A four-wheel non-linear two-degree-of-freedom vehicle model simulation system and method

Abstract

The present invention discloses a four-wheel non-linear two-degree-of-freedom vehicle model simulation system and method. The system includes a two-degree-of-freedom vehicle body dynamics model of the whole vehicle, a four-wheel composite working condition magic tire model, an Ackermann angle calculation model, a four-wheel sideslip angle calculation model, a four-wheel dynamic vertical load calculation model, and a Carsim software module. The vehicle model is a four-wheel model, which considers the sideslip angle hysteresis response caused by the lateral relaxation length of the tire, and can provide a more accurate tire sideslip angle than the two-wheel model. The vertical load transfer between the left and right wheels and the unsprung mass are considered, thereby improving the estimation accuracy of the tire vertical load. The composite working condition tire model considers the non-linear sideslip stiffness and the friction ellipse relationship between the lateral force and the longitudinal force, and can provide a more accurate tire lateral force. The present invention can improve the input accuracy of the tire model without introducing new degrees of freedom, and further improve the simulation accuracy of the steady-state and dynamic responses of the two-degree-of-freedom vehicle model.

Description

Technical Field

[0001] The present invention relates to the field of vehicle motion characteristic simulation, and particularly relates to a four-wheel nonlinear two-degree-of-freedom vehicle model simulation system and method. Background Art

[0002] Vehicle dynamics models are often used to help automotive engineers simulate and analyze the motion responses of vehicles under different working conditions. They are applied in the development and testing of chassis domain control systems such as unmanned trajectory tracking control systems, electronic vehicle stability control systems, and steer-by-wire road feel simulation systems.

[0003] Currently, the more widely used vehicle dynamics model is the two-degree-of-freedom model (two-wheel model), that is, only the lateral and yaw motions of the vehicle are considered. According to the expression of its tire cornering stiffness, it can be divided into a linear two-degree-of-freedom model and a nonlinear two-degree-of-freedom model. Usually, the yaw angular velocity, center-of-mass side slip angle, lateral acceleration, etc. calculated by the model output are used as model accuracy evaluation indicators. In the linear two-degree-of-freedom model, the tire cornering force is expressed as the product of the tire cornering angle and the cornering stiffness. According to the cornering characteristics of the tire, when the cornering angle is small, the tire cornering stiffness is approximately a fixed constant. In the linear model, the local cornering stiffness is used as the overall cornering stiffness. This simplification makes the two-degree-of-freedom model only applicable to working conditions with small cornering angles. In simulation tests and practical applications, the accuracy of the linear two-degree-of-freedom model is poor and it cannot accurately express the motion characteristics of the vehicle. To improve the output accuracy of the two-degree-of-freedom model, Patent CN202210774277.4 provides a method for correcting the yaw angular velocity gain of a two-degree-of-freedom vehicle model, which corrects the output of the two-degree-of-freedom model by measuring the yaw angular velocity gain of a real vehicle at different vehicle speeds. This method has high requirements for the measurement accuracy of vehicle sensors and the performance of the processor, and it cannot reflect the change of the tire cornering force of a real vehicle through the model, so its application range is narrow. Patent CN202380021092.9 uses the Magic Formula tire model to represent the tire cornering force on the basis of the two-degree-of-freedom model. Although the nonlinear cornering stiffness of the tire is considered, due to the characteristics of the two-wheel two-degree-of-freedom vehicle model itself, its calculation accuracy of the tire cornering angle and vertical load is not high, and the calculation error of the tire cornering force is still large. At high speeds, this error may even cause the model to become unstable.

[0004] Considering that the yaw angular velocity, center-of-mass side slip angle, and lateral acceleration of the two-degree-of-freedom vehicle model are all calculated based on the tire cornering force. Starting from the influence of tire forces on vehicle dynamics, the combination of the tire model and vehicle dynamics is very important, and how to improve the input accuracy of the tire model has become one of the problems that need to be solved urgently. At the same time, in order to ensure that the vehicle model is not too complex, it is also particularly crucial how to improve the output accuracy of the two-degree-of-freedom vehicle model without introducing new degrees of freedom. Summary of the Invention

[0005] The present invention provides a four-wheel non-linear two-degree-of-freedom vehicle simulation method and system to ensure the simulation accuracy and stability under high-speed conditions, thereby solving the problems of poor accuracy and stability of existing linear two-degree-of-freedom two-wheel vehicle models and non-linear two-degree-of-freedom two-wheel vehicle models.

[0006] To solve the above problems, the present invention provides the following solutions:

[0007] A four-wheel non-linear two-degree-of-freedom vehicle model simulation system, which includes a two-degree-of-freedom vehicle body dynamics model, a four-wheel composite condition magic tire model, an Ackermann angle calculation model, a four-wheel sideslip angle calculation model, a four-wheel dynamic vertical load calculation model, and a Carsim software module;

[0008] In the two-degree-of-freedom vehicle body dynamics model, the steering angles θ fl 、θ fr of the left front wheel and the right front wheel are obtained through the Ackermann angle calculation model,

[0009] the tire side forces F yfl 、F yfr 、F yrl and F yrr of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel are calculated through the four-wheel composite condition magic tire model;

[0010] The four-wheel composite condition magic tire model includes an MF pure sideslip model, an MF pure longitudinal slip model, and a composite condition formula;

[0011] The composite condition formula is:

[0012]

[0013] wherein, F x represents the longitudinal force of a certain tire, F y represents the lateral force of a certain tire, σ is the normalized slip ratio, σ x is the composite condition longitudinal slip ratio, σ y is the composite condition lateral slip ratio, F y0 、F x0 respectively represent the lateral force and longitudinal force of the tire under the pure sideslip and pure longitudinal slip conditions of the tire, and are calculated through the MF pure sideslip model and the MF pure longitudinal slip model;

[0014]

[0015] wherein, α is the tire sideslip angle, and κ is the tire longitudinal slip ratio;

[0016] In the MF pure slip angle model and the MF pure longitudinal slip model, the peak factor, shape factor, stiffness factor, and curvature factor are all linearly related to the tire vertical load F z and are obtained by fitting the lateral and longitudinal slip characteristic data of the tire;

[0017] In the magic tire model under the four-wheel combined working conditions, the tire slip angle is obtained through the four-wheel angle calculation model. In this model, considering the hysteretic response of the tire slip angle, a first-order relaxation system is used to represent the non-steady-state response of the tire slip angle. The relationship between the four-wheel hysteretic slip angle and the tire slip angle in this model is:

[0018]

[0019] where α fl-delay , α fr-delay , α rl-delay , α rr-delay are the hysteretic slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and α fl , α fr , α rl , α rr are the tire slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively. l fl , l fr , l rl , l rr are the slip relaxation lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and are calculated using the empirical formula given in the Carsim software module or obtained by fitting according to experimental data;

[0020] In the vehicle coordinate system, the expressions for the tire slip angles of each tire are:

[0021]

[0022] Thus, with the longitudinal speed v x of the vehicle center of mass, the lateral speed v y of the vehicle center of mass, the yaw angular velocity ω r , the slip relaxation lengths l fl , l fr , l rl , l rr of the left front wheel, right front wheel, left rear wheel, and right rear wheel, and the steering angles θ fl , θ fr of the left front wheel and right front wheel obtained from the Ackermann steering angle calculation model as inputs, the hysteretic slip angles α fl-delay , α fr-delay , α rl-delay , α rr-delay of the left front wheel, right front wheel, left rear wheel, and right rear wheel are output as the inputs of the four-wheel dynamic vertical load calculation model.

[0023] Among them, the two-degree-of-freedom vehicle body dynamics model is as follows:

[0024]

[0025] In this model, a vehicle coordinate system established with the vehicle body's center of mass as the coordinate origin is adopted. The positive direction of the X-axis, i.e., the longitudinal direction, is the forward direction of the vehicle. The positive direction perpendicular to the ground upward is the positive direction of the Z-axis. The positive direction of the Y-axis, i.e., the lateral direction, is set according to the right-hand rule;

[0026] In this model, m is the sprung mass of the vehicle, is the lateral acceleration of the vehicle's center of mass, v x is the longitudinal speed of the vehicle's center of mass, ω r is the yaw angular velocity of the vehicle, F yfl , F yfr , F yrl , F yrr are the tire side slip forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, θ fl , θ fr are the steering angles of the left front wheel and right front wheel respectively, I z is the moment of inertia of the vehicle about the Z-axis,

[0027] is the yaw angular acceleration of the vehicle, a is the distance from the vehicle body's center of mass to the front axle, b is the distance from the vehicle body's center of mass to the rear axle, and B is the wheelbase of the vehicle's front and rear wheels;

[0028] The outputs of this model are the sideslip angle β of the vehicle's center of mass, the yaw angular velocity ω r , the lateral speed v y of the vehicle's center of mass, and the lateral acceleration a y of the vehicle's center of mass.

[0029] Preferably, the Ackermann steering angle calculation model is as follows:

[0030]

[0031] In the Ackermann steering angle calculation model, L is the wheelbase of the vehicle's front and rear axles, θ sw is the steering wheel angle, and i sw is the angular transmission ratio of the steering system.

[0032] Preferably, the MF pure side slip model is expressed as:

[0033]

[0034] Preferably, the MF pure longitudinal slip model is expressed as:

[0035]

[0036] D1 and D2 are peak factors, C1 and C2 are shape factors, B1 and B2 are stiffness factors, and E1 and E2 are curvature factors.

[0037] Preferably, the four-wheel dynamic vertical load calculation model is obtained, and the model formula is:

[0038]

[0039] In this model, F zfl , F zfr , F zrl , F zrr are the vertical loads of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, which are the output parameters of the model; the input parameters of the model are the vehicle centroid lateral acceleration a y output by the two-degree-of-freedom vehicle body dynamics model; m s is the total mass of the front and rear suspensions, m t is the total mass of the four wheels, g is the acceleration due to gravity, and h is the height of the vehicle's centroid.

[0040] Preferably, in the four-wheel steering angle calculation model, the side slip relaxation length of each tire uses the empirical formula in the Carsim software model, which is obtained by multiplying the initial value of the tire side slip length by the tire side slip relaxation length ratio. The initial value of the tire side slip length is calculated by looking up a table based on the tire hysteresis side slip angle, and the tire side slip relaxation length ratio is calculated by looking up a table based on the tire normalized vertical load; the tire normalized vertical load is obtained by dividing the actual vertical load obtained from the four-wheel dynamic vertical load calculation model by the tire nominal load.

[0041] Preferably, the parameters B1, B2, C1, C2, D1, D2, E1, and E2 in the four-wheel composite condition magic tire model all satisfy the following linear relationship with the tire vertical load F z :

[0042]

[0043] In the formula: a1, a2, a3, a4, a5, a6, a7, a8, a9, a 10 , a 11 , a 12 , a 13 , a 14 , a 15 , a 16 , a 17 are all parameters to be fitted.

[0044] The present invention also provides a simulation method based on the four-wheel nonlinear two-degree-of-freedom vehicle model simulation system. The steps of this method are as follows:

[0045] Step 1: Obtain the side slip and longitudinal slip characteristic data of the tire;

[0046] Step 2: Identify the parameters to be fitted in the magic formula tire model calculation formula of the four-wheel composite working condition magic tire model;

[0047] Step 3: Establish the four-wheel composite working condition magic tire model in Matlab / Simulink using the fitting parameters obtained in Step 2;

[0048] Step 4: Obtain the following vehicle structure parameters: sprung mass m, body yaw moment of inertia I z , distance a from the center of mass to the front axle, distance b from the center of mass to the rear axle, center of mass height h, track width B, total tire mass m t and total mass m of the front and rear suspensions s ;

[0049] Step 5: Establish a vehicle coordinate system with the center of mass of the body as the coordinate origin. The positive direction of the X-axis, i.e., longitudinally, is the forward direction of the vehicle, the positive direction of the Z-axis is vertically upward from the ground, and the positive direction of the Y-axis, i.e., laterally, is set according to the right-hand rule;

[0050] Step 6: Establish the two-degree-of-freedom body dynamics model and the Ackermann angle calculation model based on the vehicle structure parameters obtained in Step 4;

[0051] Step 7: Establish the four-wheel steering angle calculation model and the four-wheel dynamic vertical load calculation model based on the vehicle structure parameters obtained in Step 4;

[0052] Step 8: Connect the signal interfaces between the models as follows:

[0053] The Carsim software module outputs the steering wheel angle θ sw to the Ackermann angle calculation model, and the Ackermann angle calculation model outputs the steering angles θ fl 、θ fr of the left front wheel and the right front wheel to the two-degree-of-freedom body dynamics model; The Carsim software module also outputs the longitudinal speed v of the vehicle center of mass x to the two-degree-of-freedom body dynamics model and the longitudinal tire slip ratio κ to the four-wheel composite working condition magic tire model;

[0054] The inputs of the four-wheel composite working condition magic tire model are the hysteresis side slip angles α fl-delay 、α fr-delay 、α rl-delay 、α rr-delay of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel output by the four-wheel steering angle calculation model, zfl 、F zfr 、F zrl 、F zrr; The lateral tire forces F of the left front wheel, right front wheel, left rear wheel, and right rear wheel output by the four-wheel composite condition magic tire model yfl , F yfr , F yrl and F yrr are used as the inputs of the two-degree-of-freedom vehicle body dynamics model;

[0055] The two-degree-of-freedom vehicle body dynamics model outputs the sideslip angle β of the vehicle center of mass, the yaw angular velocity ω r , the lateral velocity v of the vehicle center of mass y and the lateral acceleration a of the vehicle center of mass y ; Among them, the lateral acceleration a of the vehicle center of mass y is connected in series with a Memory module and used as the input of the four-wheel dynamic vertical load model;

[0056] The four-wheel steering angle calculation model uses the longitudinal velocity v of the vehicle center of mass output by the Carsim software module x , the lateral velocity v of the vehicle center of mass output by the two-degree-of-freedom vehicle body dynamics model y and the yaw angular velocity ω r , and the side slip relaxation lengths l of the left front wheel, right front wheel, left rear wheel, and right rear wheel obtained by fitting fl , l fr , l rl , l rr , and the steering angles θ of the left front wheel and right front wheel obtained by the Ackermann steering angle calculation model fl , θ fr as the inputs;

[0057] Step 9: Set the required steering conditions in Carsim, conduct co-simulation with the Simulink model, and verify the accuracy of the model.

[0058] Preferably, in step 8, the side slip relaxation lengths of the tires in the four-wheel steering angle calculation model are obtained by multiplying the initial value of the tire side slip length by the tire side slip relaxation length ratio using the empirical formula in the Carsim software model;

[0059] The initial value of the tire side slip relaxation length is obtained by looking up the one-dimensional table of the initial value of the tire side slip relaxation length with the tire hysteresis side slip angle;

[0060] The tire side slip relaxation length ratio is obtained by looking up the one-dimensional table of the tire side slip relaxation length ratio with the normalized vertical load of the tire; the normalized vertical load of the tire is obtained by dividing the actual vertical load obtained by the four-wheel dynamic vertical load calculation model by the tire nominal load.

[0061] Preferably, the specific method for obtaining the side slip and longitudinal slip characteristic data of the tire in step 1 is selected from one of the following methods:

[0062] (1)Conduct side slip and longitudinal slip bench tests on the actual tire to obtain the side force - side slip angle characteristics and longitudinal force - longitudinal slip rate characteristics of the tire under pure side slip and pure longitudinal slip conditions;

[0063] (2)Select the required tire size in the Carsim software module to obtain the tire lateral force data under 8 characteristic vertical loads with the tire side slip angle ranging from 0° to 26° and the tire longitudinal force data under 8 characteristic vertical loads with the slip rate ranging from 0% to 100% provided by the software, which are used as the side slip and longitudinal slip characteristic data of the tire.

[0064] Preferably, the method for identifying the parameters to be fitted in the magic formula of the magic tire model under four - wheel combined working conditions in step 2 is as follows:

[0065] Step 1): When using the tire data provided by the Carsim software module in step 1, certain data processing is required: change all the characteristic load data in the first row of the original data to 0;

[0066] Step 2): Use the curve fitting toolbox in Matlab software for parameter identification; import the lateral force data corresponding to a single characteristic vertical load and the independent variable side slip angle in step 1 into the Matlab workspace in matrix form. In the curve fitting toolbox, select the side slip angle as the X data and the lateral force as the Y data, and fit the basic equation of the lateral force of the magic formula to obtain the values of the four parameters B1, C1, D1, and E1 in the equation under a single load.

[0067] Step 3): Replace the other characteristic vertical load data and repeat step 2) to obtain the values of the fitted B1, C1, D1, and E1 parameters under 8 characteristic vertical loads.

[0068] Step 4): Import the 8 characteristic vertical load values and the corresponding values of the B1, C1, D1, and E1 parameters into the Matlab workspace in matrix form. In the curve fitting toolbox, select the characteristic vertical load as the X data and one of the parameters as the Y data, and then use polynomial regression to fit the linear relationship between the parameter and the vertical load, and record the fitting equation.

[0069] Step 5): Repeat the operation in step 4) until the fitting equations of all the B1, C1, D1, and E1 parameters are obtained.

[0070] Step 6): Use the fitting equations of the B1, C1, D1, and E1 parameters obtained in step 4) and step 5) to replace the B1, C1, D1, and E1 parameters in the basic equation of the lateral force of the magic formula, and the calculation formula of the magic tire model under pure side slip conditions can be obtained.

[0071] Step 7): Replace the sideslip angle with the longitudinal slip rate data, and repeat Steps 2) to 6) to obtain the calculation formula of the Magic Formula tire model under the pure longitudinal slip condition.

[0072] Preferably, the steps of establishing the Magic tire model for the four-wheel combined condition in Matlab / Simulink by using the fitting parameters obtained in Step 2 are as follows:

[0073] Use the fitting parameters obtained in Step 2 to establish the Magic Formula tire model under the pure sideslip condition and the Magic Formula tire model under the pure longitudinal slip condition in Matlab / Simulink.

[0074] Take the lateral force F of the tire under the pure sideslip condition and the longitudinal force F of the tire under the pure longitudinal slip condition output by the Magic Formula tire model under the pure sideslip condition and the Magic Formula tire model under the pure longitudinal slip condition. y0 and the longitudinal force F of the tire under the pure longitudinal slip condition; establish the Magic tire model for the four-wheel combined condition according to the following formula: x0 ;

[0075]

[0076] In the formula: σ is the normalized slip rate, σ x is the longitudinal slip rate under the combined condition, σ y is the lateral slip rate under the combined condition, F x is the longitudinal force under the combined condition, F y is the lateral force under the combined condition.

[0077] Advantages of the present invention:

[0078] In the simulation system of the present invention, the vehicle model is a four-wheel model, which considers the hysteresis response of the sideslip angle caused by the lateral relaxation length of the tire, and can provide a more accurate tire sideslip angle than the two-wheel model. The vertical load transfer between the left and right wheels and the unsprung mass are considered, thereby improving the estimation accuracy of the tire vertical load. The combined-condition tire model considers the non-linear sideslip stiffness and the friction ellipse relationship between the lateral force and the longitudinal force, and can provide a more accurate tire lateral force. Using the present invention can improve the input accuracy of the tire model without introducing new degrees of freedom, and further improve the simulation accuracy of the steady-state and dynamic responses of the two-degree-of-freedom vehicle model. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order to more conveniently illustrate the technical solutions and implementation steps adopted in the present invention, the drawings used in the present invention are briefly introduced below.

[0080] Figure 1 It is a schematic diagram of a four-wheel two-degree-of-freedom vehicle dynamics model.

[0081] Figure 2It is a schematic diagram of the tire coordinate system.

[0082] Figure 3 It is a schematic diagram of the change in the front axle load during vehicle steering.

[0083] Figure 4 It is the simulation flow chart of the four-wheel non-linear two-degree-of-freedom vehicle model provided by the present invention.

[0084] Figure 5 It is the connection method and signal flow diagram between modules. Specific implementation manner

[0085] The specific implementation manner of the present invention will be explained below in conjunction with the accompanying drawings of the specification.

[0086] The vehicle dynamics model of the whole vehicle with four wheels and two degrees of freedom adopted in the present invention is as Figure 1 shown. This model considers the lateral and yaw motions of the vehicle body. In Figure 1 , a vehicle coordinate system is established with the center of mass of the vehicle body as the coordinate origin. Let the forward direction of the vehicle be the positive direction of the X-axis, and the direction perpendicular to the ground be the positive direction of the Z-axis. This vehicle coordinate system conforms to the right-hand rule, that is, when the thumb points to the positive direction of the Z-axis, the four fingers point from the positive direction of the X-axis to the positive direction of the Y-axis. According to Figure 1 the force relationship in, the lateral motion balance equation of the vehicle body is established as follows:

[0087] (1)

[0088] In the formula: F y is the lateral resultant force acting on the vehicle, m is the sprung mass of the vehicle, F yfl , F yfr , F yrl , F yrr are the ground lateral reaction forces (tire side force) acting on the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, θ fl , θ fr are the steering angles of the left front wheel and right front wheel respectively.

[0089] The yaw motion balance equation of the vehicle body is established as follows:

[0090] (2)

[0091] In the formula: M z is the resultant moment of the vehicle about the Z-axis, a is the distance from the center of mass of the vehicle body to the front axle, b is the distance from the center of mass of the vehicle body to the rear axle, and B is the wheelbase of the vehicle.

[0092] According to Newton's second law, the lateral resultant force ∑F y acting on the vehicle is equal to the product of the vehicle mass and the lateral acceleration. Similarly, the resultant moment ∑M zIt is equal to the product of the moment of inertia of the vehicle about the Z-axis and the angular acceleration, ∑F y , ∑M z can be expressed as:

[0093] (3)

[0094] In the formula: a y is the lateral acceleration of the vehicle body center of mass, I z is the moment of inertia of the vehicle about the Z-axis, is the yaw angular acceleration of the vehicle.

[0095] In the above formula, the lateral acceleration a y can be expressed as:

[0096] (4)

[0097] In the formula: v x is the longitudinal speed of the vehicle center of mass, ω r is the yaw angular velocity of the vehicle, is the lateral acceleration of the vehicle center of mass.

[0098] From equations (1) to (4), the two-degree-of-freedom body dynamics model of the whole vehicle with four wheels is established as follows:

[0099] (5)

[0100] The vehicle parameters that need to be obtained include: the sprung mass m of the vehicle, the distance a from the vehicle body center of mass to the front axle, the distance b from the vehicle body center of mass to the rear axle, and the vehicle front and rear track widths B.

[0101] The inputs of the whole vehicle model are the left front wheel and right front wheel steering angles θ fl , θ fr and the longitudinal speed v of the center of mass x . Different from the traditional two-wheel two-degree-of-freedom vehicle model, the left and right front wheel steering angles of the model are no longer assumed to be the same angle. Calculated by the Ackermann formula, the calculation formula for the turning radius R of the vehicle is:

[0102] (6)

[0103] In the formula: L is the wheelbase of the vehicle's front and rear axles, θ sw is the steering wheel angle, i sw is the angular transmission ratio of the steering system.

[0104] The left and right front wheel steering angle formulas are established as:

[0105] (7)

[0106] So far, only the steering wheel input angle needs to be measured, and the left and right front wheel angles can be calculated according to the angular transmission ratio of the steering system and the Ackermann formula, thus completing the derivation of the calculation formula of the Ackermann angle calculation model.

[0107] The lateral force of the tire is equal in magnitude and opposite in direction to the side force. In Equation (5), the vehicle lateral acceleration and yaw rate are mainly affected by the lateral forces (side forces) of the four wheels. When the tire side slip angle is small, the side force is approximately linearly related to the side slip angle. When the tire side slip angle is large, the tire tread and the ground will reach the adhesion limit and lateral slip will occur. At this time, the side force is non-linearly related to the side slip angle and gradually decreases. The conventional linear two-degree-of-freedom vehicle model simplifies the side force as the product of a fixed side slip stiffness and the side slip angle, resulting in a reduction in the accuracy of the tire side force in the case of large side slip angles. The present invention uses the magic formula tire model under composite conditions to describe the side slip characteristics of the tire, considering the influence of the vertical load change of the tire and the friction ellipse on the tire side force while accurately expressing the non-linear side slip stiffness of the tire.

[0108] The magic formula tire model is given as follows:

[0109] (8)

[0110] (9)

[0111] In the formula: F y0 、F x0 respectively represent the lateral force and longitudinal force of the tire under pure side slip and pure longitudinal slip conditions, α is the tire side slip angle, κ is the tire longitudinal slip ratio, D1, D2 are peak factors, C1, C2 are shape factors, B1, B2 are stiffness factors, E1, E2 are curvature factors, and B1, B2, C1, C2, D1, D2, E1, E2 are all linearly related to the tire vertical load F z and can be obtained through parameter identification based on tire longitudinal slip and side slip experimental data.

[0112] The relationship formula obtained through parameter identification in the present invention is as follows:

[0113]

[0114] In the formula: a1, a2, a3, a4, a5, a6, a7, a8, a9, a 10 、a 11 、a 12 、a 13 、a 14 、a 15 、a 16 、a 17 are all parameters to be fitted.

[0115] Under the longitudinal slip and side slip composite condition, the tire longitudinal force Fx 、Lateral force F y is expressed as follows:

[0116] (10)

[0117] In the formula: σ is the normalized slip ratio, σ x is the longitudinal slip ratio under the combined working conditions, σ y is the lateral slip ratio under the combined working conditions.

[0118] The mutual relationship and specific expressions among the slip ratios in Equation (10) are:

[0119] (11)

[0120] So far, a four-wheel combined working condition magic tire model with tire sideslip angle and longitudinal slip ratio as inputs and lateral force and longitudinal force under the combined working conditions as outputs has been established. Since the sideslip force is used in the vehicle model and the sideslip angle and the sideslip force have opposite signs, the lateral force output by the tire model needs to be multiplied by a negative sign to make it the sideslip force.

[0121] The tire coordinate system established in the present invention is as Figure 2 shown, with the sideslip force direction shown in Figure 2 as the positive direction and the sideslip angle direction shown as the negative direction. The tire sideslip angle can be expressed as the angle between the tire rolling direction and the tire movement direction, that is, the difference between the tire steering angle and the tire course angle. Among them, the tire course angle can be expressed by the arctangent of the quotient of the tire lateral speed divided by the tire longitudinal speed. Since the tire steering angle and the sideslip angle have opposite signs, after multiplying their difference by a negative sign, the tire sideslip angle is expressed as:

[0122] (12)

[0123] In the formula: v xfl 、v xfr 、v xrl 、v xrr are the longitudinal speeds of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system respectively, v yfl 、v yfr 、v yrl 、v yrr are the lateral speeds of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system respectively, α fl 、α fr 、α rl 、α rr are the sideslip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system respectively.

[0124] In the vehicle coordinate system, the speeds of each tire can use the longitudinal speed v of the vehicle center of mass x, the lateral velocity v of the vehicle's center of mass y , the yaw rate ω r is expressed to obtain the expression of the tire sideslip angle at this time:

[0125] (13)

[0126] In the two-wheel two-degree-of-freedom model, only the sideslip angle of the center of mass can be used to represent the heading angles of the front and rear axles. The sideslip angle of the center of mass is expressed as the arctangent of the lateral velocity of the vehicle body divided by the longitudinal velocity of the vehicle body, that is, arctan(v y / v x ). In contrast, due to the inherent characteristics of the four-wheel model, the equivalent amount of the vehicle body yaw rate on the four wheels can be combined in the expression of the heading angle. And because the Ackermann steering formula is used to represent the steering angles of the left and right front wheels, its steady-state expression of the tire sideslip angle is more accurate. In terms of the dynamic response of the tire sideslip, considering the hysteretic response of the tire sideslip angle, the present invention uses a first-order relaxation system to represent the non-steady-state response of the tire sideslip angle, and represents the relationship between the four-wheel hysteretic sideslip angle and the sideslip angle in formula (13) as follows.

[0127] (14)

[0128] Where: α fl-delay , α fr-delay , α rl-delay , α rr-delay are the hysteretic sideslip angles of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel respectively, and l fl , l fr , l rl , l rr are the sideslip relaxation lengths of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel respectively.

[0129] So far, a four-wheel angle calculation model has been established, and the four-wheel hysteretic sideslip angle in this model is used to replace the sideslip angle as the input of the four-wheel composite working condition magic tire model.

[0130] In the two-wheel two-degree-of-freedom vehicle model, the vertical loads of the front and rear axles are fixed values, which are calculated according to the position of the center of mass as follows:

[0131] (15)

[0132] Where: F zf is the front axle vertical load, F zr is the rear axle vertical load, and g is the acceleration due to gravity. Dividing the front and rear axle vertical loads by 2 can obtain the single-wheel vertical load.

[0133] When the vehicle is performing a high-speed turning motion on a horizontal road surface, the vertical loads on each wheel are not fixed values. Due to the centrifugal effect, there is a vertical load transfer between the left and right wheels. The schematic diagram of the load change on the front axle during the vehicle turning process is as shown in Figure 3 shown. In Figure 3 , taking the position of the vehicle body's center of mass as the coordinate origin and the positive direction of the X-axis (out of the paper) as the vehicle's forward direction, a vehicle coordinate system is established. Assuming that the vehicle is in a left-turning working condition and the direction of the lateral acceleration is the same as the positive direction of the Y-axis, then the direction of the centrifugal force acting on the vehicle body is the same as the negative direction of the Y-axis. Taking moments about the right front wheel, the following equilibrium equation can be obtained:

[0134] (16)

[0135] In the formula: F zfl is the vertical load of the left front wheel, B is the vehicle's wheelbase (assuming the front and rear axle wheelbases are the same), m f is the mass of the front axle, F cL is the centrifugal force acting on the vehicle body, and h is the height of the vehicle body's center of mass.

[0136] The expressions for the mass of the vehicle's front axle and the centrifugal force are as follows:

[0137] (17)

[0138] After substituting Equation (17) into Equation (16), the expression for the vertical load of the left front wheel can be obtained as:

[0139] (18)

[0140] In Equation (18), only the vertical load of the wheel caused by the sprung mass is considered. The actual vertical load of the wheel is also affected by the unsprung mass. After considering the wheel mass and the suspension mass in Equation (18) (assuming the front suspension and the rear suspension masses are the same), the final calculation formula for the vertical load of the left front wheel can be obtained:

[0141] (19)

[0142] In the formula: m s is the total mass of the suspension, and m t is the total mass of the four wheels.

[0143] Similarly, the dynamic vertical loads of the four wheels can be expressed as follows:

[0144] (20)

[0145] In Equation (20), the accuracy of the vertical load depends on the estimation accuracy of the lateral acceleration and the measured value of the unsprung mass.

[0146] At this point, the formula derivation of all modules of the four-wheel nonlinear two-degree-of-freedom vehicle model has been completed.

[0147] The simulation process is described in detail below. Figure 4 The simulation flow chart of the four-wheel nonlinear two-degree-of-freedom vehicle model provided by the present invention includes the following specific steps:

[0148] Step 1: Obtain the tire's cornering and longitudinal slip characteristics data; there are two methods to choose from in this step.

[0149] (1) The cornering force-slip angle characteristics and longitudinal force-longitudinal slip rate characteristics of the tire under pure cornering and pure longitudinal slip conditions are obtained by performing side slip and longitudinal slip bench tests on the actual tire.

[0150] (2) Use the tire data provided by the vehicle dynamics system simulation software Carsim. After entering the Carsim main interface, select the tire parameter module in the vehicle parameter setting module. You can select the appropriate tire size according to the simulation requirements. In the Carsim software, each tire specification has corresponding lateral force and longitudinal force data. The tire module in the software comes with tire lateral force data under 8 characteristic vertical loads with tire slip angles of 0° to 26° and tire longitudinal force data under 8 characteristic vertical loads with slip rates of 0% to 100%.

[0151] Step 2: Identify the parameters to be fitted in the magic formula tire model calculation formula in the four-wheel composite working condition magic tire model;

[0152] Step 201: When the Carsim software used in step 1 has tire data, certain data processing is required. The first row of data in the original data group is the characteristic load, and the first row of data needs to be changed to 0.

[0153] Step 202: After obtaining the tire data, it is necessary to perform parameter identification on the tire empirical or semi-empirical model used, and the identification process follows: first local, then overall. Since the Magic Formula tire model invented by Professor Pacejka has a high characterization accuracy for tire characteristics, the Magic Formula tire model is used in the present invention, and the basic formula for characterizing the tire lateral force is provided as follows:

[0154]

[0155] Where: F y0 is the tire lateral force under pure slip condition, B1, C1, D1, E1 are the parameters to be identified, and α is the tire slip angle.

[0156] The basic formula for characterizing the longitudinal force is as follows:

[0157]

[0158] In the formula: F x0 is the longitudinal force of the tire under pure longitudinal slip condition, B2, C2, D2, E2 are the parameters to be identified, and κ is the longitudinal slip ratio of the tire.

[0159] Step 203: The present invention uses the Curve Fitting Toolbox in Matlab software for parameter identification. Taking the identification of cornering characteristics parameters as an example, first, the lateral force data corresponding to the single characteristic vertical load and the independent variable (cornering angle) in Step 201 need to be imported into the Matlab workspace in matrix form. In the Curve Fitting Toolbox, select the cornering angle as the X data and the lateral force as the Y data. Then select the fitting type as a custom equation, input the basic equation of the lateral force of the magic formula, and the numerical values of the four parameters B1, C1, D1, and E1 in the equation under a single load can be automatically fitted.

[0160] Step 204: Repeat Step 203 using the remaining lateral force data of the single characteristic vertical load tires, and record the numerical values of the B1, C1, D1, and E1 parameters fitted under 8 kinds of characteristic vertical loads.

[0161] Step 205: Import the numerical values of 8 kinds of characteristic vertical loads and the corresponding numerical values of the B1, C1, D1, and E1 parameters into the Matlab workspace in matrix form. Taking the parameter B1 as an example, in the Curve Fitting Toolbox, select the characteristic vertical load as the X data and B1 as the Y data, and then use polynomial regression. Select an appropriate polynomial degree according to the fitting evaluation index in the Curve Fitting Toolbox, and a linear relationship between the parameter B1 and the vertical load can be obtained, and record the fitting equation. Note: The original unit of the characteristic vertical load numerical value is N. To ensure the fitting accuracy and unify the unit with the input of the magic formula tire model, it needs to be converted to kN before import.

[0162] The linear relationships between the parameters C1, D1, and E1 and the vertical load can be obtained by repeating Step 205, and record the corresponding fitting equations.

[0163] Step 207: Replace the B1, C1, D1, and E1 parameters in the basic formula of the tire lateral force in Step 003 with the obtained fitting equations of the B1, C1, D1, and E1 parameters, and the magic formula tire model under pure cornering condition can be obtained.

[0164] Step 208: The parameter identification of the tire longitudinal slip characteristics can refer to Steps 203 to 207. Replace the tire cornering angle in the steps with the longitudinal slip ratio, and use the corresponding data for identification. The process is similar.

[0165] Step 3: Use the fitting parameters obtained in Step 2 to establish a magic tire model for four-wheel combined working conditions in Matlab / Simulink;

[0166] Use the fitting parameters obtained in Step 2 to establish a magic formula tire model under pure cornering conditions and a magic formula tire model under pure longitudinal slip conditions using Matlab / Simulink.

[0167] Take the lateral force F of the tire under pure cornering conditions and the longitudinal force F of the tire under pure longitudinal slip conditions output by the magic formula tire model under pure cornering conditions and the magic formula tire model under pure longitudinal slip conditions. y0 and the longitudinal force F of the tire under pure longitudinal slip conditions; Establish a magic tire model for four-wheel combined working conditions according to the following formula: x0 ;

[0168]

[0169] In the formula: σ is the normalized slip ratio, σ x is the longitudinal slip ratio under combined working conditions, σ y is the lateral slip ratio under combined working conditions, F x is the longitudinal force under combined working conditions, F y is the lateral force under combined working conditions.

[0170] Since the angles in Matlab are calculated in radians, it is necessary to convert the tire cornering angle from degrees to radians.

[0171] The established combined working condition tire model is used to calculate the lateral forces when there are cornering and longitudinal slip simultaneously for the left front wheel, right front wheel, left rear wheel, and right rear wheel. When the longitudinal slip ratio is 0, this model can also be used as a pure cornering condition model. Multiply the obtained lateral force by a negative sign to obtain the tire cornering force to meet the requirements of the vehicle dynamics equilibrium equation.

[0172] Step 4: Obtain the following vehicle structure parameters: sprung mass m, body yaw moment of inertia I z , distance a from the center of mass to the front axle, distance b from the center of mass to the rear axle, height h of the center of mass, track width B, total tire mass m t and total mass m of the front and rear suspensions s ;

[0173] Step 5: Establish a vehicle coordinate system with the center of mass of the vehicle body as the coordinate origin. The positive direction of the X-axis, i.e., longitudinally, is the forward direction of the vehicle, the positive direction of the Z-axis is vertically upward from the ground, and the positive direction of the Y-axis, i.e., laterally, is set according to the right-hand rule, as Figure 1 shown.

[0174] Step 6: Establish the two-degree-of-freedom vehicle body dynamics model based on the vehicle structure parameters obtained in Step 4: The establishment of the vehicle coordinate system and the derivation of the dynamics model have been described in the above equations (1) to (5). The four-wheel nonlinear two-degree-of-freedom vehicle dynamics equilibrium equation is established as follows:

[0175]

[0176] where: m is the sprung mass, I z is the yaw moment of inertia of the vehicle body, a is the distance from the center of mass to the front axle, b is the distance from the center of mass to the rear axle, B is the track width, F yfl , F yfr , F yrl , F yrr are the tire side forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, θ fl , θ fr are the left front wheel and right front wheel angles respectively, v x is the longitudinal velocity of the center of mass, v y is the lateral velocity of the center of mass, ω r is the yaw angular velocity.

[0177] In Simulink, establish a four-wheel two-degree-of-freedom vehicle body model according to the above equilibrium equation. During the modeling process, in order to avoid the singularity phenomenon, all integrators in the model use discretized integrators and the initial values are set to the eps function.

[0178] Establish the Ackermann angle calculation model as follows: The relationship between the left front wheel angle, right front wheel angle and the steering wheel angle satisfies the following equation:

[0179]

[0180] where: L is the wheelbase of the vehicle, θ sw is the steering wheel angle, i sw is the angular transmission ratio of the steering system.

[0181] If the steering wheel angle output by Carsim is used for the front wheel angle calculation, since the steering wheel angle in Carsim is in degree unit, the left front wheel angle and the right front wheel angle also need to be converted to radian system according to Step 011.

[0182] Step 7: Establish a four-wheel deflection angle calculation model and a four-wheel dynamic vertical load calculation model based on the vehicle structure parameters obtained in Step 4;

[0183] The derivation of the four-wheel deflection angle calculation model can be seen in Figure 2 and equations (12) to (14). Now, the tire hysteresis side deflection angle calculation equation is given as follows:

[0184]

[0185] where: α fl , α fr , α rl , α rr are the sideslip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system respectively, and α fl-delay , α fr-delay , α rl-delay , α rr-delay are the hysteresis sideslip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and l fl , l fr , l rl , l rr are the sideslip relaxation lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively.

[0186] The sideslip relaxation length of the tire can be calculated using the empirical formula given in the Carsim software or fitted according to experimental data. In this invention, the sideslip relaxation length of the tire in the Carsim software is obtained by multiplying the initial value of the sideslip length of the tire by the sideslip relaxation length ratio of the tire. The initial value of the sideslip length of the tire is calculated by looking up a table based on the hysteresis sideslip angle of the tire, and the sideslip relaxation length ratio of the tire is calculated by looking up a table based on the normalized vertical load of the tire. The normalized vertical load of the tire is the actual vertical load divided by the nominal load of the tire.

[0187] The formula derivation of the four-wheel dynamic vertical load calculation model can be combined with Equations (15) to (20) and Figure 3 , and the vehicle four-wheel dynamic vertical load equation is given as follows:

[0188]

[0189] where: m s is the total mass of the front and rear suspensions, m t is the total mass of the four wheels, g is the acceleration due to gravity, and h is the height of the vehicle's center of mass.

[0190] The input of the model is the lateral acceleration of the vehicle body, and the output of the model is the four-wheel vertical load. The unit of the calculated value of the model is N, and it is necessary to unify the unit with the vertical load required by the Magic Formula tire model. Therefore, the calculated value of the vertical load obtained is divided by 1000.

[0191] Step 8: Connect the signal interfaces between the models, and the connection method and signal flow diagram between the models are as Figure 4 shown. Figure 4 clearly shows the input-output relationship between the models, specifically as follows:

[0192] The Carsim software module outputs the steering wheel angle θ swTo the Ackermann steering angle calculation model, the Ackermann steering angle calculation model outputs the steering angles θ of the left front wheel and the right front wheel fl 、θ fr To the two-degree-of-freedom vehicle body dynamics model; The Carsim software module also outputs the longitudinal velocity v of the vehicle mass center to the two-degree-of-freedom vehicle body dynamics model x and the longitudinal slip ratio κ of the tire to the four-wheel composite working condition magic tire model;

[0193] The inputs of the four-wheel composite working condition magic tire model are the hysteresis cornering angles α of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel output by the four-wheel steering angle calculation model fl-delay 、α fr-delay 、α rl-delay 、α rr-delay and the vertical loads F of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel output by the four-wheel dynamic vertical load calculation model zfl 、F zfr 、F zrl 、F zrr ; The tire cornering forces F of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel output by the four-wheel composite working condition magic tire model yfl 、F yfr 、F yrl and F yrr are used as the inputs of the two-degree-of-freedom vehicle body dynamics model;

[0194] The two-degree-of-freedom vehicle body dynamics model outputs the sideslip angle β of the vehicle mass center, the yaw rate ω r 、the lateral velocity v of the vehicle mass center y and the lateral acceleration a of the vehicle mass center y ; Among them, the lateral acceleration a of the vehicle mass center y is connected in series with a Memory module and used as the input of the four-wheel dynamic vertical load model;

[0195] The four-wheel steering angle calculation model uses the longitudinal velocity v of the vehicle mass center output by the Carsim software module x 、the lateral velocity v of the vehicle mass center output by the two-degree-of-freedom vehicle body dynamics model y and the yaw rate ω r , the cornering relaxation lengths l of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel obtained by fitting fl 、l fr 、l rl 、l rr and the steering angles θ of the left front wheel and the right front wheel obtained by the Ackermann steering angle calculation model fl 、θ fr as inputs; After correctly connecting each module, the system is closed-loop.

[0196] Step 9: Set the required steering conditions in Carsim, conduct co-simulation with the Simulink model, and verify the accuracy of the model. Thus, the entire process of system simulation is completed.

Claims

1. A four-wheel nonlinear two-degree-of-freedom vehicle model simulation system, characterized in that: The system includes a two-degree-of-freedom vehicle body dynamics model, a four-wheel compound working condition magic tire model, an Ackerman angle calculation model, a four-wheel side slip angle calculation model, a four-wheel dynamic vertical load calculation model and a Carsim software module; The left and right front wheel turning angles θ in the two-degree-of-freedom vehicle body dynamics model fl ,θ fr The Ackerman angle calculation model is used to obtain: The tire cornering force F of the left front wheel, right front wheel, left rear wheel and right rear wheel yfl 、F yfr 、F yrl and F yrr Obtained through calculation of the magic tire model for four-wheel composite conditions; The four-wheel compound working condition magic tire model includes an MF pure sideslip model, an MF pure longitudinal slip model and a compound working condition formula; The composite working condition formula is: Among them, F x Indicates the longitudinal force of a tire, F y represents the lateral force of a tire, σ is the normalized slip rate, σ x is the longitudinal slip rate under composite working conditions, σ y is the lateral slip rate under combined working conditions, F y0 、F x0 They respectively represent the lateral force and longitudinal force of the tire under pure cornering and pure longitudinal sliding conditions, which are calculated by the MF pure cornering model and the MF pure longitudinal sliding model; Among them, α is the tire side slip angle, κ is the tire longitudinal slip rate; The peak factor, shape factor, stiffness factor and curvature factor in the MF pure cornering model and the MF pure longitudinal slip model are all related to the tire vertical load F z There is a linear relationship, which is obtained by fitting the tire's side slip and longitudinal slip characteristic data; In the magic tire model of four-wheel compound working conditions, the tire slip angle is obtained through the four-wheel slip angle calculation model. The model takes into account the hysteresis response of the tire slip angle and uses a first-order relaxation system to represent the non-steady-state response of the tire slip angle. The relationship between the four-wheel hysteresis slip angle and the tire slip angle in the model is: where α fl-delay , α fr-delay , α rl-delay , α rr-delay are the hysteresis slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, α fl , α fr , α rl , α rr are the tire slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. fl , l fr , l rl , l rr are the slack lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, which are calculated using the empirical formula given in the Carsim software module or obtained by fitting based on experimental data; In the vehicle coordinate system, the tire side slip angle expression of each tire is: Therefore, the longitudinal velocity v of the vehicle center of mass x , lateral velocity v of vehicle center of mass y , yaw angular velocity ω r , the lateral relaxation length l of the left front wheel, right front wheel, left rear wheel and right rear wheel fl , l fr , l rl , l rr , and the left and right front wheel turning angles θ obtained by the Ackerman turning angle calculation model fl ,θ fr As input, the output is the hysteresis slip angle α of the left front wheel, right front wheel, left rear wheel, and right rear wheel fl-delay , α fr-delay , α rl-delay , α rr-delay As the input of the four-wheel dynamic vertical load calculation model; a is the distance from the center of mass of the vehicle body to the front axle, b is the distance from the center of mass of the vehicle body to the rear axle, and B is the front and rear wheelbase of the vehicle.

2. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 1, characterized in that: The two-degree-of-freedom vehicle body dynamics model is: The model uses a vehicle coordinate system with the center of mass of the vehicle body as the origin. The positive direction of the X-axis, i.e. the longitudinal direction, is the vehicle's forward direction. The direction perpendicular to the ground and upward is the positive direction of the Z-axis. The positive direction of the Y-axis, i.e. the lateral direction, is set according to the right-hand rule. In this model, m is the sprung mass of the vehicle. is the lateral acceleration of the vehicle center of mass, v x is the longitudinal velocity of the vehicle center of mass, ω r is the vehicle yaw rate, F yfl 、F yfr 、F yrl 、F yrr are the tire cornering forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, θ fl ,θ fr are the left front wheel and right front wheel turning angles, I z is the vehicle's moment of inertia around the Z axis, is the vehicle's yaw angular acceleration, a is the distance from the center of mass of the vehicle to the front axle, b is the distance from the center of mass of the vehicle to the rear axle, and B is the front and rear wheelbase of the vehicle; The output of the model is the vehicle's center of mass sideslip angle β, yaw rate ω r , lateral velocity v of vehicle center of mass y and the lateral acceleration of the vehicle's center of mass a y .

3. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 2, characterized in that: The Ackerman angle calculation model is: In the Ackerman turning angle calculation model, L is the wheelbase of the front and rear axles of the vehicle, θ sw is the steering wheel angle, i sw is the angular transmission ratio of the steering system.

4. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 3, characterized in that: The MF pure sideslip model is expressed as: F y0 =D1sin{C1arctan[B1α-E1(B1α-arctanB1α) The MF pure longitudinal sliding model is expressed as: F x0 =D2sin{C2arctan[B2κ-E2(B2κ-arctanB2κ) D1 and D2 are peak factors, C1 and C2 are shape factors, B1 and B2 are stiffness factors, and E1 and E2 are curvature factors.

5. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 4, characterized in that: The model formula of the four-wheel dynamic vertical load calculation model is: In this model, F zfl 、F zfr 、F zrl 、F zrr are the vertical loads of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, and are the output parameters of the model; the input parameter of the model is the lateral acceleration a of the vehicle center of mass output by the two-degree-of-freedom vehicle body dynamics model y ;m s is the total mass of the front and rear suspension, m t is the total mass of the four wheels, g is the acceleration due to gravity, and h is the height of the center of mass of the vehicle.

6. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 5, characterized in that: The relaxed cornering length of each tire in the four-wheel slip angle calculation model uses the empirical formula in the Carsim software model, which is obtained by multiplying the initial value of the tire cornering length and the tire cornering relaxation length ratio. The initial value of the tire cornering relaxation length is calculated by looking up the table of the tire hysteresis slip angle, and the tire cornering relaxation length ratio is calculated by looking up the table of the tire normalized vertical load; the normalized vertical load of the tire is obtained by dividing the actual vertical load obtained by the four-wheel dynamic vertical load calculation model by the nominal load of the tire.

7. The four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 6, characterized in that: The parameters B1, B2, C1, C2, D1, D2, E1, and E2 in the four-wheel composite working condition magic tire model are all related to the tire vertical load F z The following linear relationship is satisfied: <h2 style=";text-align:left;direction:ltr">B1=a1F<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> +a2 <h2 style=";text-align:left;direction:ltr">C<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> =a3F<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> +a4 <h2 style=";text-align:left;direction:ltr">E1 = a8F<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> +a9 C2=a 13 <h2 style=";text-align:left;direction:ltr">E2=a<h2 style=";text-align:left;direction:ltr"> 17 In the formula: a1, a2, a3, a4, a5, a6, a7, a8, a9, a 10 、a 11 、a 12 、a 13 、a 14 、a 15 、a 16 、a 17 These are parameters to be fitted.

8. A simulation method based on the four-wheel nonlinear two-degree-of-freedom vehicle model simulation system as claimed in claim 7, characterized in that: The steps of this method are as follows: Step 1: Obtain tire side slip and longitudinal slip characteristic data; Step 2: Identify the parameters to be fitted in the magic formula tire model calculation formula in the four-wheel composite working condition magic tire model; Step 3: Use the fitting parameters obtained in step 2 to establish a four-wheel composite working condition magic tire model in Matlab / Simulink; Step 4: Obtain the following vehicle structural parameters: sprung mass m, vehicle body yaw moment of inertia I z , distance from center of mass to front axle a, distance from center of mass to rear axle b, center of mass height h, wheelbase B, total tire mass m t and the total mass of the front and rear suspension m s ; Step 5: The vehicle coordinate system is established with the center of mass of the vehicle body as the coordinate origin. The positive direction of the X axis, i.e. the longitudinal direction, is the forward direction of the vehicle. The direction perpendicular to the ground and upward is the positive direction of the Z axis. The positive direction of the Y axis, i.e. the lateral direction, is set according to the right-hand rule. Step 6: establishing the two-degree-of-freedom vehicle body dynamics model and the Ackerman angle calculation model based on the vehicle structure parameters obtained in step 4; Step 7: Establish a four-wheel deflection angle calculation model and a four-wheel dynamic vertical load calculation model based on the vehicle structural parameters obtained in step 4; Step 8: Connect the signal interfaces between the models as follows: Carsim software module outputs steering wheel angle θ sw To the Ackerman turning angle calculation model, the Ackerman turning angle calculation model outputs the left front wheel and right front wheel turning angle θ fl ,θ fr to the two-degree-of-freedom body dynamics model; the Carsim software module also outputs the vehicle center of mass longitudinal velocity v to the two-degree-of-freedom body dynamics model x , output tire longitudinal slip rate κ to the magic tire model of four-wheel composite working conditions; The input of the four-wheel compound working condition magic tire model is the hysteresis side slip angle α of the left front wheel, right front wheel, left rear wheel and right rear wheel output by the four-wheel slip angle calculation model. fl-delay , α fr-delay , α rl-delay , α rr-delay , and the vertical loads F of the left front wheel, right front wheel, left rear wheel, and right rear wheel output by the four-wheel dynamic vertical load calculation model zfl 、F zfr 、F zrl 、F zrr ; The tire cornering force F of the left front wheel, right front wheel, left rear wheel and right rear wheel output by the magic tire model of the four-wheel compound working condition yfl 、F yfr 、F yrl and F yrr As input to the two-degree-of-freedom vehicle body dynamics model; The two-degree-of-freedom vehicle body dynamics model outputs the vehicle's center of mass sideslip angle β and yaw rate ω r , lateral velocity v of vehicle center of mass y and the lateral acceleration of the vehicle's center of mass a y ; The lateral acceleration of the vehicle's center of mass is a y A Memory module is connected in series as the input of the four-wheel dynamic vertical load model; The four-wheel deflection angle calculation model uses the vehicle center of mass longitudinal velocity v output by the Carsim software module x , the lateral velocity v of the vehicle center of mass output by the two-degree-of-freedom body dynamics model y and yaw rate ω r , the lateral relaxation length l of the left front wheel, right front wheel, left rear wheel and right rear wheel obtained by fitting fl , l fr , l rl , l rr , and the left and right front wheel turning angles θ obtained by the Ackerman turning angle calculation model fl ,θ fr is the input; Step 9: Set the required steering conditions in Carsim, perform co-simulation with the Simulink model, and verify the accuracy of the model.

9. The simulation method of the four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 8, characterized in that: In step 8, the slack length of each tire in the four-wheel slip angle calculation model is obtained by multiplying the initial value of the tire slack length by the ratio of the tire slack length using the empirical formula in the Carsim software model; The initial value of the tire cornering relaxation length is obtained by looking up the one-dimensional table of initial values ​​of the tire cornering relaxation length by inputting the tire hysteresis slip angle; The tire cornering relaxation length ratio is obtained by inputting the tire normalized vertical load into a tire cornering relaxation length ratio one-dimensional table for lookup; the tire normalized vertical load is obtained by dividing the actual vertical load obtained by the four-wheel dynamic vertical load calculation model by the tire nominal load.

10. The simulation method of the four-wheel nonlinear two-degree-of-freedom vehicle model simulation system according to claim 8, characterized in that: The specific method for obtaining the tire's side slip and longitudinal slip characteristic data in step 1 is selected from one of the following methods: (1) Performing cornering and longitudinal slip bench tests on actual tires to obtain the cornering force-slip angle characteristics and longitudinal force-longitudinal slip rate characteristics of the tires under pure cornering and pure longitudinal slip conditions; (2) Select the required tire size in the Carsim software module, and obtain the tire lateral force data under 8 characteristic vertical loads with a side slip angle of 0° to 26° and the tire longitudinal force data under 8 characteristic vertical loads with a slip rate of 0% to 100%, as the tire side slip and longitudinal slip characteristic data; The method for identifying the parameters to be fitted in the magic formula tire model calculation formula in the four-wheel composite working condition magic tire model in step 2 is: Step 1): When using the tire data provided by the Carsim software module in step 1, some data processing is required: Change all the characteristic load data in the first row of the original data to 0; Step 2): Use the curve fitting toolbox in Matlab software to identify parameters; import the lateral force data corresponding to the single characteristic vertical load in step 1) and the independent variable sideslip angle into the Matlab workspace in matrix form, select the sideslip angle as X data and the lateral force as Y data in the curve fitting toolbox, fit the lateral force basic equation of the magic formula, and obtain the values ​​of the four parameters B1, C1, D1, and E1 in the equation under a single load; Step 3) Replace other characteristic vertical load data and repeat step 2) to obtain the values ​​of B1, C1, D1, and E1 parameters fitted under 8 characteristic vertical loads; Step 4) Import the eight characteristic vertical load values ​​and the corresponding B1, C1, D1, and E1 parameter values ​​into the Matlab workspace in matrix form. Select the characteristic vertical load as X data and one of the parameters as Y data in the curve fitting toolbox, and then use polynomial regression to fit the linear relationship between the parameter and the vertical load, and record the fitting equation; Step 5): Repeat step 4) until the fitting equations of all parameters of B1, C1, D1, and E1 are obtained; Step 6): Use the B1, C1, D1, E1 parameter fitting equations obtained in step 4) and step 5) to replace the B1, C1, D1, E1 parameters of the magic formula lateral force basic equation, and obtain the magic formula tire model calculation formula under pure side slip conditions; Step 7): Replace the sideslip angle with the longitudinal slip rate data, and repeat steps 2) to 6) to obtain the magic formula tire model calculation formula under pure longitudinal slip conditions; In step 3, the steps for establishing the four-wheel compound working condition magic tire model in Matlab / Simulink using the fitting parameters obtained in step 2 are as follows: Using the fitting parameters obtained in step 2, the magic formula tire model under pure side slip conditions and the magic formula tire model under pure longitudinal slip conditions are established using Matlab / Simulink. The tire lateral force F under pure cornering condition output by the magic formula tire model under pure cornering condition and the magic formula tire model under pure longitudinal slip condition y0 and the tire longitudinal force F under pure longitudinal sliding conditions x0 , the magic tire model of four-wheel composite working conditions is established according to the following formula: σ is the normalized slip rate, σ x is the longitudinal slip rate under composite working conditions, σ y is the lateral slip rate under combined working conditions, F x is the longitudinal force under composite working condition, F y is the lateral force under composite working conditions.

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