Wheel-ground contact model establishment method suitable for soft road surface

Abstract

The invention relates to a wheel-ground contact model establishing method suitable for a soft road surface, in particular to a novel wheel-ground contact model establishing method suitable for the soft road surface based on a Bekker tire model and a linear tire model, and the method comprises the following steps: analyzing and simplifying a Bekker model; in combination with the linearized tire model, a wheel-ground contact model suitable for the soft road surface is established; a Matlab / Simulink model used for simulation verification is set up; and a Chrono simulation experiment is carried out to obtain the fitting effect of the built model on the longitudinal and lateral forces of the tire. According to the wheel-ground contact model theoretical derivation and experimental verification method suitable for the soft road surface, the influence of ground deformation on longitudinal and lateral force of tires is fully considered, the complexity of the model is reduced through combination of a complex model (Bekker model) and a simple model (linearized tire model), and the method can be used for vehicle control.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle motion control, and in particular to a vehicle dynamics control method for off-road conditions. Background Art

[0002] In the field of vehicle motion control, the wheel-ground contact model is a prerequisite for establishing an accurate vehicle model and developing motion control algorithms. Therefore, it is crucial to establish an accurate and practical wheel-ground contact model to improve the performance of vehicle motion control. As a classic tire model, the Bekker model is particularly suitable for soft roads and is valued for its ability to describe the nonlinear characteristics of tires under different road conditions. However, the complexity of the Bekker model brings challenges in practical applications, especially in vehicle control systems that require real-time response. Complex models not only increase the computational burden, but may also affect the real-time and reliability of the control algorithm.

[0003] At present, the main evaluation method for tire force fitting is to obtain the true value of tire force during driving through experiments and compare it with the model calculation value. The main problems of this method are model establishment and true value acquisition and experimental verification:

[0004] 1) Model building: In vehicle control systems, the computational efficiency of the model is a key factor, and the tire model needs to be able to calculate quickly to provide real-time feedback. Therefore, an overly complex model may cause computational delays and affect control performance, while the special wheel-ground contact conditions on soft roads will inevitably lead to increased model complexity;

[0005] 2) True value acquisition and experimental verification: Obtaining accurate tire performance data requires a large number of experiments, which is not only costly but also may be limited by experimental conditions. The quality and quantity of experimental data directly affect the accuracy and reliability of the model. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention proposes a method for establishing a wheel-ground contact model suitable for soft roads, which is an innovative wheel-ground contact model. The model significantly reduces the complexity of the Bekker model by simplifying the mathematical expression, and obtains the additional resistance of the tire due to ground deformation. This simplification not only reduces the consumption of computing resources, but also maintains the accurate fitting of the model to the tire force, making it more suitable for real-time vehicle control applications.

[0007] Technical solution:

[0008] A method for establishing a wheel-ground contact model suitable for soft roads is provided, which is a new method for establishing a wheel-ground contact model suitable for soft roads based on the Bekker tire model and the linearized tire model.

[0009] The following steps are involved:

[0010] Step 1: Analyze and simplify the Bekker model;

[0011] Step 2: Combine the linearized tire model to establish a wheel-ground contact model suitable for soft roads.

[0012] In the embodiment, a Matlab / Simulink model is further constructed for simulation verification; the Chrono simulation experiment obtains the fitting effect of the constructed model on the longitudinal and lateral forces of the tire.

[0013] Beneficial Effects

[0014] The invention provides a theoretical derivation and experimental verification method of a wheel-ground contact model suitable for soft roads, which fully considers the influence of ground deformation on the longitudinal and lateral forces of the tire. By combining a complex model (Bekker model) with a simple model (linearized tire model), the model complexity is reduced and can be used for vehicle control.

[0015] The model of the present invention combines the low complexity of the linearized tire model with the high precision of Bekker, and realizes the rapid and accurate prediction of the longitudinal and lateral forces of the tire. The establishment of this model not only improves the handling and stability of the vehicle on soft roads, but also provides more efficient and reliable theoretical support for the design of vehicle control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The following is a schematic diagram of the implementation process and logic of the method according to the embodiment of the present invention;

[0017] Figure 2 This is the fitting effect of the tire force on soft road surface according to the embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0019] Example 1

[0020] The present invention combines the Bekker model and the linearized tire model, targets the vehicle motion information under soft road conditions, aims to accurately obtain the tire force, and establishes a wheel-ground contact model suitable for soft roads, thereby providing more reliable vehicle dynamics parameters for the establishment of the vehicle model and the operation of the vehicle control system. It mainly includes the following steps:

[0021] Step 1: Simplify the Bekker model

[0022] 1.1 Derivation of the integral form of the Bekker model

[0023] First, according to the Coulomb equation, the relationship between soil shear stress and normal stress can be obtained:

[0024] τ max =c+σ max tanφ

[0025] Among them, τ max is the maximum shear stress on the contact surface, σ max is the maximum normal stress on the contact surface, c and φ are soil cohesion and internal friction angle, respectively, which are inherent parameters of the soil.

[0026] When a vehicle travels on soft ground, it will inevitably cause soil deformation, that is, the tires will sink, resulting in geometric quantities such as wheel sinking amount, wheel contact angle, and wheel liftoff angle.

[0027] According to geometry, the wheel sinking amount can be calculated using the following formula:

[0028] z(θ)=r(cosθ-cosθ1)

[0029] Where r represents the effective radius of the wheel, θ1 represents the angle from the starting point of contact with the terrain to the point of maximum stress, and correspondingly θ2 represents the angle from the point of maximum stress to the point of separation from the terrain.

[0030] According to Bekker, the positive pressure between the tire and the soil is related to the wheel sinking amount and the inherent parameters of the soil. The pressure-sinking relationship is:

[0031]

[0032] Where n and k c and k φ are the subsidence index, soil cohesion coefficient and soil friction coefficient, which are determined by a flat plate sinking test.

[0033] In addition, according to Bekker, the soil shear stress can be calculated as:

[0034] τ=τ max (1-exp(-j / k))

[0035] Where k is the shear modulus and j represents the soil deformation, which can be calculated by the following formula:

[0036]

[0037] According to Coulomb's formula, Bekker's theory and wheel sinking geometry, the integral form of the soil force on the tire can be obtained:

[0038]

[0039] 1.2 Derivation of the additional ground resistance formula

[0040] According to the derivation process of step 1.1, the complete tire force calculation formula can only be given in the form of integration, which has high calculation cost. It also contains a large number of parameters that need to be obtained in real time. Parameters such as soil cohesion and internal friction angle cannot be measured in real time by sensors and are difficult to estimate in practice. Therefore, it is necessary to reduce the complexity of the formula through some reasonable assumptions and simplifications, and solve the additional force from the soft ground in real time as a correction term to improve the linear tire model.

[0041] Assumption 1: θ2 = 0 ° , θ2 is the angle from the maximum stress point to the terrain detachment contact point, which is generally small and can be ignored.

[0042] Assumption 2: The maximum shear and normal stresses occur at the same point, located at (θ1+θ2) / 2, that is, θ m =θ1 / 2.

[0043] Assumption 3: The shear and normal stress distribution curves are approximately linear, that is, in actual calculation and solution, the stress at each location can be obtained by linear calculation of the maximum stress.

[0044] Assumption 4: The left and right wheels are subjected to the same forces.

[0045] With the help of the above assumptions, the following deduction can be made:

[0046] θ1=arccos((rz) / r)

[0047] A=rbθ1

[0048]

[0049] τ max =c+σ max tanφ

[0050] Therefore, the expression for the additional soil resistance on the tire due to wheel sinking when the vehicle is driving on a soft road is as follows:

[0051]

[0052] in is the additional lateral and longitudinal soil resistance of the tire, k is the stress coefficient. Due to the existence of assumptions 2 and 3, the resultant force on the contact surface between the tire and the ground can be expressed by the maximum stress.

[0053] Step 2: Combining the Bekker model with the linearized tire model

[0054] Additional ground resistance obtained in step 1 and It is a correction term, which is combined with the linearized tire model to obtain a tire model suitable for tire force fitting on soft roads.

[0055] 2.1 Derivation of Linearized Tire Model

[0056] First, it is necessary to derive the linear tire model formula. On soft roads, the vehicle will not pass at too high a speed, that is, the tire side slip angle will not be too large, so the linear tire model can be used as a reference.

[0057] The linearized tire model assumes that when the vehicle is driving, the actual driving direction of the wheel will deviate from the wheel center plane, resulting in a tire slip angle. When the tire slip angle is small, the lateral force on the tire can be approximately expressed as a linear function of the tire slip angle:

[0058] F y =C α α

[0059] Where: C α is the tire cornering stiffness, and α is the tire slip angle.

[0060] Similarly, when the slip is small, the linearized tire model assumes that the tire longitudinal force is proportional to the slip:

[0061] F x =C s ·S

[0062] Where: C s is the longitudinal stiffness of the tire, and S is the wheel slip rate.

[0063] The present invention ignores axle load transfer and suspension deformation, and regards the four-wheel vehicle model as consisting of two bicycle models.

[0064] From the linear tire model formula, we know that the tire longitudinal force F x , lateral force F y The solution requires the longitudinal stiffness C s , lateral stiffness C α , tire slip angle α and wheel slip rate S, where the longitudinal and lateral stiffness are fixed parameters of the vehicle and are known.

[0065] The longitudinal slip of the wheel can be described as:

[0066]

[0067] Among them, V xis the longitudinal speed of the vehicle, R is the effective radius of the wheel, and ω is the angular velocity of the wheel.

[0068] When the wheel has lateral elasticity, the direction of the wheel will deviate from the direction of the wheel plane. The angle between the displacement direction of the tire contact mark center and the X-axis is defined as the tire slip angle. According to theoretical mechanics knowledge, the tire slip angle can be expressed as:

[0069]

[0070] Among them, V y is the lateral speed of the vehicle, δ is the front wheel turning angle, a and b are the distances from the center of mass of the vehicle to the front axle and rear axle respectively, is the vehicle yaw angular velocity.

[0071] Through the above derivation, all the parameters for calculating tire force are obtained. Then, under the assumption of linear tire model, the lateral and longitudinal forces on the tire can be expressed as:

[0072]

[0073] Among them, f represents the parameters related to the front wheel, and r represents the parameters related to the rear wheel.

[0074] 2.2 Combined Bekker and Linearized Tire Model

[0075] According to the derivation of the additional ground resistance and the linear tire model in step 1.2 and step 2.1, a tire model suitable for soft roads is built. Due to its unique ground characteristics, soft ground will cause tire slippage in most cases, resulting in less friction than general roads. Therefore, the linear tire model can be changed proportionally to make it suitable for soft ground. Combining the additional ground resistance formula and the linear tire model obtained in step 1.2 and step 2.1, the final form of the wheel-ground contact model can be obtained:

[0076]

[0077] F xr =k xr C sr ·S r

[0078] F yr =k yr C αr α r

[0079] Among them, the subscripts f and r represent the parameters related to the front and rear wheels respectively, and k yf , k xf is the linearization scale factor of the tire model. Since the rear wheel trajectory basically coincides with the front wheel, the additional ground resistance is ignored.

[0080] Since this formula is a linear combination of the linear tire model and the additional soil resistance, the respective coefficients can be obtained by a simple least squares method.

[0081] Step 3: Build a soft road simulation environment

[0082] Step 2.2 has given a complete wheel-ground contact model, which now needs to be verified. However, due to the special soft road conditions, ground parameters such as cohesion and internal friction angle are difficult to measure. How to obtain accurate model parameters and correct tire force reference values ​​is the difficulty of the present invention.

[0083] This embodiment uses Chrono software to define the experimental environment, establishes a Chrono-Simulink joint simulation environment, obtains model parameters in real time, and outputs the true value and calculated value of tire force. Soft road surface is the working condition faced by off-road vehicles. In order to ensure the rationality of the experiment, this embodiment redefines key parameters such as the mass, wheelbase, track width, and tire lateral stiffness of the experimental vehicle. In order to provide the model with parameters that are difficult to measure, such as soil cohesion, internal friction angle, and settlement index, this embodiment redefines the road surface parameters to ensure the accuracy of the model parameters.

[0084] Double lane change is a common working condition for evaluating vehicle driving performance. This embodiment uses this as the vehicle motion trajectory to observe whether the model can achieve tire force fitting. The process is that the vehicle moves from the original lane to the adjacent parallel lane within a certain distance through the driver's operation of the steering wheel, and then returns to the original lane. During this period, the vehicle should not exceed the lane boundary line.

[0085] Step 4: Collect joint simulation data, adjust and verify the model

[0086] According to step 3, the experimental conditions such as vehicle, ground, and working conditions are set up to conduct a joint simulation experiment. The Chrono-Simulink joint simulation experiment environment can obtain various signals during vehicle driving in real time, and by adjusting the weight coefficient, the model calculation value of the tire force is fitted.

[0087] 4.1 Joint simulation experiment

[0088] Start the Chrono-Simulink joint simulation. In this example, the vehicle is traveling on a soft road at a speed v ref =40km / h for a single double lane change. During this period, when the road conditions remain unchanged, the vehicle speed, wheel slip rate, tire sideslip angle, spindle position and tire force signals are collected.

[0089] 4.2 Data post-processing and parameter adjustment

[0090] According to the simulation results obtained in step 4.1, extract the effective fragments of the collected signal and adjust the model parameter k x ,k y ,k xf ,k yf , and obtain the calculated value of tire force based on the wheel-ground contact model.

[0091] 4.3 Error calculation

[0092] According to the tire force calculation value obtained in step 4.2, refer to the normalized root mean square error calculation formula to calculate the percentage error between the calculated value and the tire force measurement value:

[0093]

[0094] The above description is only a description of the preferred embodiments of the present application, and is not intended to limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical contents shall be deemed as equivalent effective embodiments and shall fall within the scope of protection of the technical solution of the present application.

Claims

1. A method for establishing a wheel-ground contact model suitable for soft roads, characterized in that: The following steps are involved: Step 1: Analyze and simplify the Bekker model; Step 2: Combine the linearized tire model to establish a wheel-ground contact model suitable for soft roads.

2. A method for establishing a wheel-ground contact model suitable for soft roads as claimed in claim 1, characterized in that: Step 1: Simplify the Bekker model Step 1.1 Derive the integral form of the Bekker model First, according to the Coulomb equation, the relationship between soil shear stress and normal stress is obtained: t max =c+σ max tanf Among them, τ max is the maximum shear stress on the contact surface, σ max is the maximum normal stress on the contact surface, c and φ are the soil cohesion and internal friction angle, respectively, and are the inherent parameters of the soil; When a vehicle is driving on soft ground, the deformation of the soil, that is, the tire sinks, produces geometric quantities such as wheel sinking amount, wheel contact angle, and wheel ground lift angle. Based on geometry, the wheel sinking amount is calculated using the following formula: z(θ)=r(cosθ-cosθ1) Where r represents the effective radius of the wheel, θ1 represents the angle from the point where the terrain starts to contact to the point where the maximum stress is, and correspondingly θ2 represents the angle from the point where the maximum stress is to the point where the terrain leaves contact; According to the Bekker model, the positive pressure between the tire and the soil is related to the wheel sinking amount and the inherent parameters of the soil. The pressure-sinking relationship is: Where n and k c and k φ are the subsidence index, soil cohesion coefficient, and soil friction coefficient, which are determined by plate sinking tests; In addition, according to Bekker, the soil shear stress is calculated as: τ=τ max (1-exp(-j / k)) Where k is the shear modulus and j represents the soil deformation, which is calculated by the following formula: According to Coulomb's formula, Bekker's theory and wheel sinking geometry, the integral form of the soil force on the tire is obtained: Step 1.2 Derive the additional ground resistance formula The additional force from soft ground is solved in real time as a correction term to improve the linear tire model; Assumption 1: θ2 = 0, θ2 is the angle from the maximum stress point to the terrain detachment point, which is small and can be ignored; Assumption 2: The maximum shear and normal stresses occur at the same point, located at (θ1+θ2) / 2, that is, θ m =θ1 / 2; Assumption 3: The shear and normal stress distribution curves are approximately linear, that is, in actual calculation and solution, the stress at each location is obtained by linear calculation of the maximum stress; Assumption 4: The left and right wheels are subjected to the same forces; With the help of the above assumptions, the following deduction is made: θ1=arccos((rz) / r) A=rbθ1 t max =c+σ max tanf Therefore, the expression for the additional soil resistance of the tire due to wheel sinking when the vehicle is driving on a soft road is as follows: in is the additional lateral and longitudinal soil resistance of the tire, k is the stress coefficient. Due to the existence of assumptions 2 and 3, the resultant force on the contact surface between the tire and the ground can be expressed by the maximum stress; Step 2: Combining the Bekker model with the linearized tire model Additional ground resistance obtained in step 1 and is a correction term, which is combined with the linearized tire model to obtain a tire model suitable for tire force fitting on soft roads; Step 2.1 Derive the linear tire model First, the linear tire model formula is derived; on soft roads, the linearized tire model is used as a reference; it is determined by the linearized tire model that when the vehicle is driving, the actual driving direction of the wheel will deviate from the wheel center plane, resulting in a tire slip angle. When the tire slip angle is small, the lateral force on the tire can be approximately expressed as a linear function of the tire slip angle: F y =C α ·a Where: C α is the tire cornering stiffness, α is the tire slip angle; Similarly, when the slip is small, the linearized tire model confirms that the tire longitudinal force is proportional to the slip: F x =C s ·S Where: C s is the longitudinal stiffness of the tire, S is the wheel slip rate; Ignoring axle load transfer and suspension deformation, the four-wheel vehicle model is considered to consist of two bicycle models; From the linear tire model formula, we know that the tire longitudinal force F x , lateral force F y The solution requires the longitudinal stiffness C s , lateral stiffness C α , tire slip angle α and wheel slip rate S, where longitudinal and lateral stiffness are fixed parameters of the vehicle and are known; The longitudinal slip of the wheel is described as: Among them, V x is the longitudinal speed of the vehicle, R is the effective radius of the wheel, and ω is the angular velocity of the wheel; When the wheel has lateral elasticity, the direction of the wheel will deviate from the direction of the wheel plane. The angle between the displacement direction of the tire contact mark center and the X-axis is defined as the tire slip angle. According to theoretical mechanics knowledge, the tire slip angle is expressed as: Among them, V y is the lateral speed of the vehicle, δ is the front wheel turning angle, a and b are the distances from the center of mass of the vehicle to the front axle and rear axle respectively, is the vehicle yaw angular velocity; Through the above derivation, all the parameters for calculating tire force are obtained. Then, under the assumption of linear tire model, the lateral and longitudinal forces on the tire are expressed as: F xf =C sf ·S f F xr =C sr ·S r Among them, f represents the parameters related to the front wheel, and r represents the parameters related to the rear wheel; Step 2.2 Combining Bekker and Linearized Tire Models According to the derivation of the additional ground resistance and the linear tire model in steps 1.2 and 2.1, a tire model suitable for soft roads is constructed.

3. A method for establishing a wheel-ground contact model suitable for soft roads as claimed in claim 1, characterized in that: Due to its unique ground characteristics, soft ground will cause tire slip in most cases, resulting in the friction provided by the ground being less than that of ordinary roads. Therefore, the linear tire model is changed proportionally to make it suitable for soft ground. Combining the additional ground resistance formula obtained in steps 1.2 and 2.1 with the linear tire model, the final form of the wheel-ground contact model is obtained: F xr =k xr C sr ·S r F yr =k yr C αr ·a r Among them, the subscripts f and r represent the parameters related to the front and rear wheels respectively, and k yf , k xf is the linearized tire model scale factor. Since the rear wheel trajectory basically coincides with the front wheel, the additional ground resistance is ignored. Since this formula is a linear combination of the linear tire model and the additional soil resistance, the respective coefficients are obtained by a simple least squares method.

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