Four-wheel nonlinear two-degree-of-freedom vehicle model simulation system and method

Abstract

The invention discloses a four-wheel nonlinear two-degree-of-freedom vehicle model simulation system and method. The system comprises a two-degree-of-freedom vehicle body dynamics model of a whole vehicle, a four-wheel composite working condition magic tire model, an Ackerman corner calculation model, a four-wheel side slip angle calculation model, a four-wheel dynamic vertical load calculation model and a Carsim software module. The vehicle model is a four-wheel model, side slip angle hysteresis response caused by the tire lateral relaxation length is considered, and the tire side slip angle more accurate than that of a two-wheel model can be provided. And the vertical load transfer and unsprung mass of the left and right wheels are considered, so that the estimation precision of the vertical load of the tire is improved. According to the composite working condition tire model, the nonlinear cornering stiffness and the friction ellipse relation between the lateral force and the longitudinal force are considered, and more accurate tire cornering force can be provided. According to the method, the input precision of the tire model can be improved without introducing a new degree of freedom, so that the steady-state and dynamic response simulation precision of the two-degree-of-freedom vehicle model is improved.

Description

Technical Field

[0001] The invention relates to the field of vehicle motion characteristic simulation, and in particular 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 response of vehicles under different working conditions. They are used in the development and testing of chassis control systems such as unmanned driving trajectory tracking control systems, electronic body stability control systems, and wire-controlled steering road feel simulation systems.

[0003] The most widely used vehicle dynamics model is the two-degree-of-freedom model (two-wheel model), which only considers the lateral and yaw motions of the vehicle. According to the way it expresses the tire cornering stiffness, it can be divided into a linear two-degree-of-freedom model and a nonlinear two-degree-of-freedom model. The yaw angular velocity, center of mass slip angle, lateral acceleration, etc. output by the model are usually calculated 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 slip angle and the cornering stiffness. According to the tire's cornering characteristics, when the slip 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 slip angles. In simulation tests and actual applications, the linear two-degree-of-freedom model has poor accuracy and cannot accurately express the vehicle's motion characteristics. In order to improve the output accuracy of the two-degree-of-freedom model, patent CN202210774277.4 provides a two-degree-of-freedom vehicle model yaw rate gain correction method, which corrects the output of the two-degree-of-freedom model by measuring the yaw rate gain of the actual vehicle at different vehicle speeds. This method has high requirements on the measurement accuracy of the vehicle sensor and the performance of the processor, and it cannot reflect the changes in the tire cornering force of the real vehicle through the model, and its scope of use is narrow. Patent CN202380021092.9 uses the Magic Formula tire model to represent the tire cornering force based on the two-degree-of-freedom model. Although the nonlinear cornering stiffness of the tire is taken into account, due to the characteristics of the two-wheel two-degree-of-freedom vehicle model itself, the calculation accuracy of the tire slip 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 rate, center of mass sideslip angle, and lateral acceleration of the two-degree-of-freedom vehicle model are all calculated based on the tire cornering force. From the perspective of the impact of tire force on vehicle dynamics, the combination of tire model and vehicle dynamics is very important. 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 complicated, how to improve the output accuracy of the two-degree-of-freedom vehicle model without introducing new degrees of freedom is also particularly critical. Summary of the invention

[0005] The present invention provides a four-wheel nonlinear two-degree-of-freedom vehicle simulation method and system to ensure the simulation accuracy and stability under high-speed conditions, thereby solving the problem of poor accuracy and stability of existing linear two-degree-of-freedom two-wheel vehicle models and nonlinear 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 nonlinear two-degree-of-freedom vehicle model simulation system, the system comprising a two-degree-of-freedom vehicle body dynamics model, a four-wheel compound working condition magic tire model, an Ackerman turning angle calculation model, a four-wheel side slip angle calculation model, a four-wheel dynamic vertical load calculation model and a Carsim software module;

[0008] 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:

[0009] 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;

[0010] 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;

[0011] The composite working condition formula is:

[0012]

[0013] 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;

[0014]

[0015] Among them, α is the tire side slip angle, κ is the tire longitudinal slip rate;

[0016] 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;

[0017] 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:

[0018]

[0019] 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;

[0020] In the vehicle coordinate system, the tire side slip angle expression of each tire is:

[0021]

[0022] 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 input to the four-wheel dynamic vertical load calculation model.

[0023] Wherein, the two-degree-of-freedom vehicle body dynamics model is:

[0024]

[0025] 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.

[0026] 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,

[0027] 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;

[0028] 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 .

[0029] Preferably, the Ackerman angle calculation model is:

[0030]

[0031] 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.

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

[0033]

[0034] Preferably, the MF pure longitudinal sliding 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 The vertical loads of the left front wheel, right front wheel, left rear wheel and right rear wheel are the output parameters of the model; the input parameters of the model are 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.

[0040] Preferably, the slack 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 slack length and the tire slack length ratio. The initial value of the tire slack length is calculated by looking up the table of the tire hysteresis slip angle, and the tire slack 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.

[0041] Preferably, 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:

[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 These are 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 the method are as follows:

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

[0046] 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;

[0047] Step 3: Use the fitting parameters obtained in step 2 to establish a four-wheel composite working condition magic tire model in Matlab / Simulink;

[0048] 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 ;

[0049] 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.

[0050] 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;

[0051] 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;

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

[0053] 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;

[0054] 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;

[0055] The two-degree-of-freedom vehicle body dynamics model outputs the vehicle's center of mass sideslip angle β and yaw angular velocity 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;

[0056] 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;

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

[0058] Preferably, in step 8, the slack length of each tire in the four-wheel deflection angle calculation model is obtained by multiplying the initial value of the tire slack length by the ratio of the tire slack length using an empirical formula in the Carsim software model;

[0059] 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;

[0060] 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.

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

[0062] (1) Perform 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;

[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 tire slip angles ranging from 0° to 26° and the tire longitudinal force data under 8 characteristic vertical loads with slip rates ranging from 0% to 100%, as the tire's lateral slip and longitudinal slip characteristic data.

[0064] Preferably, the method for identifying the parameters to be fitted of the magic formula tire model calculation formula in the four-wheel composite working condition magic tire model in step 2 is:

[0065] 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;

[0066] 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 the X data and the lateral force as the Y data in the curve fitting toolbox, fit the magic formula of the lateral force basic equation, and obtain the values ​​of the four parameters B1, C1, D1, and E1 in the equation under a single load;

[0067] 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;

[0068] 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. 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 step 4) until the fitting equations of all parameters of B1, C1, D1, and E1 are obtained;

[0070] 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 to obtain the magic formula tire model calculation formula under pure side slip conditions;

[0071] 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.

[0072] Preferably, in step 3, the steps of establishing a four-wheel composite working condition magic tire model in Matlab / Simulink using the fitting parameters obtained in step 2 are as follows:

[0073] 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.

[0074] 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:

[0075]

[0076] Where: 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.

[0077] Beneficial effects of the present invention:

[0078] The vehicle model in the simulation system of the present invention is a four-wheel model, which takes into account the hysteresis response of the slip angle caused by the lateral relaxation length of the tire, and can provide a more accurate tire slip angle than a two-wheel model. The vertical load transfer of the left and right wheels and the unsprung mass are taken into account, thereby improving the estimation accuracy of the vertical load of the tire. The composite working condition tire model takes into account the nonlinear cornering stiffness and the friction ellipse relationship between the lateral force and the longitudinal force, and can provide a more accurate tire cornering force. The present invention can improve the input accuracy of the tire model without introducing new degrees of freedom, thereby improving the steady-state and dynamic response simulation accuracy 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 following briefly introduces the drawings used in the present invention.

[0080] Figure 1 Schematic diagram of the four-wheel two-degree-of-freedom vehicle dynamics model.

[0081] Figure 2Schematic diagram of tire coordinate system.

[0082] Figure 3 Schematic diagram of the front axle load change during vehicle steering.

[0083] Figure 4 A simulation flow chart of a four-wheel nonlinear two-degree-of-freedom vehicle model provided by the present invention.

[0084] Figure 5 It is the connection method and signal flow diagram between each module. DETAILED DESCRIPTION

[0085] The specific implementation of the present invention will be explained below with reference to the accompanying drawings.

[0086] The vehicle dynamics model of the whole vehicle with four wheels and two degrees of freedom used in the present invention is as follows: Figure 1 As shown in Figure 1, this model takes into account the lateral and yaw motions of the vehicle body. Figure 1 In the , the vehicle coordinate system is established with the center of mass of the vehicle body as the coordinate origin, the vehicle's forward direction is the positive direction of the X axis, and the direction perpendicular to the ground is the positive direction of the Z axis. The 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 of the vehicle body is established as follows:

[0087] (1)

[0088] Where: F y is the lateral force on the vehicle, m is the sprung mass of the vehicle, and F yfl 、F yfr 、F yrl 、F yrr The ground lateral reaction force (tire cornering force) on the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, θ fl ,θ fr They are the left front wheel and right front wheel turning angles respectively.

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

[0090] (2)

[0091] Where: M z is the resultant moment of the vehicle around the Z axis, 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.

[0092] According to Newton's second law, the lateral force ∑F acting on the vehicle is y Equal to the product of vehicle mass and lateral acceleration. Similarly, the total moment of the vehicle around the Z axis ∑M zEqual to the product of the vehicle's moment of inertia around the Z axis and its angular acceleration, ∑F y ,∑M z It can be expressed as:

[0093] (3)

[0094] Where: a y is the lateral acceleration of the vehicle body center of mass, I z is the vehicle's moment of inertia around the Z axis, is the vehicle yaw angular acceleration.

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

[0096] (4)

[0097] Where: v x is the longitudinal velocity of the vehicle center of mass, ω r is the vehicle yaw angular velocity, is the lateral acceleration of the vehicle's center of mass.

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

[0099] (5)

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

[0101] The input of the vehicle model is the left front wheel and right front wheel steering angle θ fl ,θ fr and the longitudinal velocity of the center of mass v x , which is different from the traditional two-wheel two-degree-of-freedom vehicle model, the left and right front wheel turning angles of the model are no longer assumed to be the same angle. The calculation formula of the vehicle turning radius R is calculated by the Ackerman formula:

[0102] (6)

[0103] Where: 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.

[0104] The formula for establishing the left and right front wheel turning angles is:

[0105] (7)

[0106] At this point, we only need to measure the steering wheel input angle to calculate the left and right front wheel angles according to the steering system angular transmission ratio and the Ackerman formula, thus completing the derivation of the calculation formula for the Ackerman angle calculation model.

[0107] The tire cornering force is the same as the lateral force in magnitude but opposite in direction. In formula (5), the lateral acceleration and yaw rate of the vehicle are mainly affected by the four-wheel lateral force (cornering force). When the tire slip angle is small, the cornering force is approximately linearly related to the slip angle. When the tire slip angle is large, the tire tread and the ground will reach the adhesion limit and produce lateral slip. At this time, the cornering force is nonlinearly related to the slip angle and gradually decreases. The conventional linear two-degree-of-freedom vehicle model simplifies the cornering force to the product of the fixed cornering stiffness and the slip angle, resulting in a decrease in the accuracy of the tire cornering force under large slip angles. The present invention uses a magic formula tire model of a composite working condition to describe the tire's cornering characteristics. While accurately expressing the nonlinear cornering stiffness of the tire, it also takes into account the influence of the tire's vertical load changes and the friction ellipse on the tire cornering force.

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

[0109] (8)

[0110] (9)

[0111] Where: F y0 、F x0 They represent the lateral force and longitudinal force of the tire under pure sideslip and pure longitudinal slip conditions respectively, α is the tire sideslip angle, κ is the tire longitudinal slip rate, D1 and D2 are peak factors, C1 and C2 are shape factors, B1 and B2 are stiffness factors, E1 and E2 are curvature factors, and B1, B2, C1, C2, D1, D2, E1, and E2 are all related to the tire vertical load F. z Linear correlation can be obtained by parameter identification based on tire longitudinal slip and lateral deviation test data.

[0112] The relational expression 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 These are parameters to be fitted.

[0115] Under the combined conditions of longitudinal slip and lateral deviation, the tire longitudinal force Fx , lateral force F y It is expressed as follows:

[0116] (10)

[0117] Where: 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 composite working conditions.

[0118] The relationship and specific expression between the various slip rates in formula (10) are as follows:

[0119] (11)

[0120] So far, a four-wheel compound working condition magic tire model has been established, which takes tire slip angle and longitudinal slip rate as input and outputs lateral force and longitudinal force under compound working conditions. Since the cornering force is used in both vehicle models, and the slip angle and cornering force have opposite signs, the lateral force output by the tire model needs to be multiplied by a negative sign to convert it into cornering force.

[0121] The present invention establishes a tire coordinate system such as Figure 2 As shown, in Figure 2 The direction of the cornering force shown in is the positive direction, and the direction of the slip angle shown in is the negative direction. The tire slip angle can be expressed as the angle between the tire rolling direction and the tire moving direction, that is, the difference between the tire steering angle and the tire heading angle. Among them, the tire heading angle can be expressed by the inverse tangent of the value divided by the tire lateral velocity and the tire longitudinal velocity. Since the tire steering angle and the slip angle have opposite signs, after multiplying their difference by a negative sign, the tire slip angle is expressed as:

[0122] (12)

[0123] Where: 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, 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, α fl , α fr , α rl , α rr They are the side slip 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 speed of each tire can be expressed using the longitudinal velocity v of the vehicle's center of mass x, lateral velocity v of vehicle center of mass y , yaw angular velocity ω r Indicates that the tire slip angle expression is obtained at this time:

[0125] (13)

[0126] In the two-wheel two-degree-of-freedom model, only the center of mass slip angle can be used to represent the heading angle of the front and rear axles. The center of mass slip angle is expressed as the arc tangent 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 comparison, due to the inherent characteristics of the four-wheel model, the equivalent amount of the vehicle body yaw angular velocity on the four wheels can be combined in the expression of the heading angle, and since the Ackerman steering formula is used to represent the left and right front wheel steering angles, the steady-state expression of the tire slip angle is more accurate. In terms of the dynamic response of tire slip, the present invention takes into account the hysteresis response of the tire slip angle, uses a first-order relaxation system to represent the non-steady-state response of the tire slip angle, and expresses the relationship between the four-wheel hysteresis slip angle and the slip angle in formula 13 as follows.

[0127] (14)

[0128] Where: α fl-delay , α fr-delay , α rl-delay , α rr-delay They are the left front wheel hysteresis slip angle, the right front wheel hysteresis slip angle, the left rear wheel hysteresis slip angle, and the right rear wheel hysteresis slip angle, respectively. fl , l fr , l rl , l rr They are the relaxed length of the left front wheel, the relaxed length of the right front wheel, the relaxed length of the left rear wheel, and the relaxed length of the right rear wheel.

[0129] So far, a four-wheel slip angle calculation model has been established, and the four-wheel hysteresis slip angle in the model is used instead of the slip angle as the input of the four-wheel compound working condition magic tire model.

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

[0131] (15)

[0132] Where: F zf is the vertical load on the front axle, F zr is the vertical load on the rear axle, g is the acceleration of gravity, and the vertical load on the front and rear axles can be divided by 2 to get the vertical load on a single wheel.

[0133] When a vehicle is turning at high speed on a horizontal road, the vertical load on each wheel is not a fixed value. Due to the centrifugal effect, there is a vertical load transfer between the left and right wheels. The load change diagram of the front axle during the vehicle turning process is shown in the figure below. Figure 3 As shown. Figure 3 The vehicle coordinate system is established with the center of mass of the vehicle body as the origin of the coordinates and the positive direction of the X-axis (out of the paper) as the vehicle's forward direction. Assuming that the vehicle is in a left turn, the direction of the lateral acceleration is the same as the positive direction of the Y-axis, then the direction of the centrifugal force on the vehicle body is the same as the negative direction of the Y-axis, and the balance equation can be obtained by taking the moment of the right front wheel as follows:

[0134] (16)

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

[0136] The expression of vehicle front axle mass and centrifugal force is as follows:

[0137] (17)

[0138] After substituting formula 17 into formula 16, the vertical load expression of the left front wheel can be obtained as follows:

[0139] (18)

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

[0141] (19)

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

[0143] Similarly, the four-wheel dynamic vertical load can be expressed as follows:

[0144] (20)

[0145] In Equation 20, the accuracy of the vertical load depends on the accuracy of the estimate of the lateral acceleration and the measurement 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] Where: F x0 is the longitudinal force of the tire under pure longitudinal slip conditions, B2, C2, D2, E2 are the parameters to be identified, and κ is the longitudinal slip rate of the tire.

[0159] Step 203: The present invention uses the Curve Fitting Toolbox in Matlab software to perform parameter identification. Taking the identification of the side slip characteristic parameters as an example, first, the side slip data and the independent variable (side slip angle) corresponding to the single characteristic vertical load in step 201 need to be imported into the Matlab workspace in matrix form, and the side slip angle is selected as the X data and the side force is selected as the Y data in the Curve Fitting Toolbox. Then, the fitting type is selected as a custom equation, and the basic side force equation of the magic formula is input, and the 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 single characteristic vertical load tire lateral force data, and record the values ​​of the fitted B1, C1, D1, and E1 parameters under the eight characteristic vertical loads.

[0161] Step 205: Import the eight characteristic vertical load values ​​and the corresponding B1, C1, D1, and E1 parameter values ​​into the Matlab workspace in matrix form. Taking parameter B1 as an example, select the characteristic vertical load as X data and B1 as Y data in the curve fitting toolbox, and then use polynomial regression to select the appropriate polynomial degree according to the fitting evaluation index in the curve fitting toolbox. The linear relationship between parameter B1 and the vertical load can be obtained, and the fitting equation is recorded. Note: The original characteristic vertical load value unit is N. In order to ensure the fitting accuracy and unify the units with the input of the magic formula tire model, it needs to be converted to kN before importing.

[0162] Step 206: The linear relationship between the parameters C1, D1, E1 and the vertical load can be obtained by repeating step 205, and the corresponding fitting equation is recorded.

[0163] Step 207: Use the obtained B1, C1, D1, E1 parameter fitting equation to replace the B1, C1, D1, E1 parameters of the tire lateral force basic formula in step 003, and obtain the magic formula tire model under the pure sideslip condition.

[0164] Step 208: Parameter identification of tire longitudinal slip characteristics can refer to steps 203 to 207, replacing the tire side slip angle in the steps with the longitudinal slip rate, and using the corresponding data for identification, the process is similar.

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

[0166] 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.

[0167] 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:

[0168]

[0169] Where: 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.

[0170] Since the angles in Matlab are calculated in radians, the tire slip angle needs to be converted from degrees to radians.

[0171] The established compound tire model is used to calculate the lateral force of the left front wheel, right front wheel, left rear wheel, and right rear wheel when there is both cornering and longitudinal slip. When the longitudinal slip rate is 0, this model can also be used as a pure cornering model. The tire cornering force is obtained by multiplying the obtained lateral force by a negative sign to meet the requirements of the vehicle dynamics balance equation.

[0172] 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 ;

[0173] 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, such as Figure 1 shown.

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

[0175]

[0176] Where: m is the sprung mass, I z is the lateral 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 wheelbase, and 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, 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, a four-wheel two-degree-of-freedom vehicle body model is established according to the above balance equations. During the modeling process, in order to avoid the occurrence of singular points, all integrators in the model use discretized integrators and set the initial value to the eps function.

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

[0179]

[0180] Where: L is the vehicle wheelbase, 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 to calculate the front wheel angle, since the steering wheel angle in Carsim is in degrees, the left front wheel angle and the right front wheel angle also need to be converted to radians 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 structural parameters obtained in step 4;

[0183] The derivation of the four-wheel deflection calculation model is shown in Figure 2 And equations (12) to (14), the calculation equation of tire hysteresis slip angle is given as follows:

[0184]

[0185] Where: α fl , α fr , α rl , α rr are the side slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system, α fl-delay , α fr-delay , α rl-delay , α rr-delay They are the hysteresis 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 They are the slack lengths of the left front wheel, right front wheel, left rear wheel and right rear wheel respectively.

[0186] The tire side loose length can be calculated using the empirical formula given in the Carsim software or fitted according to experimental data. The present invention uses the tire side loose length in the Carsim software. In the Carsim software, the side loose length is obtained by multiplying the tire side loose length initial value and the tire side loose length ratio. The tire side loose length initial value is calculated by looking up the table by the tire hysteresis side slip angle, and the tire side loose length ratio is calculated by looking up the table by the tire normalized vertical load. The tire normalized vertical load is the actual vertical load divided by the tire nominal load.

[0187] The formula for the calculation model of the four-wheel dynamic vertical load can be derived by combining equations (15) to (20) and Figure 3 , the dynamic vertical load equation of the four wheels of the vehicle is given as follows:

[0188]

[0189] Where: 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 vehicle's center of mass.

[0190] The model input is the lateral acceleration of the vehicle body, and the model output is the vertical load on the four wheels. The unit of the model calculation value is N, which needs to be consistent with the vertical load required by the magic formula tire model, so the vertical load calculation value is divided by 1000.

[0191] Step 8: Connect the signal interfaces between the models. The connection between the models is as shown in the signal flow diagram. Figure 4 shown. Figure 4 The input-output relationship between the models is clearly shown in the figure, as follows:

[0192] Carsim software module outputs steering wheel angle θ swTo 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;

[0193] 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;

[0194] The two-degree-of-freedom vehicle body dynamics model outputs the vehicle's center of mass sideslip angle β and yaw angular velocity 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;

[0195] 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 After each module is correctly connected, the system closed loop is realized.

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

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 input to the four-wheel dynamic vertical load calculation model.

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 1, 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 1, characterized in that: The MF pure sideslip model is expressed as: The MF pure longitudinal sliding model is expressed as: 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 1, characterized in that: The four-wheel dynamic vertical load calculation model is obtained, and the model formula is: In this model, F zfl 、F zfr 、F zrl 、F zrr The vertical loads of the left front wheel, right front wheel, left rear wheel and right rear wheel are the output parameters of the model; the input parameters of the model are 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 1, 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 1, 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: 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 1, 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 structural 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 angular velocity 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 For 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) Perform 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 to obtain the tire lateral force data under 8 characteristic vertical loads with side slip angles ranging from 0° to 26° and the tire longitudinal force data under 8 characteristic vertical loads with slip rates ranging from 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 the X data and the lateral force as the Y data in the curve fitting toolbox, fit the magic formula of the lateral force basic equation, 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. 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 to obtain the magic formula tire model calculation formula under pure side slip conditions; Step 7): Replace the slip 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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