mechanical property data and build tire models, i.e., virtual sample delivery. Tire mechanical property data can be obtained based on explicit finite element simulation, but affected by the level of computer hardware, finite element simulation requires a lot of time and server resources, which seriously affects the efficiency of tire modeling.

[0003] At present, there are three methods to obtain tire longitudinal force in finite element simulation:

[0004] Method 1: Use quasi-steady-state sweeping to simulate. In the simulation task, the longitudinal slip rate of the tire starts from 0 and is slowly loaded to a certain large slip rate until it reaches a steady state. The longitudinal slip rate loading rate in the whole process is slow. In this method, the movement rate of the tire is slow under each simulation task, the simulation time is long, and the simulation results are prone to vibration instability.

[0005] Method 2: Simulate by calculating the slip rate one by one. In the simulation task, the tire is loaded to each slip rate in turn and moves for a period of time to reach a steady state; however, this method sets a large number of simulation tasks, the overall simulation time is long, and the required simulation resources are high.

[0006] Method 3: Use high-frequency transient large longitudinal slip simulation, that is, the slip rate is quickly swept from 0 to a certain large slip rate in a short time to obtain a transient longitudinal slip curve; then combine the longitudinal relaxation length to predict the steady-state longitudinal force curve. In this method, the number of simulation tasks is small, and the simulation time of rapid sweeping is short, but because it is difficult to obtain an accurate longitudinal relaxation length, the predicted steady-state longitudinal slip curve has a large error with the actual one. Summary of the invention

[0007] In view of the technical problems existing in the prior art, the purpose of the present invention is to provide a method for predicting the longitudinal force of a tire based on finite element transient simulation when the accurate longitudinal relaxation length cannot be obtained.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The method for predicting tire longitudinal force based on finite element transient simulation includes the following steps:

[0010] S1. Perform pure longitudinal slip simulation in finite element simulation software, obtain finite element simulation data, set simulation conditions, perform steady-state simulation under small slip rate and transient simulation under large slip rate, and extract simulation calculation results, including nominal slip rate κ, simulated longitudinal force F under small slip rate xm (average value after stabilization) and simulated transient longitudinal force F under large slip ratio xFEA wait;

[0011] S2, randomly generate a set of magic formula model parameters, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , combined with the slip rate sequence extracted by the longitudinal sliding sweep under large slip rate, the effective slip rate κ is calculated using formulas (6)-(8) e and the steady-state longitudinal force F x :

[0012] F x =D x sin[C x arctan{B x κ-E x (B x κ-arctan(B x κ))}]+S Vx (6)

[0013]

[0014] Among them, C Fx Indicates the effective slip rate κ e The stiffness at the nominal slip rate κ is used as the secant stiffness approximation; B x , C x , D x 、E x , S Vx is the parameter to be optimized, V x is the tire rotation speed;

[0015] S3, the effective slip rate κ e Substitute into formula (9) to calculate the transient longitudinal force F under large slip ratio: xsim , and then calculate the transient longitudinal force F under large slip rate according to formula (10): xsim and simulated transient longitudinal force F xFEA The error ε1 is:

[0016] F xsim =D x sin[Cx arctan{B x κ e -E x (B x κ e -arctan(B x κ e ))}]+S Vx (9)

[0017]

[0018] Let the effective slip ratio κ e The longitudinal force F under the small slip rate (or peak slip rate) corresponding to the simulation condition is calculated. xmsim ;

[0019] S4. Calculate the longitudinal force F under small slip rate according to formula (11): xmsim and simulated longitudinal force F xm The error ε2 is:

[0020] ε2=|F xmsim -F xm | (11);

[0021] S5. Use the particle swarm optimization algorithm to optimize and output the magic formula model parameters with the smallest error ε1 and error ε2, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , and obtain the optimal parameters; then substitute the initial slip rate sequence into the optimized model to calculate the steady-state longitudinal force F x .

[0022] Preferably, it also includes: S6, extracting the braking simulation calculation results, including the longitudinal force under small negative slip value and the transient longitudinal force under large negative slip value; then repeating steps S2-S5, calculating the steady-state braking longitudinal force, and finally obtaining a complete steady-state longitudinal slip force curve.

[0023] Preferably, in step S1, the simulation calculation results also include simulation time t, load F z wait.

[0024] Preferably, in step S1, the simulation working conditions include tire pressure, load, slip rate, rolling speed, sampling frequency, etc.;

[0025] Preferably, the small slip ratio is in the range of 5% to 8%; and the large slip ratio is greater than 30%.

[0026] Beneficial effects of the present invention:

[0027] (1) Starting from the transient mechanical characteristics of the tire, the present invention considers the influence of the damping characteristics on tire relaxation in finite element simulation, establishes the relationship between the nominal slip rate and the effective slip rate during transient longitudinal slip of the tire, and an identification process for predicting the steady-state longitudinal force from the transient longitudinal force without relying on the relaxation length, thereby achieving the high-precision prediction of the steady-state longitudinal force of the tire using a small amount of simulation data.

[0028] (2) For the tire longitudinal slip condition, the present invention only utilizes the simulation of four longitudinal slip conditions (two small slip ratio (positive and negative values) simulations and two large slip ratio (positive and negative values) simulations) to obtain the transient longitudinal force response characteristics of the tire, and then can predict the steady-state longitudinal force of the complete tire longitudinal slip (driving and braking), greatly reducing the simulation time and simulation resource usage.

[0029] (3) The prediction method disclosed in the present invention takes into account the damping characteristics in finite element simulation and can therefore be used for related research on other transient characteristics of tires. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A flow chart of a method for predicting tire longitudinal force based on finite element transient simulation proposed by the present invention;

[0031] Figure 2 This is the finite element simulation result diagram of transient longitudinal force under 1% tire slip rate;

[0032] Figure 3 The comparison result diagram of the effective slip rate and the nominal slip rate under the slip rate of 30% is shown;

[0033] Figure 4 It is a fitting curve diagram of transient longitudinal force and simulated transient longitudinal force at 30% slip rate;

[0034] Figure 5 The comparison chart of the predicted result of the steady-state longitudinal force of the tire with a load of 2500N and the steady-state simulation result;

[0035] Figure 6 The comparison chart of the predicted result of the steady-state longitudinal force of the tire with a load of 4000N and the steady-state simulation result;

[0036] Figure 7 This is a comparison chart between the predicted results of the steady-state longitudinal force of a 5500N load tire and the steady-state simulation results. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] The present invention provides a method for predicting tire longitudinal force based on finite element transient simulation. By using a small amount of finite element simulation results and adopting an optimization solution method, the values ​​of magic formula model parameters can be obtained, including B x , C x , D x 、E x , S Vx Etc., and then predict and calculate the steady-state longitudinal force. The principle of this prediction method is explained below:

[0039] In the finite element simulation of the six-component tire force, in order to eliminate the oscillation of the data and obtain a more stable longitudinal force, it is necessary to add additional damping on the basis of the tire's own damping to suppress the oscillation of the data. When calculating the transient longitudinal force, it is necessary to consider the influence of damping on the transient response. In order to more accurately express the longitudinal relaxation characteristics considering the influence of damping, the following derivation is performed:

[0040] Assume that the carcass is a spring-damped parallel system, where the carcass damping is c x , carcass stiffness is k cx , in the transient longitudinal sliding process, the following equations (1) to (3) are established:

[0041]

[0042] Where u represents the carcass deformation, κ e represents the effective slip ratio, C Fx Indicates the effective slip rate κ e The stiffness at

[0043]

[0044] Taking the derivative of both sides of formula (1), we get:

[0045]

[0046] Right now

[0047] Therefore, the nominal slip rate κ and effective slip rate κ of the transient longitudinal slip simulation process are e Satisfies the above differential equation.

[0048] It can be seen that for a given nominal slip rate κ input, the effective slip rate κ e With carcass damping c x , carcass stiffness k cx , Road speed V x And the stiffness C at the effective slip rate Fx There is a relationship. Fx The secant stiffness approximation at the nominal slip rate κ is used, while the effective slip rate κ e With carcass damping c x It needs to be obtained through longitudinal force curve fitting.

[0049] Reference Figure 1 , a method for predicting tire longitudinal force based on finite element transient simulation, comprising the following steps:

[0050] S1. Perform pure longitudinal slip simulation in finite element simulation software, obtain finite element simulation data, set simulation conditions, mainly including tire pressure, load, slip rate, rolling speed, sampling frequency, etc., respectively perform steady-state simulation under small slip rate (or peak slip rate) (according to experience, any slip rate between 5% and 8%) and transient simulation under large slip rate (above 30%), extract simulation calculation results, mainly including simulation time t, nominal slip rate κ, load F z , Simulated longitudinal force F under small slip rate xm (average value after stabilization) and simulated transient longitudinal force F under large slip ratio xFEA ;

[0051] S2. Since it is impossible to confirm the longitudinal force of the tire during steady-state longitudinal slip, an iterative solution is used here to predict the steady-state longitudinal force F x : Randomly generate a set of magic formula model parameters, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , combined with the slip rate sequence extracted by the longitudinal sliding sweep under large slip rate, the effective slip rate κ is calculated using formulas (6)-(8) e and the steady-state longitudinal force F x ;

[0052] F x =D x sin[C x arctan{B x κ-E x (B x κ-arctan(B x κ))}]+S Vx (6)

[0053]

[0054] Among them, C Fx is the effective slip rate κ e The stiffness at the nominal slip rate κ is used as the secant stiffness approximation; B x , C x , D x 、E x , S Vx is the parameter to be optimized, V x is the tire rotation speed;

[0055] S3, the effective slip rate κ e Substitute into formula (9) to calculate the transient longitudinal force F under large slip ratio: xsim , and then calculate the transient longitudinal force F under large slip rate according to formula (10): xsim and simulated transient longitudinal force F xFEA The error ε1 is:

[0056] F xsim =D x sin[C x arctan{B x κ e -E x (B x κ e -arctan(B x κ e ))}]+S Vx (9)

[0057]

[0058] Let the effective slip rate κ in formula (9) be e (value) is the small slip rate (or peak slip rate) corresponding to the simulation condition, and the longitudinal force F under this small slip rate is calculated. xmsim ;

[0059] S4. Calculate the longitudinal force F under small slip rate according to formula (11): xmsim and simulated longitudinal force F xm The error ε2 is:

[0060] ε2=|F xmsim -F xm | (11)

[0061] S5. Use the particle swarm optimization algorithm to optimize and output the transient longitudinal force F under large slip rate xsim and simulated transient longitudinal force F xFEA The error ε1 and the longitudinal force F at small slip ratexmsim and simulated longitudinal force F xm The magic formula model parameters when the error ε2 is the smallest include B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , and obtain the optimal parameters; then substitute the initial slip rate sequence into the optimized model to calculate the steady-state longitudinal force F x .

[0062] S6. Extract the braking simulation calculation results, including the longitudinal force under a small negative slip ratio and the transient longitudinal force under a large negative slip ratio, and then repeat steps S2-S5 to calculate the steady-state braking longitudinal force, and finally obtain a complete steady-state longitudinal slip force curve.

[0063] like Figure 2 The following is the simulation result of longitudinal sliding with a slip ratio of 1%. Figure 2 The results show that the steady-state longitudinal force curve is not smooth. Due to the influence of simulation conditions, it is impossible to obtain an accurate and smooth longitudinal force curve. Therefore, it is also impossible to calculate the carcass damping c by fitting the relaxation length through this curve. x , carcass stiffness k cx .

[0064] Through the above Figure 2 The analysis of the results shows that the relaxation length or 1% slip rate cannot be used for prediction. To complete the prediction, it is necessary to solve the problem of transition zone accuracy. The slip rate in this area is large and highly sensitive to the damping value. Considering that a transient curve cannot complete the prediction and the 1% slip rate curve oscillation cannot be used, a steady-state value can be introduced as the objective function at the rear transition zone position, which can not only ensure the accuracy of the steady-state longitudinal force in the transition zone, but also realize the prediction of the complete curve.

[0065] Example 1

[0066] The prediction is performed with a small slip ratio of 8% and a large slip ratio of 30%. Specifically, the method for predicting the longitudinal force of a tire based on finite element transient simulation includes the following steps:

[0067] A1. Perform pure longitudinal slip simulation in finite element simulation software, obtain 8% slip rate finite element simulation data, perform steady-state simulation under 8% slip rate and transient simulation under 30% slip rate, extract simulation calculation results, including simulation time t, nominal slip rate κ, load F z , Simulated longitudinal force F at 8% slip rate x8(average value after stabilization) and simulated transient longitudinal force F at 30% slip rate xFEA ;

[0068] A2. Randomly generate a set of magic formula model parameters, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , combined with the slip rate sequence extracted by the longitudinal sliding sweep under the slip rate of 30%, the effective slip rate κ is calculated using formulas (6)-(8) e and the steady-state longitudinal force F x ;

[0069] F x =D x sin[C x arctan{B x κ-E x (B x κ-arctan(B x κ))}]+S Vx (6)

[0070]

[0071] A3. Set the effective slip rate κ e Substituting into formula (9), calculate the transient longitudinal force F at 30% slip ratio: xsim , and the transient longitudinal force F at 30% slip ratio is calculated according to the following formula (10): xsim and simulated transient longitudinal force F xFEA The error ε1 is:

[0072] F xsim =D x sin[C x arctan{B x κ e -E x (B x κ e -arctan(B x κ e ))}]+S Vx (9)

[0073]

[0074] Let the effective slip rate κ in formula (9) be e =8, calculate the longitudinal force F at 8% slip rate x8sim ;

[0075] A4. Calculate the longitudinal force F at 8% slip rate according to the following formula x8sim and simulated longitudinal force F x8 The error ε2 is:

[0076] ε2=|F x8sim -F x8 | (11);

[0077] A5. Use the particle swarm optimization algorithm to optimize and output the magic formula model parameters with the smallest error ε1 and error ε2, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , and obtain the optimal parameters; then substitute the initial slip rate sequence into the optimized model to calculate the steady-state driving longitudinal force F x ;

[0078] A6. Extract the braking simulation calculation results, including the longitudinal force at -8% slip rate and the transient longitudinal force at -30% slip rate, and then repeat steps S2-S5 to calculate the steady-state braking longitudinal force, and finally obtain a complete steady-state longitudinal force curve.

[0079] The nominal slip ratio (i.e. input slip ratio) and effective slip ratio obtained by the above prediction method are compared, and the results are shown in Figure 3 , Figure 3 The results show that compared with the nominal slip rate (8%, 30%), the effective slip rate has an obvious hysteresis.

[0080] like Figure 4 As shown, it is the fitting result of transient longitudinal force and transient simulated longitudinal force under 30% slip rate. Figure 4 The results show that the fitting accuracy of the entire transient response process is high.

[0081] The predicted results of tire longitudinal force under different loads (2500N, 4000N, 5500N) are compared with the simulation results. Figure 5-Figure 7 .

[0082] Depend on Figure 5-Figure 7 The results show that the predicted steady-state longitudinal force curve of the tire is in good agreement with the longitudinal force curve obtained by actual simulation, with a low error.

[0083] The prediction method of the present invention is used to predict the steady-state longitudinal force of the 235 / 50R19 (drive) tire and the 235 / 50R19 (brake) tire, and the accuracy of the steady-state longitudinal force obtained is compared with the accuracy of directly fitting the steady-state simulation data using the MF model. The results are shown in Table 1.

[0084] Table 1

[0085]

[0086] It can be seen from the results in Table 1 that the prediction method of the present invention has a high prediction accuracy and can be used for virtual tire modeling to replace a large number of finite element simulations, thereby greatly reducing the simulation resources and time occupied and improving the simulation efficiency.

[0087] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and improved concepts of the present invention within the technical scope disclosed by the present invention, and they should be covered by the protection scope of the present invention.

Claims

1. A method for predicting tire longitudinal force based on finite element transient simulation, characterized in that: The following steps are involved: S1. Perform pure longitudinal slip simulation in finite element simulation software, obtain finite element simulation data, set simulation conditions, perform steady-state simulation under small slip rate and transient simulation under large slip rate, and extract simulation calculation results, including nominal slip rate κ, simulated longitudinal force F under small slip rate xm And the simulated transient longitudinal force F under large slip ratio xFEA ; S2, randomly generate a set of magic formula model parameters, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , combined with the slip rate sequence extracted by longitudinal sliding sweep under large slip rate, the effective slip rate κ is calculated using formulas (6)-(8) e and the steady-state longitudinal force F x : F x =D x sin[C x silver{B x κ-E x (B x κ-arctan(B x κ))}]+S Vx (6) Among them, C Fx Indicates the effective slip rate κ e The stiffness at the nominal slip rate κ is used as the secant stiffness approximation; B x , C x , D x 、E x , S Vx is the parameter to be optimized, V x is the tire rotation speed; S3, the effective slip rate κ e Substitute into formula (9) to calculate the transient longitudinal force F under large slip ratio: xsim , and then calculate the transient longitudinal force F under large slip rate according to formula (10): xsim and simulated transient longitudinal force F xFEA The error ε1 is: F xsim =D x sin[C x silver{B x κ e -AND x (B x κ e -arctane(B x κ e ))}]+S Vx (9) Let the effective slip rate κ in formula (9) be e is the small slip rate corresponding to the simulation condition, and the longitudinal force F under this small slip rate is calculated. xmsim ; S4. Calculate the longitudinal force F under small slip rate according to formula (11): xmsim and simulated longitudinal force F xm The error ε2 is: ε2=|F xmsim -F xm | (11); S5. Use the particle swarm optimization algorithm to optimize and output the magic formula model parameters with the smallest error ε1 and error ε2, including B x , C x , D x 、E x , S Vx , and carcass damping c x , carcass stiffness k cx , and obtain the optimal parameters; then substitute the initial slip rate sequence into the optimized model to calculate the steady-state longitudinal force F x .

2. The method for predicting tire longitudinal force based on finite element transient simulation according to claim 1, characterized in that: Also includes: S6. extracting braking simulation calculation results, including longitudinal force under small negative slip ratio and transient longitudinal force under large negative slip ratio; Then, steps S2-S5 are repeated to calculate the steady-state braking longitudinal force, and finally a complete steady-state longitudinal sliding force curve is obtained.

3. The method for predicting tire longitudinal force based on finite element transient simulation according to claim 1, characterized in that: In step S1, the simulation calculation results also include simulation time t, load F z .

4. The method for predicting tire longitudinal force based on finite element transient simulation according to claim 1, characterized in that: The simulation working conditions include tire pressure, load, slip rate, rolling speed, and sampling frequency.

5. The method for predicting tire longitudinal force based on finite element transient simulation according to claim 1, characterized in that: The small slip ratio has a value range of 5% to 8%; the large slip ratio has a value of more than 30%.

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