Variable load working condition commercial vehicle four-wheel vertical load dynamic estimation system and simulation method

Abstract

The application provides a four-wheel vertical load dynamic estimation system and simulation method of a variable load working condition commercial vehicle, relates to the field of vehicle motion characteristic simulation, and is composed of a nonlinear three-degree-of-freedom vehicle body model, a tire model, a four-wheel side slip angle / slip rate calculation model, a four-wheel vertical load solving model and a mass center position and spring mass estimation model. The mass center position and spring mass estimation model can be combined with the vehicle static axle load to estimate the mass center and mass related information, and correct the parameters in the vehicle body model and the vertical load solving model. The four-wheel vertical load and load transfer rate of the commercial vehicle can be obtained under the premise that the wheels are not additionally modified.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vehicle motion characteristics simulation, in particular to a four-wheel vertical load dynamic estimation system and simulation method for a commercial vehicle under variable load conditions. BACKGROUND

[0002] According to statistics, 33% of truck collision accidents are caused by vehicle rollover, and the direct factor affecting vehicle rollover is the lateral transfer of tire vertical load. For commercial vehicles, they need to frequently load and unload goods, and the commercial vehicles are driven under heavy load conditions for a long time. The increase in the mass of the goods causes the movement of the vehicle mass center position, and the change in the mass center position and the increase in the mass simultaneously cause the increase in the tire load transfer amount. At the same time, the increase in the tire load also increases the risk of tire burst. If the tire vertical load of the commercial vehicle can be obtained in real time, the above risks can be effectively avoided or reduced. Therefore, the dynamic estimation of the tire vertical force is particularly important for the driving safety of the commercial vehicle.

[0003] At present, various methods are used in the tire vertical force estimation system. Patent CN202011254568.8 proposes a tire vertical force estimation system based on multi-sensor fusion. This method estimates the tire ground contact angle and then obtains the tire vertical force based on the MEMS accelerometer, wheel speed sensor, tire pressure sensor, and simplified tire model. This method has high requirements for the sampling rate and accuracy of the MEMS accelerometer. When the tire rolls at medium and high speeds, the lack of sampling rate will increase the difficulty of extracting tire characteristic data points. Patent CN201810303802.8 proposes a tire vertical force estimation system based on binocular vision. This method uses a binocular camera installed inside the vehicle body to obtain road surface information, combines the Kalman filter algorithm with the inertial measurement sensor signal to obtain the vehicle body attitude, and then combines the load transfer model to estimate the tire vertical force. This method does not consider the change in the vehicle mass center position, and the mass center positions of the commercial vehicle under empty load and full load are quite different, making it difficult to determine the installation position of the inertial measurement sensor. It is only suitable for passenger cars with little change in the mass center position. Patent CN202410038879.2 discloses a tire vertical force dynamic measurement system based on strain sensors. The strain sensor measurement element installed inside the tire obtains the voltage signal when the strain gauge deforms, and the tire force corresponding to the voltage signal of different periods is calibrated through experiments and tire dynamics model to represent the tire vertical force. At present, this method verifies fewer working conditions, only the tire low-speed straight driving condition, and has limited application range.

[0004] The common problems existing in the tire force estimation / measuring system described in the above patents include: 1, unable to obtain the tire static load; 2, need to make additional modifications in the tire / vehicle system; 3, without considering the change of the vehicle's mass center position; 4, the system has a small range of working conditions. At present, the on-board weighing system has been commercialized and applied, which can effectively measure the vehicle static axle load through the strain sensor installed on the commercial vehicle axle. How to fully utilize the obtained vehicle static axle load to correct the mass center position and then dynamically estimate the tire vertical load has become one of the problems to be solved. At the same time, how to establish a high-precision tire force estimation model without additional modifications to the commercial vehicle is also particularly key. SUMMARY

[0005] In view of the above problems, the present application provides a variable load working condition commercial vehicle four-wheel vertical load dynamic estimation system and simulation method, the scheme is as follows:

[0006] The variable load working condition commercial vehicle four-wheel vertical load dynamic estimation system comprises a nonlinear vehicle body three-degree-of-freedom model, a composite working condition Unitire tire model, a mass center position and spring mass estimation model, and a four-wheel vertical load solving model.

[0007] The formula of the nonlinear vehicle body three-degree-of-freedom model is as follows:

[0008] (1)

[0009] In formula (1), m s is the spring mass, a x is the longitudinal acceleration of the vehicle body mass center, a y is the lateral acceleration of the vehicle body mass center, I z is the rotational inertia of the vehicle body around the Z axis, ω r is the vehicle body yaw rate, B1 is the front axle track, B2 is the rear axle track, l f is the front axle track, l r is the rear axle track, v x and v y are the longitudinal and lateral speeds of the vehicle body mass center; F x and F y are the longitudinal and lateral forces of the four wheels, F x11 , F x12 , F x21 , and F x22 respectively represent the longitudinal forces of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, F y11 , F y12 , F y21 , and F y22 respectively represent the lateral forces of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel; θ is the front wheel steering angle, θ 11 , and θ 12respectively represent the left front wheel, right front wheel steering angle;

[0010] The model takes four-wheel longitudinal force F x , four-wheel lateral force F y , mass center longitudinal velocity v x and left and right front wheel angle θ as input, and the solved variables are vehicle body mass center longitudinal acceleration a x , vehicle body mass center lateral acceleration a y and yaw rate ω r ;

[0011] Among the input variables, the mass center longitudinal velocity v x is obtained according to the vehicle speed analysis, and the left and right front wheel angle θ is converted from the steering wheel angle θ sw according to the Ackerman angle formula, which is:

[0012] (2)

[0013] In formula (2), θ sw is the steering wheel angle, L is the vehicle wheelbase, i ag is the steering system angle transmission ratio; wherein the vehicle wheelbase L and the steering system angle transmission ratio i ag are known constant values;

[0014] The four-wheel longitudinal force F x and the four-wheel lateral force F y are obtained by solving the composite working condition Unitire tire model; the solved vehicle body mass center longitudinal acceleration a x and the vehicle body mass center lateral acceleration a y input the four-wheel vertical load solving model to calculate the vertical load of the four wheels, and the formula is as follows:

[0015] (3)

[0016] In formula (3), F z11 , F z12 , F z21 , F z22 are the vertical loads of the left front wheel, right front wheel, left rear wheel and right rear wheel respectively; h s is the mass center height of the sprung mass, h f is the height of the front axle roll center, h r is the height of the rear axle roll center, m susp-f is the front axle suspension mass, m susp-r is the rear axle suspension mass, and m t is the tire mass;

[0017] M rollf is the front axle vehicle body roll moment, and M rollr is the rear axle vehicle body roll moment;

[0018] (4)

[0019] In formula (4), K rollf is the front axle roll stiffness, K rollr is the rear axle roll stiffness, m f is the front axle equivalent mass, h df is the distance from the front axle sprung mass center to the roll center, h d is the distance from the rear axle sprung mass center to the roll center, is the front axle body roll angle, is the rear axle body roll angle, which can be expressed as:

[0020] (5)

[0021] After solving, the load transfer ratio is calculated according to the four-wheel vertical load, as follows:

[0022] (6)

[0023] In formula (6), LTR is the four-wheel load transfer ratio;

[0024] The input of the four-wheel vertical load solving model is the body longitudinal acceleration a x and the body lateral acceleration a y obtained in the nonlinear body three-degree-of-freedom model, as well as the body longitudinal velocity v x , the sprung mass m s , the sprung mass center height h s , the front wheelbase l f , and the rear wheelbase l r ; the output is the four-wheel vertical load F z and the load transfer ratio LTR; wherein the sprung mass m s , the sprung mass center height h s , the front wheelbase l f , and the rear wheelbase l r are estimated by the center of mass position and sprung mass estimation module.

[0025] The formula of the center of mass position and sprung mass estimation module is:

[0026] (7)

[0027] In formula (7), F zfa and F zra are the static front and rear axle loads of the vehicle, respectively, F zfae and F zraerespectively are the static front and rear axle loads when the vehicle is empty, m0 is the mass of the cargo, m1 is the mass of the cab, m2 is the mass of the cargo box, h0 is the height of the mass center of the cargo, h1 is the height of the mass center of the cab, and h2 is the height of the mass center of the cargo box; F zfa , F zra , F zfae , F zrae is obtained by the strain sensor.

[0028] The formula of the composite working condition Unitire tire model is:

[0029] (8)

[0030] In formula (8), is the Unitire dimensionless longitudinal slip rate, is the Unitire dimensionless lateral slip rate, is the Unitire dimensionless total slip rate, x is the longitudinal friction coefficient of the tire, y is the lateral friction coefficient, is the dimensionless total shear force, x and K y are the longitudinal slip and lateral deflection stiffness of the tire, respectively, and E is a curvature factor, x , K y , and E all need to be obtained through parameter identification; when the parameters are identified using the pure working condition method, the curvature factor E needs to be distinguished according to the working condition, and the curvature factor corresponding to the pure longitudinal slip working condition is denoted as E1, and the curvature factor corresponding to the pure lateral deflection working condition is denoted as E2.

[0031] μ 0x , μ 0y , μ mx , μ my , μ hx , μ hy , V mx , V my , N x , N y is a parameter to be identified, the parameters of the pure longitudinal slip working condition in formula (8) are K x , E1, μ 0x , μ mx , μ hx , V mx , N x , and the parameters of the pure lateral deflection working condition are K y , E2, μ 0y , μ my , μ hy , V my , N y , the above-mentioned to-be-identified parameters and the vertical load F zThere is a linear relationship, which is obtained by polynomial or linear fitting;

[0032] The parameters required to be input in the Unitire semi-empirical tire model are Unitire lateral slip rate S y , Unitire longitudinal slip rate S x and vertical load F z ; wherein the Unitire longitudinal slip rate S x , the lateral slip rate S y is converted from the slip rate κ and the side slip angle α according to the following formula:

[0033] (9)

[0034] The vertical load F z of the tire is obtained by a four-wheel vertical load solving model.

[0035] In the Unitire semi-empirical tire model, κ in the input Unitire longitudinal slip rate S x is replaced by the hysteresis longitudinal slip rate κ d , and α is replaced by the hysteresis side slip angle α d ;

[0036] The hysteresis side slip angle α d , the hysteresis longitudinal slip rate κ d is obtained by a four-wheel side slip angle / slip rate calculation model; in the four-wheel side slip angle / slip rate calculation model, the hysteresis side slip angle α d of each wheel is represented as α delay11 , α delay12 , α delay21 , α delay22 , and the formula is as follows:

[0037] (10)

[0038] In formula (10), α delay11 , α delay12 , α delay21 , α delay22 are the hysteresis side slip angles of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively, l y11 , l y12 , l y21 , l y22 are the relaxation side slip lengths of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively; α 11 , α 12 , α 21 , α 22 are the side slip angles of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively.

[0039] (11)

[0040] In formula (11), v wx11 , v wx12 , v wx21 , v wx22 are the longitudinal velocities of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel in the tire coordinate system, respectively; v wy11 , v wy12 , v wy21 , v wy22 are the lateral velocities of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel in the tire coordinate system, respectively.

[0041] (12)

[0042] In formula (12), v x11 , v x12 , v x21 , v x22 are the longitudinal velocities of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel in the vehicle coordinate system, respectively; v y11 , v y12 , v y21 , v y22 are the lateral velocities of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel in the vehicle coordinate system, respectively.

[0043] (13)

[0044] The calculation of the relaxed side slip length of each tire is in accordance with the general empirical formula built in the Trucksim software, which is expressed as the product of the normalized relaxed side slip length and the normalized load and the side slip proportion factor:

[0045] (14)

[0046] In formula (14), gain y is the side slip proportion factor, l ys is the normalized relaxed side slip length, F zs is the normalized load, and r is the effective rolling radius of the tire; the normalized load F zs is the actual vertical load F z of the tire divided by the rated load that the tire can bear; the normalized relaxed side slip length l is fitted using a Gaussian function in combination with the data in Trucksim, and the fitting formula is as follows:

[0047] (15)

[0048] In formula (15), l1~l 12 are the fitting parameters of the normalized relaxed side slip length.

[0049] the hysteresis longitudinal slip ratio κ of each wheel in the four-wheel side slip angle / slip ratio calculation model d denoted by κ delay11 , κ delay12 , κ delay21 , κ delay22 , the formula is as follows:

[0050] (16)

[0051] In formula (16), κ delay11 , κ delay12 , κ delay21 , κ delay22 are the hysteresis longitudinal slip ratios of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, l x11 , l x12 , l x21 , l x22 are the relaxation lengths of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively; κ 11 , κ 12 , κ 21 , κ 22 are the longitudinal slip ratios of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively;

[0052] (17)

[0053] In formula (17), ω w11 , ω w12 , ω w21 , ω w22 are the angular velocities of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, and r is the effective rolling radius of the tire;

[0054] (18)

[0055] In formula (18), F x11 , F x12 , F x21 , F x22 are the longitudinal forces of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, T r11 , T r12 , T r21 , T r22 are the rolling resistance torques of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, and T d is the wheel driving torque;

[0056] (19)

[0057] In formula (19), R surf is the rolling resistance torque road surface coefficient, and Rc R is the rolling resistance moment constant component v R is the rolling resistance moment velocity component

[0058] In equation (16), the representation of the relaxed longitudinal slip length of each wheel also adopts the general empirical formula in Trucksim:

[0059] (20)

[0060] In equation (20), gain x is the longitudinal slip ratio factor, l xs is the normalized relaxed longitudinal slip length; the normalized relaxed longitudinal slip length is fitted using a Gaussian function in combination with the data in Trucksim;

[0061] The fitting formula is as follows:

[0062] (21)

[0063] In equation (21), l 13 ~l 24 is the normalized relaxed side slip length fitting parameter.

[0064] The input of the four-wheel side slip angle / slip ratio calculation model is the vehicle body longitudinal velocity v x , the vehicle body lateral velocity v y , the vehicle body yaw rate ω r , the left and right front wheel steering angles θ, the tire longitudinal force F x and the tire vertical load F z , wherein the vehicle body longitudinal velocity v x and the vehicle body lateral velocity v y are obtained according to the vehicle speed analysis, the left and right front wheel steering angles θ are also converted from the steering wheel steering angle θ sw according to the Ackerman steering angle formula; the vehicle body yaw rate ω r is obtained according to the calculation of the nonlinear vehicle body three-degree-of-freedom model, and the tire longitudinal force F x is obtained according to the calculation of the Unitire semi-empirical tire model;

[0065] The tire vertical load F z required by the four-wheel side slip angle / slip ratio calculation model is obtained according to the calculation of the four-wheel vertical load solving model.

[0066] The linear relationship between the to-be-identified parameters in the composite working condition Unitire tire model and the vertical load is as follows:

[0067] (22)

[0068] In equation (22), a1~a 33To be fitted parameters related to vertical load.

[0069] The application also proposes a simulation method of the four-wheel vertical load dynamic estimation system of the variable load working condition commercial vehicle, and the steps of the method are as follows:

[0070] Step 001: Obtain the basic parameters required by the load estimation system, including the moment of inertia I z of the vehicle body around the Z axis s , the sprung mass m susp-f of the vehicle when it is empty susp-r , the mass of the tire m t , the wheelbase l f of the front and rear axles r , the front and rear axle track B1 and B2, the height h se of the sprung mass center of the vehicle when it is empty, which is measured in the center of gravity test and is a known quantity in the model, the initial value of the height h s of the sprung mass center of the vehicle, the roll angle stiffness K rollf of the front axle rollr , the roll angle stiffness K w of the rear axle, the wheel rotational inertia I 2 , and the free rolling radius of the tire, i.e., the tire radius r.

[0071] Among them, the length unit is unified as m, the mass unit is unified as kg, the rotational inertia unit is unified as kg / m 2 , and the roll angle stiffness unit is N m / rad.

[0072] Step 002: After obtaining the necessary modeling parameters, the vehicle dynamics model can be established in Simulink according to the nonlinear three-degree-of-freedom model; the model takes the four-wheel longitudinal force F x , the four-wheel lateral force F y , the center of mass longitudinal velocity v x , and the left and right front wheel angle θ as input, and the variables to be solved are the body center of mass longitudinal acceleration a x , the body center of mass lateral acceleration a y , and the yaw angular velocity ω r .

[0073] In this step, in order to avoid algebraic loops in the system, a Memory module is connected in series on the body longitudinal acceleration and the body lateral acceleration, and the initial value of the discretized integrator is set as an eps function to avoid singular points in the system; the initial value of the integrator in the lateral motion balance equation is assigned to the vehicle speed in Trucksim;

[0074] Step 003: Obtain the experimental data of the tire under pure longitudinal sliding and pure lateral deflection conditions, or use the built-in 305 / 75 R22.5 tire data in Trucksim software;

[0075] Step 004: Import the tire longitudinal force data under pure longitudinal slip and tire lateral force data under pure cornering into Matlab;

[0076] Step 005: Use the curve fitting toolbox in Matlab to perform parameter identification. First, import the tire longitudinal force data under pure longitudinal slip and single characteristic vertical load into the Matlab workspace. Then, use the longitudinal slip ratio as the independent variable to perform self-defined equation fitting.

[0077] Step 006: After fitting the tire longitudinal force under single characteristic load, record the values of K x , μ 0x , μ mx , μ hx , V mx , N x , and E1. Repeat step 006 until the tire longitudinal force under all characteristic loads is fitted and the values of the above identification parameters are recorded.

[0078] Step 007: According to the values of the 7 identification parameters under different characteristic loads recorded in step 006, perform polynomial fitting of each identification parameter with respect to vertical load F z using the fitting equation shown in equation (22).

[0079] Step 008: Record the fitting equations of K x , μ 0x , μ mx , μ hx , V mx , N x , and E1. Substitute each fitting equation into the Unitire semi-empirical model and establish a mathematical model using matlab function in Simulink.

[0080] Step 009: Repeat steps 005 to 008 using tire lateral force data under pure cornering to complete the fitting equations of K y , E2, μ 0y , μ my , μ hy , V my , N y , and substitute each fitting equation into the Unitire semi-empirical model to establish a Unitire mathematical model under complex conditions.

[0081] Step 010: Establish a hysteresis cornering angle / hysteresis slip ratio calculation model in Simulink according to equations (10) to (21).

[0082] Step 011: Four-wheel vertical load solving model is established in Simulink according to formula (3)~(5);

[0083] Step 012: Spring mass and mass center position estimation model is established according to formula (7);

[0084] Step 013: The input and output signals of the above modules are connected to the corresponding interface in Simulink, as follows:

[0085] The input of three-degree-of-freedom vehicle body dynamics model is the vehicle speed signal v and steering wheel angle θ output by Trucksim sw The output is vehicle body yaw rate ω r , vehicle body longitudinal speed v x , vehicle body lateral speed v y , vehicle body longitudinal acceleration a x , and vehicle body lateral acceleration a y .

[0086] The input of Unitire tire model is hysteresis side slip angle α d , hysteresis slip rate κ d , and tire vertical load F z The output is tire longitudinal force F x , and tire lateral force F y .

[0087] The input of four-wheel side slip angle / slip rate calculation model is vehicle body longitudinal speed v x , vehicle body lateral speed v y , vehicle body yaw rate ω r , left and right front wheel angle θ, tire longitudinal force F x , tire vertical load F z , front wheelbase l f , and rear wheelbase l r The output is hysteresis side slip angle α d , and hysteresis longitudinal slip rate κ d .

[0088] The input of four-wheel vertical load solving model is vehicle body longitudinal acceleration a x , vehicle body lateral acceleration a y , and vehicle body longitudinal speed v x The output is four-wheel vertical load F z and load transfer rate LTR.

[0089] The input of mass center position and spring mass estimation module is front and rear axle static load F zfa , F zra The output is spring mass m s , and spring mass center height h sFront wheelbase l f Rear wheelbase l r After the above modules are correctly connected, the system closed loop can be realized.

[0090] The beneficial effects of the present application are as follows:

[0091] The tire model in the present application is a composite working condition Unitire semi-empirical model, which internalizes the friction ellipse in the model, and can provide more accurate tire longitudinal and lateral forces than the Similarity model under longitudinal sliding and lateral deflection composite working conditions. The four-wheel lateral deflection angle / slip rate calculation model describes the hysteresis characteristics of the tire using a first-order system, and can provide more accurate dynamic response than the conventional model. The four-wheel vertical load solving model considers the body roll and the unsprung mass, and can provide more accurate tire vertical force than the conventional load transfer model. The present application combines the mass center position and the sprung mass estimation model, and can correct the parameters in the body model and the vertical load solving model based on the mass center and mass related information estimated from the static axle load of the vehicle. The present application can obtain the four-wheel vertical load and load transfer rate of the commercial vehicle under multiple working conditions without additional modification of the wheels. BRIEF DESCRIPTION OF DRAWINGS

[0092] Figure 1 Schematic diagram of a nonlinear three-degree-of-freedom body dynamics model

[0093] Figure 2 Schematic diagram of a tire coordinate system and a rotation model

[0094] Figure 3 Schematic diagram of a load transfer model

[0095] Figure 4 Schematic diagram of a sprung mass distribution

[0096] Figure 5 System simulation flowchart

[0097] Figure 6 Signal flowchart of the load dynamic estimation system

[0098] Figure 7 Comparison of friction ellipses

[0099] Figure 8 Composite working condition tire force prediction effect: (a) longitudinal force prediction effect under composite working conditions, (b) lateral force prediction effect under composite working conditions, (c) longitudinal force prediction error, (d) lateral force prediction error

[0100] Figure 9 Vehicle unloaded vertical force estimation results: (a) unloaded 40km / h angle step working condition vertical force, (b) unloaded 60km / h angle step working condition vertical force, (c) unloaded 40km / h load transfer rate, (d) unloaded 60km / h load transfer rate

[0101] Figure 10 Vehicle full load vertical force estimation results: (a) vertical force of 60 km / h corner step working condition, (b) vertical force of 60 km / h steering ramp input, (c) full load 60 km / h load transfer rate, (d) full load 60 km / h load transfer rate. DETAILED DESCRIPTION

[0102] The technical solutions of the present application will be further explained and described in the form of specific embodiments.

[0103] First, a Cartesian coordinate system is established with the vehicle body mass center position as the origin, the forward direction of the vehicle is defined as the X-axis, the direction perpendicular to the ground is defined as the Z-axis, and the Y-axis direction is determined according to the right-hand rule, as shown in Figure 1 .

[0104] A nonlinear three-degree-of-freedom model of the vehicle body is established, with three degrees of freedom being the rotational freedom of the vehicle body around the Z-axis, the lateral motion freedom of the vehicle body, and the longitudinal motion freedom of the vehicle body. The longitudinal force balance equation, the lateral force balance equation, and the yaw moment balance equation are used for description, and the specific formulas are as follows:

[0105] (1)

[0106] In formula (1), m s is the sprung mass, a x is the longitudinal acceleration of the vehicle body mass center, a y is the lateral acceleration of the vehicle body mass center, I z is the rotational inertia of the vehicle body around the Z-axis, ω r is the yaw angular velocity of the vehicle body, B1 is the front axle track, B2 is the rear axle track, l f is the front axle distance, l r is the rear axle distance, v x , v y are the longitudinal and lateral velocities of the vehicle body mass center; F x , F y are the longitudinal and lateral forces of the four wheels, F x11 , F x12 , F x21 , F x22 represent the longitudinal forces of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, F y11 , F y12 , F y21 , F y22 are the lateral forces of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively; θ is the front wheel steering angle, θ 11 , θ 12 represent the steering angles of the left front wheel and the right front wheel, respectively.

[0107] This model takes the longitudinal forces Fx , four-wheel lateral force F y , center of mass longitudinal velocity v x and left and right front wheel steering angle θ are inputs, and the variables to be solved are the body center of mass longitudinal acceleration a x , body center of mass lateral acceleration a y and yaw rate ω r .

[0108] Since the left and right front wheel steering angles of an actual vehicle are difficult to measure, the steering wheel steering angle θ sw is used in the above model. According to Ackerman steering geometry, the left and right front wheel steering angles are expressed as follows in the basic form:

[0109] (2)

[0110] In equation (2), θ sw is the steering wheel steering angle, L is the wheelbase of the vehicle, i ag is the steering angle transmission ratio; wherein the wheelbase L and the steering angle transmission ratio i ag are constant values;

[0111] The four-wheel longitudinal forces F x , four-wheel lateral forces F y in the nonlinear three-degree-of-freedom model are obtained by relying on the Unitire semi-empirical model. As a high-precision semi-empirical model in all working conditions, the Unitire semi-empirical tire model uses a specific tire slip ratio as input. The longitudinal slip ratio S x and the lateral slip ratio S y defined in the Unitire model are as follows:

[0112] (3)

[0113] In equation (3), v sx is the longitudinal slip speed of the tire, v sy is the lateral slip speed of the tire, Ω is the tire rotation speed, and r is the effective rolling radius of the tire.

[0114] The longitudinal slip ratio S x and the lateral slip ratio S y in equation (3) are converted from the tire slip ratio κ and the tire side slip angle α specified in the SAE J670-2022 standard as follows:

[0115] (4)

[0116] In equation (4), α is the tire side slip angle.

[0117] From the above equation, when the tire is in pure side slip condition, i.e. S x = 0, S y=-tanα.

[0118] To describe the limiting relationship between the longitudinal and lateral forces of the tire under combined braking, steering, and slip conditions, some scholars have proposed the friction ellipse assumption. This assumption states that the resultant force of the tire's longitudinal and lateral forces does not exceed the product of the tire's vertical load and the tire-road friction coefficient, as shown in the following formula:

[0119] (5)

[0120] In equation (5), F x For the longitudinal force of the tire, F y For the lateral force of the tire, μ x μ is the longitudinal friction coefficient of the tire. y This is the tire's lateral friction coefficient.

[0121] Currently, the Similarity prediction method is widely used to describe tire force limits under combined operating conditions. This method calculates the total tire force direction angle, using the longitudinal and lateral forces under pure operating conditions as input, and combines this angle to solve for the longitudinal and lateral forces under combined operating conditions. This method can indirectly reflect the tire force boundaries under combined operating conditions. However, because the actual combined slip ratio direction is not completely consistent with the total tire shear force direction, the prediction accuracy under large slip angles or high loads is not ideal. For commercial vehicle tires, which are frequently under high load conditions, the Similarity prediction method is not entirely applicable. The formula for the Similarity prediction method is given below:

[0122] (6)

[0123] In equation (6), σ x For Similarity, the dimensionless longitudinal slip ratio, σ y F is the dimensionless lateral slip ratio of Similarity, σ is the dimensionless total slip ratio of Similarity, and F x0 F is the longitudinal force of the tire under pure longitudinal slip conditions. y0 This refers to the lateral force of the tire under pure lateral slip conditions.

[0124] In the Unitire semi-empirical tire model, the ratio of tire longitudinal and lateral forces to adhesion forces is used to define the dimensionless longitudinal slip ratio and dimensionless lateral slip ratio. The force boundary conditions of the friction ellipse are directly internalized into the dimensionless total slip ratio, ensuring that the tire longitudinal and lateral forces always satisfy the friction ellipse assumption. The formulas for the Unitire dimensionless slip ratio and tire forces are as follows:

[0125] (7)

[0126] In equation (7): Unitire dimensionless longitudinal slip ratio, Unitire dimensionless lateral slip ratio, Unitire dimensionless total slip ratio, Unitire dimensionless total shear force, K x Unitire dimensionless total shear force, K y are the tire longitudinal and lateral stiffness, E is the curvature factor, K x , K y , E are all obtained by parameter identification.

[0127] When using the pure condition method to identify parameters, the curvature factor E needs to be distinguished according to the working condition. The curvature factor corresponding to the pure longitudinal slip condition is denoted as E1, and the curvature factor corresponding to the pure lateral slip condition is denoted as E2.

[0128] The tire longitudinal friction coefficient μ x and the lateral friction coefficient μ y The modified Savkoor dynamic friction coefficient is used instead of:

[0129] (8)

[0130] In formula (8), μ 0x , μ 0y , μ mx , μ my , μ hx , μ hy , V mx , V my , N x , N y are the parameters to be identified under the pure longitudinal slip and pure lateral slip conditions.

[0131] So far, the Unitire tire model has a total of 14 parameters to be identified under the pure longitudinal slip and pure lateral slip conditions. The parameters under the pure longitudinal slip condition are K x , E1, μ 0x , μ mx , μ hx , V mx , N x , and the parameters under the pure lateral slip condition are K y , E2, μ 0y , μ my , μ hy , V my , N y . The above-mentioned parameters to be identified have a linear relationship with the vertical load F z , and are obtained by polynomial or linear fitting;

[0132] In this embodiment, the longitudinal slip ratio is used as the independent variable to fit the tire longitudinal force under a single characteristic load to obtain the parameters for the pure longitudinal slip condition. Then, the characteristic load is changed multiple times to obtain the parameters for the pure longitudinal slip condition under multiple characteristic loads. Then, the identified parameters are fitted with the characteristic load as the independent variable. Similarly, the lateral slip ratio is used as the independent variable to fit the tire lateral force under a single characteristic load to obtain the parameters for the pure lateral slip condition. Then, the characteristic load is changed multiple times to obtain the parameters for the pure lateral slip condition under multiple characteristic loads. Then, the identified parameters are fitted with the characteristic load as the independent variable.

[0133] Using the above method, the parameters to be identified and the vertical load satisfy the following linear relationship:

[0134] (9)

[0135] In equation (9), a1~a 33 These are the parameters to be fitted, which are related to the vertical load.

[0136] The parameter required for the Unitire semi-empirical tire model is the tire slip angle α (which can be further converted into the Unitire lateral slip ratio S according to formula (4)). y ), Unitire longitudinal slip ratio S x and vertical load F z ;

[0137] To further improve accuracy, the Unitire semi-empirical tire model takes hysteresis slip angle, hysteresis longitudinal slip ratio, and vertical load as inputs. The hysteresis slip angle and hysteresis longitudinal slip ratio are obtained through a four-wheel slip angle / slip ratio calculation model.

[0138] Modeling hysteresis sideslip angle and hysteresis slip ratio requires obtaining the tire's longitudinal and lateral velocities in the tire coordinate system. According to... Figure 1 By applying the longitudinal and lateral velocities of the vehicle body in the vehicle coordinate system to the four wheels, we can obtain:

[0139] (10)

[0140] In equation (10), v x11 v x12 v x21 v x22 These represent the longitudinal velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the vehicle coordinate system, v. y11 v y12 v y21 v y22 These represent the lateral velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the vehicle coordinate system.

[0141] Tire coordinate system as follows Figure 2(a) As shown, the longitudinal and lateral velocities of the four wheels in the tire coordinate system can be expressed as:

[0142] (11)

[0143] In equation (11), v wx11 , v wx12 , v wx21 , v wx22 are the longitudinal velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system, respectively, and v wy11 , v wy12 , v wy21 , v wy22 are the lateral velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system, respectively.

[0144] In combination with equation (11), the tire side slip angle can be expressed as the inverse tangent of the ratio of the lateral velocity to the longitudinal velocity in the tire coordinate system, as shown below:

[0145] (12)

[0146] In equation (12), a 11 , a 12 , a 21 , a 22 are the side slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0147] Due to the viscoelastic properties of the tire, when the tire is subjected to a lateral force, the rim first rotates, and the deformation of the tire body lags behind, and the tire side slip angle cannot reach a steady state until the tire rolls a certain distance. During this period, the distance rolled when the tire side slip force reaches 63.2% of the steady-state value is the relaxation side slip length. In combination with the relaxation side slip length, the tire hysteresis side slip angle can be expressed as a first-order system with respect to the tire side slip angle:

[0148] (13)

[0149] In equation (13), a delay11 , a delay12 , a delay21 , a delay22 are the hysteresis side slip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, and l y11 , l y12 , l y21 , l y22 are the relaxation side slip lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0150] The calculation of the relaxation cornering length of each tire is in accordance with the general empirical formula built in the Trucksim software, which is expressed as the product of the normalized relaxation cornering length and the normalized load, the cornering stiffness factor:

[0151] (14)

[0152] In formula (14), gain y is the cornering stiffness factor, l ys is the normalized relaxation cornering length, F zs is the normalized load, and r is the effective rolling radius of the tire; the normalized load F zs is the actual vertical load of the tire divided by the rated load that the tire can bear.

[0153] is the longitudinal slip ratio of the tire, the wheel rotational angular velocity needs to be obtained, and the wheel rotation model is shown in (b). Assuming that the vehicle is rear-wheel driven, the wheel rotational angular velocity can be solved by establishing a tire torque balance equation according to the rigid body fixed-axis rotation theorem: Figure 2

[0154] (15)

[0155] In formula (15), I w is the wheel rotational inertia, ω w11 , ω w12 , ω w21 , and ω w22 are the rotational angular velocities of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, T r11 , T r12 , T r21 , and T r22 are the rolling resistance torques of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively, T d is the wheel driving torque, R surf is the rolling resistance torque road coefficient, R c is the rolling resistance torque constant component, and R v is the rolling resistance torque speed component.

[0156] After the wheel rotational angular velocity is obtained, the longitudinal slip ratio of the tire in the driving state is obtained according to the wheel rotational angular velocity, and the formula is as follows:

[0157] (16)

[0158] In formula (16), κ 11 , κ 12 , κ 21 , and κ 22 are the longitudinal slip ratios of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively.

[0159] ​Similar to the hysteresis side slip angle, the hysteresis slip ratio needs to be combined with the relaxation length of longitudinal slip, the hysteresis slip ratio of each wheel can be expressed as follows:

[0160] (17)

[0161] In formula (17), κ delay11 , κ delay12 , κ delay21 , κ delay22 are the hysteresis slip ratios of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively, l x11 , l x12 , l x21 , l x22 are the relaxation lengths of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively.

[0162] In the present application, the relaxation length of longitudinal slip is also expressed by the general empirical formula in Trucksim:

[0163] (18)

[0164] In formula (18), gain x is the longitudinal slip ratio factor, and l xs is the normalized relaxation length of longitudinal slip.

[0165] So far, the four-wheel side slip angle / slip ratio calculation model has been established, and another important input of the Unitire semi-empirical tire model is the vertical load of the wheel. When the vehicle is uniformly steering on the horizontal road, due to the action of the longitudinal inertia force and the lateral centrifugal force, there is a vertical load transfer between the front and rear wheels and between the left and right wheels of the vehicle. The established vertical load transfer model of the commercial vehicle is shown in Figure 3 .

[0166] In Figure 3 (a), the longitudinal acceleration a x of the center of mass is along the positive direction of the X axis, at this time, there is an inertia force F x opposite to the direction of a cx at the center of mass, and the relationship between the front and rear axle load changes and a x can be obtained by taking the moment at the front and rear axle contact points as follows:

[0167] (19)

[0168] In formula (19), h s is the height of the center of mass of the sprung mass, L is the wheelbase of the vehicle, l f is the distance from the center of mass of the sprung mass to the front axle, and l r is the distance from the center of mass of the sprung mass to the rear axle.

[0169] In Figure 3In (b), the direction of the X-axis is perpendicular to the plane and inward, when the vehicle is in the left-turn working condition, the lateral acceleration a y In the positive direction of the Y-axis, at this time the lateral centrifugal force F cy acts on the sprung mass center CG s , and the vehicle body rolls around the roll center CR of the rear axle. Let the sprung mass of the rear axle be m r , the vertical load of the rear axle when the vehicle is stationary be F zr , and the load of the left rear wheel be F , which can be expressed as:

[0170] (20)

[0171] In combination with equation (19) and equation (20), the sprung mass of the rear axle can be expressed as:

[0172] (21)

[0173] Generally, without considering the roll of the vehicle body, the change in the vertical load of the tire can be directly obtained by taking the moment at the single tire contact point. Taking the left rear wheel as an example, the change in the vertical load caused by the centrifugal force is as follows:

[0174] (22)

[0175] Although equation (22) can generally express the transfer relationship of the vertical load, since the influence of the roll center height on the transfer of the vertical load is ignored, this leads to the calculated change in the vertical load being too small. In order to consider the roll of the vehicle body, according to the translation principle of force in Newtonian mechanics, the point of action of the lateral centrifugal force is translated to the roll center CR, at this time there is a couple moment T roll acting on the roll center, the size of T roll is equal to the roll moment M roll of the vehicle body.

[0176] When the vehicle rolls, the roll moment M rollr of the rear axle vehicle body can be expressed as the sum of the moments generated by the lateral component of F cy and the longitudinal component of the gravity of the sprung mass m r :

[0177] (23)

[0178] In equation (23), h r is the roll center height of the rear axle, h d is the distance from the mass center of the sprung mass of the rear axle to the roll center, K rollr is the roll angular stiffness of the rear axle, is the roll angle of the vehicle body of the rear axle.

[0179] Since the roll angle is usually small, the trigonometric function in equation (23) can be expanded into a Taylor series, and the high order terms can be neglected. The roll angle of the rear axle body can be expressed as:

[0180] (24)

[0181] When the roll stiffness of the rear axle is known, the roll moment can be calculated according to the roll angle of the rear axle.

[0182] Correspondingly, the roll moment of the front axle body M rollf is expressed as:

[0183] (25)

[0184] where M rollf is the roll moment of the front axle body, is the roll angle of the front axle body, m f is the equivalent mass of the front axle, h df is the distance from the mass center of the front axle to the roll center, K rollf is the roll stiffness of the front axle.

[0185] The expression of the roll angle of the front axle is:

[0186] (26)

[0187] At this point, the vertical load change caused by the centrifugal force acting on the mass center of the spring can be expressed as follows:

[0188] (27)

[0189] Combining equation (20), equation (21) and equation (27), the vertical load of the left rear wheel can be expressed as:

[0190] (28)

[0191] In addition to the spring mass, the vertical load change of the wheel is also affected by the non-spring mass. The vertical load change caused by the centrifugal force acting on the non-spring mass is as follows:

[0192] (29)

[0193] In equation (29), F cyus is the centrifugal force received by the non-spring mass, m susp-r is the mass of the rear suspension, R is the turning radius of the vehicle, and r is the radius of the tire.

[0194] The vertical force actually received by the tire is the normal reaction force given by the ground. After considering the mass of the tire and the mass of the suspension, the vertical load of the left rear wheel can be expressed as:

[0195] (30)

[0196] In formula (30), m t is the tire mass, and g is the acceleration of gravity.

[0197] Similarly, the vertical load of each wheel can be expressed as:

[0198] (31)

[0199] As can be seen from formula (31), the vertical load of the tire is mainly affected by the changes of the longitudinal acceleration a x of the vehicle body mass center, the lateral acceleration a y of the vehicle body mass center, the sprung mass m s , the height h s of the sprung mass center, the front wheelbase l f , and the rear wheelbase l r , wherein the longitudinal acceleration a x of the vehicle body mass center and the lateral acceleration a y of the vehicle body mass center are solved by a nonlinear three-degree-of-freedom model, and the sprung mass m s , the height h s of the sprung mass center, the front wheelbase l f , and the rear wheelbase l r are usually assumed to be fixed values when the vertical force is solved, and for commercial vehicles, the vehicle body load changes will cause the change of the position of the sprung mass center, and the vertical load of the tire solved by using the fixed sprung mass and the fixed position of the sprung mass center will inevitably have a large deviation. In order to solve the problem, the application proposes a mass center position estimation model based on a vehicle-mounted weighing system, and the longitudinal and vertical positions of the sprung mass center are estimated by the static front and rear axle loads of the vehicle, so as to correct the system model.

[0200] The vehicle mass distribution schematic diagram is shown in Figure 4 The distance from the sprung mass center to the front and rear axles can be expressed as:

[0201] (32)

[0202] In formula (32), F zfa and F zra are the static axle loads of the front and rear axles of the vehicle, and m susp-f and m susp-r are the suspension masses of the front and rear axles of the vehicle.

[0203] The commonly used methods for measuring the height of the center of mass of a vehicle include lifting method, side-tilting method and swinging method. Among them, the lifting method and the side-tilting method are to lift a certain axle or a certain side of the vehicle to a certain angle, and the height of the center of mass of the vehicle is represented according to the moment balance and trigonometric function. The swinging method is to fix the vehicle on a swingable platform, and the height of the center of mass is calculated by using the period of swing of the vehicle. The above-mentioned center of mass height calculation methods all need to rely on special test bench equipment, and the measurement operation is complex and time-consuming. After the commercial vehicle loads and unloads the goods, it is not convenient to use the above-mentioned methods for measurement or estimation. In the present application, the sprung mass of the commercial vehicle is divided into three parts, which are the cab mass, the cargo box mass and the cargo mass. The height of the center of mass of the sprung mass when the commercial vehicle loads different mass of goods is estimated by the method of weighted average of mass, and the estimated height of the center of mass of the sprung mass and the static axle load of the vehicle have the following relationship:

[0204] (33)

[0205] In formula (33), m0 is the mass of the goods, m1 is the mass of the cargo box, m2 is the mass of the cab, m is the sprung mass when the vehicle is empty, h0 is the height of the center of mass of the goods, h1 is the height of the center of mass of the cargo box, h2 is the height of the center of mass of the cab, and g is the acceleration of gravity. se

[0206] In formula (33), the difference between the static total axle load of the vehicle before and after loading can be used to calculate the mass of the goods m0 and the sprung mass m s .

[0207] (34)

[0208] In formula (34), F zfae and F zrae are the static front and rear axle loads when the vehicle is empty.

[0209] When the vehicle is fully loaded, it is assumed that the height of the center of mass of the goods is half the height of the cargo box plus the height of the tire, and the heights of the centers of mass of the cargo box and the cab can be measured and calibrated by using the center of mass measurement test bench. According to the estimated sprung mass and the position of the center of mass of the sprung mass in formula (32), formula (33) and formula (34), the three-degree-of-freedom dynamics model of the vehicle body in formula (1), the four-wheel lateral velocity model in formula (10) and the vertical load solving model in formula (31) can be modified to estimate the four-wheel vertical load of the commercial vehicle under different load conditions.

[0210] At this point, the formula derivation of the four-wheel vertical load dynamic estimation system of the commercial vehicle under variable load conditions described in the present application has been completed.

[0211] The implementation steps of the method described in the present application will be explained below, Figure 5 The simulation flowchart of the four-wheel vertical load dynamic estimation system of the commercial vehicle under variable load conditions provided by the present application is as follows:​

[0212] Step 001: Obtain the basic parameters required by the load estimation system, including the vehicle body's moment of inertia about the Z-axis. z The unloaded sprung mass m of the vehicle s Front and rear axle suspension mass (m) susp-f m susp-r Tire mass m t Front and rear wheelbase l f and l r , Front and rear axle track B1 and B2, and the height of the sprung center of gravity h when the vehicle is unloaded se Front and rear axle roll stiffness K rollf K rollr Wheel rotational inertia I w 1. Tire free rolling radius (tire radius r);

[0213] Among these, the unit of length is uniformly m, the unit of mass is uniformly kg, and the unit of moment of inertia is uniformly kg / m. 2 The roll stiffness is measured in N / m / rad; the height of the sprung center of gravity h when the vehicle is unloaded. se Based on measurements from the center of gravity bench test, which is a known quantity in this invention and represents the height of the sprung center of gravity of the vehicle in the model, h is the height of the vehicle's sprung center of gravity. s The initial value of .

[0214] Step 002: After obtaining the necessary modeling parameters, the nonlinear three-degree-of-freedom model can be used in conjunction with... Figure 1 A vehicle dynamics model is built in Simulink; this model uses the longitudinal force F of the four wheels. x Lateral force F of four wheels y longitudinal velocity of the center of mass v x The input is the left and right front wheel steering angle θ, and the variable to be solved is the longitudinal acceleration a of the vehicle's center of gravity. x Lateral acceleration of the vehicle's center of gravity, a y and yaw rate ω r .

[0215] In this step, to avoid algebra loops in the system, memory modules need to be connected in series for the longitudinal acceleration and lateral acceleration of the vehicle body, and the initial value of the discretized integrator is set to the eps function to avoid singularities in the system. The initial value of the integrator in the lateral motion equilibrium equation is assigned using the vehicle speed in Trucksim.

[0216] Step 003: To obtain the longitudinal and lateral forces of the tires required in the vehicle dynamics model, a semi-empirical model of the Unitire tire needs to be established. First, experimental data of the tire under pure longitudinal slip and pure lateral slip conditions need to be obtained. In this embodiment, the 305 / 75 R22.5 tire data built into the Trucksim software is used.

[0217] Step 004: Include the tire longitudinal force data under 5 characteristic vertical load and pure slip condition and tire lateral force data under pure cornering condition in Trucksim. The first row of data is the corresponding load condition. The first row of data needs to be changed to 0 before being imported into Matlab.

[0218] Step 005: After obtaining the tire experimental data, the parameters of the Unitire semi-empirical tire model formula (7) and formula (8) need to be identified. Follow the identification process of local first, overall second, pure condition first, and composite condition second. Use the curve fitting toolbox in Matlab software to identify the parameters. Take the longitudinal force identification as an example. First, import the tire longitudinal force data into the Matlab workspace. In this step, the tire longitudinal force under a single characteristic vertical load needs to be imported. Then, use the longitudinal slip ratio as the independent variable to perform custom equation fitting.

[0219] Step 006: After fitting the tire longitudinal force under a single characteristic load, record the values of the 7 parameters K x , μ 0x , μ mx , μ hx , V mx , N x , and E1. Repeat step 006 until the tire longitudinal force under 5 characteristic loads is fitted and the values of the above identification parameters are recorded.

[0220] Step 007: According to the 7 identification parameter values under 5 characteristic loads recorded in step 006, fit each identification parameter with the following fitting equation about vertical load F z . In this step, the original vertical load unit is N. In order to improve the fitting accuracy, the vertical load unit needs to be converted to kN before fitting.

[0221] Step 008: Record the fitting equations of the 7 parameters K x , μ 0x , μ mx , μ hx , V mx , N x , and E1. Substitute each fitting equation into the Unitire model in step 005 and use matlab function to establish a mathematical model in Simulink.

[0222] Step 009: Parameter identification of tire lateral force, refer to step 005 to step 008, replace the longitudinal slip ratio with tire side slip angle and use the corresponding data to identify, similar to the identification of tire longitudinal force. When the longitudinal and lateral forces are all identified, the Unitire mathematical model of the composite working condition can be directly established by using the identified fitting equation in step 005.

[0223] In the modeling process, in order to prevent the internal lg function of the tire longitudinal and lateral friction coefficients from being less than zero and causing the model to report an error, the longitudinal slip ratio and the side slip angle are represented as non-zero positive numbers using the max function in the matlab function. Since the lateral force and the side slip angle are opposite in sign, the F y Need to multiply by a negative sign to be used as a lateral force output.

[0224] Step 010: Before establishing the hysteresis side slip angle / hysteresis slip ratio calculation model, the longitudinal and lateral velocities of the four wheels in the vehicle coordinate system need to be represented and converted to the tire coordinate system, refer to formula (10) and formula (11);

[0225] Step 011: According to the four-wheel longitudinal and lateral velocities in the tire coordinate system in step 012, the tire hysteresis side slip angle calculation formula can be modeled in Simulink according to formula (12)~formula (14);

[0226] Where, the normalized relaxation side slip length l ys The Gaussian function can be used to fit the data in Trucksim, and the fitting formula is as follows:

[0227] (35)

[0228] In formula (35), l1~l 12 are the normalized relaxation side slip length fitting parameters.

[0229] Step 012: The calculation of hysteresis slip ratio also needs to rely on the tire speed in step 010, in addition to solving the wheel angular velocity, the four-wheel angular velocity can be represented as:

[0230] (36)

[0231] In formula (36): ω w11 , ω w12 , ω w21 , ω w22 are the left front wheel, left rear wheel, right front wheel, and right rear wheel angular velocity, respectively. r11 , T r12 , T r21 , Tr22 Rolling resistance moment of left front wheel, left rear wheel, right front wheel, right rear wheel, respectively, T d Wheel driving moment, I w Wheel moment of inertia, F z11 , F z12 , F z21 , F z22 Vertical load of left front wheel, left rear wheel, right front wheel, right rear wheel, respectively, R surf Rolling resistance moment road surface coefficient, R c Rolling resistance moment constant component, R v Rolling resistance moment speed component.

[0232] The integrator initial value in the wheel speed calculation model is assigned by dividing the four-wheel longitudinal speed in the tire coordinate system in step 011 by the effective rolling radius.

[0233] To obtain the wheel driving moment in the above formula (36), in this embodiment, the error e between the actual vehicle speed and the longitudinal speed of the system vehicle body is taken as the input of the PI controller to realize vehicle speed tracking, and the control amount of the PI controller is the wheel driving moment. The control law of the continuous form PI controller can be expressed as:

[0234] (37)

[0235] In formula (37), K p is the proportional gain, K i is the integral gain.

[0236] The parameter adjustment of the PI controller can use the empirical method, that is, first increase K p to a certain order until the amplitude of the feedback signal reaches 95% of the target signal, and then increase K i to eliminate the steady-state error.

[0237] Step 013: Based on step 010 and step 012, refer to formulas (16)-(18) to model the four-wheel hysteresis slip rate κ d ; wherein the representation of the normalized relaxation side slip length can refer to the normalized relaxation side slip length fitting formula in step 011, and the fitting formula is as follows:

[0238] (38)

[0239] In formula (38), l 13 ~ l 24 is the normalized relaxation side slip length fitting parameter.

[0240] Step 014: After the modeling of the four-wheel hysteresis slip ratio and hysteresis side slip angle is completed, the tire vertical load needs to be obtained as the input of the Unitire tire model and also as the final output result; the tire vertical load is solved by a four-wheel vertical load solving model, which is modeled in Simulink with reference to formula (31);

[0241] After solving, the load transfer ratio is calculated according to the four-wheel vertical load as follows:

[0242] (39)

[0243] In formula (39), LTR is the four-wheel load transfer ratio.

[0244] Step 015: According to formulas (32)-(34), a sprung mass and mass center position estimation model can be established; the estimated sprung mass m s , the sprung mass center height h s , the front wheelbase l f , and the rear wheelbase l r ;

[0245] Step 016: According to the estimated sprung mass m s , the sprung mass center height h s , the front wheelbase l f , and the rear wheelbase l r obtained from the estimation model in step 015, the corresponding parameters of the nonlinear three-degree-of-freedom model in step 002, the four-wheel side slip angle / slip ratio calculation model in step 010, and the load solving model in step 014 are modified and replaced, so as to realize the vertical load estimation under the variable load condition.

[0246] Step 017: In Simulink, the input and output signals of the above modules are connected to the corresponding interfaces, and the signal flow diagram of the tire vertical load dynamic estimation system provided by the present application is shown in Figure 6 .

[0247] The input of the three-degree-of-freedom vehicle body dynamics model is the vehicle speed signal v and the steering wheel angle signal θ sw output by Trucksim, and the output is the vehicle body yaw rate ω r , the vehicle body longitudinal speed v x , the vehicle body lateral speed v y , the vehicle body longitudinal acceleration a x , and the vehicle body lateral acceleration a y .

[0248] The input of the Unitire tire model is the hysteresis side slip angle α d , the hysteresis slip ratio κ d , and the tire vertical load Fz , output is tire longitudinal force F x , tire lateral force F y ;

[0249] The input of four-wheel side slip angle / slip ratio calculation model is vehicle body longitudinal velocity v x , vehicle body lateral velocity v y , vehicle body yaw rate ω r , left and right front wheel steering angle θ, tire longitudinal force F x , tire vertical load F z , front wheelbase l f and rear wheelbase l r , output is hysteresis side slip angle α d , hysteresis longitudinal slip ratio κ d .

[0250] The input of four-wheel vertical load solving model is vehicle body longitudinal acceleration a x , vehicle body lateral acceleration a y , vehicle body longitudinal velocity v x , output is four-wheel vertical load F z and load transfer ratio LTR.

[0251] The input of center of mass position and sprung mass estimation module is front and rear axle static load F zfa , F zra , output is sprung mass m s , sprung mass center of mass height h s , front wheelbase l f , rear wheelbase l r , the correct connection of the above modules can realize system closed loop.

[0252] It should be noted that all integrators in Simulink model are discrete integrators, using ode45 solver for discrete solving, the simulation step in Trucksim and Simulink is consistent, both are 0.0005.

[0253] The corresponding working condition is set in Trucksim, and the accuracy of the model can be verified by joint simulation comparison with Simulink model. In Figure 7 , the tire vertical load is set to 10000N, compared with Similarity model based on magic formula (MF), the tire force boundary described by Unitire model is more consistent with the friction ellipse assumption.

[0254] Figure 8 The evaluation index of tire force prediction effect in is root mean square error RMSE, and the specific numerical results of tire force prediction error under composite working condition are given in table 1.

[0255] Table 1

[0256] Model name Unitire F x ]]> MF F x ]]> Unitire F y ]]> MF F y ]]> Root mean square error RMSE 265.4 378.5 176.2 1130.5

[0257] Unitire F x ) RMSE is reduced by 29.9% compared with the longitudinal force (MF F x ) of the Similarity model based on the magic formula, the lateral force (Unitire F y ) of the Unitire model under the combined working condition is reduced by 84.4% compared with the lateral force (MF F y ) of the Similarity model based on the magic formula. The Unitire model used in the application shows excellent tire force prediction performance under the combined working condition of braking and steering.

[0258] In Figure 9 , the output signal of the conventional load transfer model corresponds to subscript-1, the load transfer model described in the application corresponds to subscript-2, the reference model is a Trucksim high-fidelity vehicle model, and corresponds to subscript-T. The longitudinal speed of the vehicle is set to 40km / h and 60km / h respectively, and the steering wheel angle is continuously stepped 1 radian for three times. In order to compare the overall four-wheel load estimation effect, the load transfer rate error is used as an evaluation index. The maximum steady-state error of LTR of the conventional load transfer model is 21.9% at 40km / h and 26.4% at 60km / h, and the maximum steady-state error of LTR of the load transfer model described in the application is 4.8% at 40km / h and 2.6% at 60km / h.

[0259] In Figure 10 , the output signal of the center of mass position correction load transfer model described in the application corresponds to subscript-CG, the output signal of the load transfer model without considering the center of mass position has no subscript, and the output signal of the reference model corresponds to subscript-T. When the cargo mass is 4t, the vehicle speed is set to 60km / h, and the steering wheel angle is continuously angular step input and 0~202.5° ramp input respectively. When the steering wheel angle is stepped, the maximum steady-state error of LTR of the model without considering the center of mass position is 37.3%, and the maximum steady-state error of LTR of the center of mass position correction load transfer model is 3.9%. When the steering wheel is ramp input, the maximum error of the model without considering the center of mass position is 37.5%, and the maximum steady-state error of LTR of the center of mass position correction load transfer model is 4.9%.

[0260] The simulation experiment proves that the accuracy of the model proposed in the application is better than that of other existing models.

Claims

1. A dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions, characterized in that, The system includes: a nonlinear three-degree-of-freedom model of the vehicle body, a combined working condition Unitire tire model, a model for estimating the center of gravity position and sprung mass, and a model for solving the vertical loads of the four wheels; The formula for the nonlinear three-degree-of-freedom model of the vehicle body is as follows: （1） In equation (1), m s For the sprung mass, a x Let a be the longitudinal acceleration of the vehicle's center of gravity. y I is the lateral acceleration of the vehicle's center of gravity. z Let ω be the moment of inertia of the vehicle body rotating about the Z-axis. r B1 is the vehicle body yaw rate, B2 is the front axle track width, and B3 is the rear axle track width. f For the front wheelbase, l r V is the rear wheelbase. x v y The longitudinal and lateral velocities of the vehicle's center of gravity; F x F y For the longitudinal and lateral forces of the four wheels, F x11 F x12 F x21 F x22 F represents the longitudinal force on the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. y11 F y12 F y21 F y22 These represent the lateral forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; θ is the front wheel steering angle. 11 θ 12 These represent the steering angles of the left and right front wheels, respectively. The model uses the longitudinal force F of the four wheels. x Lateral force F of four wheels y longitudinal velocity of the center of mass v x The input is the left and right front wheel steering angle θ, and the variable to be solved is the longitudinal acceleration a of the vehicle's center of gravity. x Lateral acceleration of the vehicle's center of gravity, a y and yaw rate ω r ; Among the input variables, the longitudinal velocity v of the center of mass x Based on vehicle speed analysis, the left and right front wheel steering angles θ are derived from the steering wheel angle θ using the Ackermann steering angle formula. sw Transformed from, four-wheel longitudinal force F x and the lateral force F of the four wheels y The longitudinal acceleration 'a' of the vehicle's center of gravity was obtained by solving the combined working condition Unitire tire model. x And the lateral acceleration of the vehicle's center of gravity a y The vertical loads on the four wheels are calculated using the input four-wheel vertical load solution model, as shown in the following formula: （3） In equation (3), F z11 F z12 F z21 F z22 The vertical loads for the left front wheel, right front wheel, left rear wheel, and right rear wheel are respectively; h s h is the height of the center of mass of the sprung mass. f h is the height of the front axle roll center. r The rear axle roll center height, in meters. susp-f For the front axle suspension mass, m susp-r For the rear axle suspension mass, m t For tire quality, M rollf For the front axle body roll moment, M rollr This refers to the rear axle body roll moment; After solving, the load transfer rate is calculated based on the vertical loads of the four wheels, as shown in the following formula: （6） In equation (6), LTR is the four-wheel load transfer rate; The input to the four-wheel vertical load solution model is the longitudinal acceleration 'a' of the vehicle body obtained from the nonlinear three-degree-of-freedom model of the vehicle body. x and vehicle body lateral acceleration a y and the longitudinal speed v of the vehicle body x Spring load mass m s Spring load mass center of mass height h s Front wheelbase l f Rear wheelbase l r The output is the vertical load F of the four wheels. z and load transfer rate (LTR); Among them, the sprung mass m s Spring load mass center of mass height h s Front wheelbase l f Rear wheelbase l r The estimation is performed using the center of gravity position and sprung mass estimation module; The formulas for estimating the center of gravity position and sprung mass are as follows: （7） In equation (7), F zfa F zra These are the static front and rear axle loads of the vehicle, F zfae F zrae These represent the static front and rear axle loads of the vehicle when unloaded, respectively; m0 is the cargo mass, m1 is the cab mass, m2 is the cargo box mass, h0 is the cargo center of gravity height, h1 is the cab center of gravity height, and h2 is the cargo box center of gravity height; F zfa F zra F zfae F zrae Data obtained from strain sensors.

2. The dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions according to claim 1, characterized in that, The Ackermann angle formula is as follows: （2） In equation (2), θ sw Where L is the steering wheel angle, and i is the vehicle wheelbase. ag This refers to the steering system angle transmission ratio; Among them, the vehicle wheelbase L and the steering system angular transmission ratio i ag It is a known constant value.

3. The dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions according to claim 2, characterized in that, In formula (3), the front axle body roll moment M rollf and rear axle body roll moment M rollr The calculation formula is as follows: （4） In equation (4), K rollf K represents the front axle roll stiffness. rollr For rear axle roll stiffness, m f h is the equivalent mass of the front axle. df h is the distance from the center of mass of the spring-loaded front axle to the roll center. d The distance from the center of mass of the rear axle spring load to the roll center. This refers to the front axle body roll angle. The rear axle body roll angle can be expressed as: （5）。 4. The dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions according to claim 3, characterized in that, The formula for the Unitire tire model under combined operating conditions is: （8） In equation (8), Unitire is the dimensionless longitudinal slip ratio. Unitire is the dimensionless lateral slip ratio. For Unitire, μ is the dimensionless total slip ratio. x μ is the longitudinal friction coefficient of the tire. y The coefficient of lateral friction is... K is the dimensionless total shear force. x With K y These represent tire longitudinal slip and lateral stiffness, respectively; E is the curvature factor; and K... x K y Both E and E need to be obtained through parameter identification; among them, when using the pure working condition method to identify parameters, the curvature factor E needs to be distinguished according to the working condition. Let the curvature factor corresponding to the pure longitudinal slip working condition be E1, and the curvature factor corresponding to the pure lateral slip working condition be E2. μ 0x μ 0y μ mx μ my μ hx μ hy V mx V my N x N y For the parameters to be identified, the parameter K in equation (8) for the pure longitudinal slip condition is... x E1, μ 0x μ mx μ hx V mx N x The parameter for the pure sideslip condition is K. y E2, μ 0y μ my μ hy V my N y The above-mentioned parameters to be identified and the vertical load F z A linear relationship exists, which can be obtained through polynomial or linear fitting. The parameter required for the Unitire semi-empirical tire model is the Unitire lateral slip ratio S. y Unitire longitudinal slip ratio S x and vertical load F z ; where, the longitudinal slip ratio S of the unitire x Lateral slip ratio S y The following formula can be used to convert the result: （9） Tire vertical load F z The results were obtained from the four-wheel vertical load solution model.

5. The dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions according to claim 4, characterized in that, The required input for the Unitire semi-empirical tire model is the Unitire longitudinal slip ratio S. x The κ in the figure uses the hysteresis longitudinal slip ratio κ d Instead, the sideslip angle α is replaced by the hysteresis sideslip angle α. d replace; The hysteresis side slip angle α d Hysteresis longitudinal slip ratio κ d The hysteresis slip angle α of each wheel in the four-wheel slip angle / slip ratio calculation model is obtained through a four-wheel slip angle / slip ratio calculation model. d Represented as α delay11 α delay12 α delay21 α delay22 The formula is as follows: （10） In equation (10), α delay11 α delay12 α delay21 α delay22 These are the hysteresis sideslip angles for the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. y11 l y12 l y21 l y22 These are the relaxation lateral slip lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; α 11 α 12 α 21 α 22 These are the side deflection angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. （11） In equation (11), v wx11 v wx12 v wx21 v wx22 These represent the longitudinal velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system, v. wy11 v wy12 v wy21 v wy22 These represent the lateral velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the tire coordinate system, respectively. （12） In equation (12), v x11 v x12 v x21 v x22 These represent the longitudinal velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the vehicle coordinate system, v. y11 v y12 v y21 v y22 These are the lateral velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel in the vehicle coordinate system, respectively. （13） The relaxation side slip length of each tire is calculated according to the general empirical formula built into the Trucksim software, and is expressed as the product of the normalized relaxation side slip length, the normalized load, and the side slip ratio factor: （14） In equation (14), gain y For the lateral scaling factor, l ys To normalize the relaxed lateral slip length, F zs The normalized load is r, where r is the effective rolling radius of the tire; the normalized load F zs The actual tire vertical load F z Divide by the tire's rated load; normalized relaxation lateral length Then, the Gaussian function is used to fit the data from Trucksim, and the fitting formula is as follows: （15） In equation (15), l1~l 12 The fitting parameters for the normalized relaxed lateral deviation length; The hysteresis longitudinal slip ratio κ of each wheel in the four-wheel slip angle / slip ratio calculation model d Represented as κ delay11 κ delay12 κ delay21 κ delay22 The formula is as follows: （16） In equation (16), κ delay11 κ delay12 κ delay21 κ delay22 The longitudinal slip ratios of the left front wheel, right front wheel, left rear wheel, and right rear wheel are respectively, l x11 l x12 l x21 l x22 These are the slack longitudinal slip lengths of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; κ 11 κ 12 κ 21 κ 22 These are the longitudinal slip ratios of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. （17） In equation (17), ω w11 ω w12 ω w21 ω w22 These are the rotational angular velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. （18） In equation (18), F x11 F x12 F x21 F x22 The longitudinal forces T on the left front wheel, right front wheel, left rear wheel, and right rear wheel are respectively. r11 T r12 T r21 T r22 The rolling resistance torques T for the left front wheel, right front wheel, left rear wheel, and right rear wheel are respectively. d This refers to the driving torque of the wheels. （19） In equation (19), R surf R is the road surface coefficient for rolling resistance moment. c R is the constant component of the rolling resistance torque. v The velocity component of the rolling resistance torque; In equation (16), the relaxation longitudinal slip length of each wheel is also expressed using the general empirical formula in Trucksim: （20） In equation (20), gain x For the longitudinal slip ratio factor, l xs The normalized relaxation longitudinal slip length is used; the normalized relaxation longitudinal slip length is then fitted using the Gaussian function in conjunction with the data from Trucksim. The fitting formula is as follows: （21） In equation (21): l 13 ~l 24 The fitting parameters for the normalized relaxed lateral deviation length; The input to the four-wheel slip angle / slip ratio calculation model is the vehicle's longitudinal velocity v. x lateral speed of the vehicle body v y yaw rate ω of the vehicle body r Left and right front wheel steering angles θ, tire longitudinal force F x and tire vertical load F z Among them, the longitudinal velocity v of the vehicle body x and vehicle lateral speed v y Based on vehicle speed analysis, the steering angles θ of the left and right front wheels are also derived from the steering wheel angle θ using the Ackermann steering angle formula. sw Derived from; vehicle body yaw rate ω r The longitudinal force F of the tire is calculated based on a nonlinear three-degree-of-freedom vehicle body model. x Calculated based on the Unitire semi-empirical tire model; The tire vertical load F required for the four-wheel slip angle / slip ratio calculation model z The results were obtained from the four-wheel vertical load solution model.

6. The dynamic estimation system for the vertical load of four wheels of a commercial vehicle under variable load conditions according to claim 5, characterized in that, The linear relationship between the parameters to be identified and the vertical load in the Unitire tire model under combined working conditions is as follows: （22） In equation (22), a1~a 33 These are the parameters to be fitted, which are related to the vertical load.

7. The simulation method for the dynamic estimation system of vertical load on four wheels of a commercial vehicle under variable load conditions according to claim 6, characterized in that, The steps of this method are as follows: Step 001: Obtain the basic parameters required by the load estimation system, including the vehicle body's moment of inertia about the Z-axis. z The unloaded sprung mass m of the vehicle s Front and rear axle suspension mass (m) susp-f m susp-r Tire mass m t Front and rear wheelbase l f and l r , Front and rear axle track B1 and B2, and the height of the sprung center of gravity h when the vehicle is unloaded se Front and rear axle roll stiffness K rollf K rollr Wheel rotational inertia I w The free rolling radius of a tire, i.e., the tire radius r; Among these, the unit of length is uniformly m, the unit of mass is uniformly kg, and the unit of moment of inertia is uniformly kg / m. 2 The unit of roll stiffness is N m / rad; Step 002: After obtaining the necessary modeling parameters, a vehicle dynamics model can be established in Simulink based on a nonlinear three-degree-of-freedom model; this model uses the longitudinal force F of the four wheels as an example. x Lateral force F of four wheels y longitudinal velocity of the center of mass v x The input is the left and right front wheel steering angle θ, and the variable to be solved is the longitudinal acceleration a of the vehicle's center of gravity. x Lateral acceleration of the vehicle's center of gravity, a y and yaw rate ω r ; In this step, to avoid algebra loops in the system, memory modules need to be connected in series for the longitudinal acceleration and lateral acceleration of the vehicle body, and the initial value of the discretized integrator is set to the eps function to avoid singularities in the system; the initial value of the integrator in the lateral motion equilibrium equation is assigned the vehicle speed in Trucksim. Step 003: Obtain experimental data of the tire under pure longitudinal slip and pure lateral slip conditions, or use the 305 / 75 R22.5 tire data built into the Trucksim software; Step 004: Import the tire longitudinal force data under pure longitudinal slip condition and the tire lateral force data under pure sideslip condition, which include various types of vertical loads, into Matlab; Step 005: Use the curve fitting toolbox in Matlab software to identify parameters. First, import the tire longitudinal force data under a single characteristic vertical load in pure longitudinal slip condition into the Matlab workspace, and use the longitudinal slip rate as the independent variable to perform custom equation fitting. Step 006: After fitting the tire longitudinal force under a single characteristic load, K... x μ 0x μ mx μ hx V mx N x Record the values ​​of the seven parameters, including E1, and repeat step 006 until the tire longitudinal force under all characteristic loads is fitted and the values ​​of the above-mentioned identification parameters are recorded. Step 007: Based on the values ​​of the seven identification parameters recorded in Step 006 under different characteristic loads, fit each identification parameter to the vertical load F using the fitting equation shown in Equation (22). z Perform polynomial fitting; Step 008: Record K x μ 0x μ mx μ hx V mx N x The fitting equations for the seven parameters E1 are used. Each fitting equation is substituted into the Uniforme semi-empirical model and a mathematical model is built using MATLAB functions in Simulink. Step 009: Repeat steps 005 to 008 using the tire lateral force data under pure lateral bias conditions to complete the K... y E2, μ 0y μ my μ hy V my N y The fitting equations for 7 parameters were obtained, and each fitting equation was substituted into the Unitire semi-empirical model to establish the Unitire mathematical model for the composite working condition. Step 010: Based on formulas (10) to (21), establish a hysteresis sideslip angle / hysteresis slip ratio calculation model in Simulink; Step 011: Establish a four-wheel vertical load solution model in Simulink according to formulas (3) to (5); Step 012: Establish a model for estimating the sprung mass and center of mass position based on formula (7); Step 013: In Simulink, connect the input and output signals of each module to the corresponding interfaces, as follows: The inputs to the three-degree-of-freedom vehicle dynamics model are the vehicle speed signal v and the steering wheel angle θ output by Trucksim. sw The signal output is the vehicle body yaw rate ω. r longitudinal speed v of the vehicle body x lateral speed of the vehicle body v y longitudinal acceleration a of the vehicle body x Lateral acceleration of the vehicle body a y ; The input to the Unitire tire model is the hysteresis slip angle α. d Hysteresis slip ratio κ d Tire vertical load F z The output is the longitudinal force F of the tire. x Tire lateral force F y ; The input to the four-wheel slip angle / slip ratio calculation model is the vehicle's longitudinal velocity v. x lateral speed of the vehicle body v y yaw rate ω of the vehicle body r Left and right front wheel steering angles θ, tire longitudinal force F x Tire vertical load F z Front wheelbase l f and rear wheelbase l r The output is the hysteresis sideslip angle α. d Hysteresis longitudinal slip ratio κ d ; The input to the four-wheel vertical load solution model is the vehicle's longitudinal acceleration a. x Lateral acceleration of the vehicle body a y longitudinal speed v of the vehicle body x The output is the four-wheel vertical load F. z and load transfer rate (LTR); The input to the center of gravity position and sprung mass estimation module is the static load F of the front and rear axles. zfa F zra The output is the sprung mass m. s Spring load mass center of mass height h s Front wheelbase l f Rear wheelbase l r After correctly connecting the above modules, a closed-loop system can be achieved.

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