A wheel-ground contact model establishment method suitable for soft road surface

Abstract

The present application relates to a kind of wheel ground contact model establishing method suitable for soft road surface, it is a kind of new wheel ground contact model establishing method suitable for soft road surface based on Bekker tire model and linearization tire model, it includes: analysis and simplification Bekker model;Combined with linearization tire model, wheel ground contact model suitable for soft road surface is established;Matlab / Simulink model for simulation verification is built;The fitting effect of the model built is obtained to tire longitudinal force and lateral force by Chrono simulation experiment.The wheel ground contact model theoretical derivation and experimental verification method suitable for soft road surface provided by the present application, the influence of ground deformation on tire longitudinal force and lateral force is fully considered, by the combination of complex model (Bekker model) and simple model (linearization tire model), the model complexity is reduced, and it can be used for vehicle control.

Description

Technical Field

[0001] This invention relates to the field of vehicle motion control technology, and in particular to a vehicle dynamics control method for off-road conditions. Background Technology

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

[0003] Currently, 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 calculated value of the model. The main problems with this method are in two aspects: model building and true value acquisition and experimental verification.

[0004] 1) Model Building: In vehicle control systems, computational efficiency is a key factor. Tire models need to be able to calculate quickly to provide real-time feedback. Therefore, overly complex models may lead to computational delays and affect control performance. The unique wheel-to-ground contact conditions on soft road surfaces inevitably increase model complexity.

[0005] 2) Truth Value Acquisition and Experimental Validation: Obtaining accurate tire performance data requires extensive experimentation, which is not only costly but also potentially 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] To address the problems existing in current technologies, this invention proposes a method for establishing a wheel-ground contact model suitable for soft road surfaces. This innovative wheel-ground contact model significantly reduces the complexity of the Bekker model by simplifying mathematical expressions, thus obtaining the additional resistance experienced by the tire due to ground deformation. This simplification not only reduces the consumption of computational resources but also maintains the model's accurate fit to tire forces, making it more suitable for real-time vehicle control applications.

[0007] Technical solution:

[0008] A novel method for establishing wheel-ground contact models suitable for soft road surfaces is presented, based on the Bekker tire model and a linearized tire model.

[0009] Includes the following steps:

[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 road surfaces.

[0012] In this embodiment, a Matlab / Simulink model was further built for simulation verification; Chrono simulation experiments were conducted to obtain the fitting effect of the built model on the longitudinal and lateral forces of the tire.

[0013] Beneficial effects

[0014] The present invention provides a theoretical derivation and experimental verification method for wheel-ground contact model applicable to soft road surfaces. It 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 it can be used for vehicle control.

[0015] This invention's model combines the low complexity of linearized tire models with the high accuracy of Bekker models, enabling rapid and accurate prediction of longitudinal and lateral forces on the tire. The establishment of this model not only improves vehicle handling and stability on soft surfaces but also provides more efficient and reliable theoretical support for the design of vehicle control systems. Attached Figure Description

[0016] Figure 1 This is a schematic diagram illustrating the implementation process and logic of the method in the embodiments of the present invention;

[0017] Figure 2 This is an example of the fitting effect of tire force on soft road surfaces in an embodiment of the present invention. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0019] Example 1

[0020] This invention combines the Bekker model and a linearized tire model to accurately obtain tire forces under soft road surface conditions, establishing a wheel-ground contact model suitable for soft surfaces. This provides more reliable vehicle dynamic parameters for vehicle model creation and vehicle control system operation. The main steps include:

[0021] Step 1: Simplify the Bekker model

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

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

[0024] τ max =c+σ max tanφ

[0025] Where, τ max It is the maximum shear stress on the contact surface, σ max It is the maximum normal stress on the contact surface, c and φ are the soil cohesion and internal friction angle, respectively, and φ is an inherent parameter of the soil.

[0026] When a vehicle drives on soft ground, it will inevitably cause soil deformation, that is, the tire will sink, resulting in geometric quantities such as wheel sinkage, wheel ground angle, and wheel lift-off angle.

[0027] According to geometry, the wheel sinkage 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 point of initial contact with the terrain to the point of maximum stress, and θ2 represents the angle from the point of maximum stress to the point of separation from the terrain.

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

[0031]

[0032] Where n and k c and k φ These are the subsidence index, soil cohesion coefficient, and soil friction coefficient, which are determined through plate subsidence tests.

[0033] Furthermore, according to Bekker, soil shear stress can be calculated as follows:

[0034] τ=τ max (1-exp(-j / k))

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

[0036]

[0037] Based on Coulomb's formula, Bekker's theory, and the geometric relationship of wheel sinking, the integral form of the soil force acting on the tire can be derived:

[0038]

[0039] 1.2 Derivation of the formula for additional ground resistance

[0040] Based on the derivation process in step 1.1, the complete tire force calculation formula can only be given in integral form, which is computationally expensive. It also includes a large number of parameters that need to be acquired 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 to solve for the additional force from 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 point of maximum stress to the point of contact with the terrain. This angle is generally small and can be ignored.

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

[0043] Assumption 3: The shear and normal stress distribution curves are approximately linear, meaning that in actual calculations, the stress at each point can be obtained through linear calculations of the maximum stress.

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

[0045] Based on the above assumptions, the following derivation 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 experienced by the tires due to wheel sinking when a vehicle is driving on a soft road surface can be obtained as follows:

[0051]

[0052] in The additional soil resistance experienced by the tire in the lateral and longitudinal directions is denoted by k, which 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 represented by the maximum stress.

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

[0054] The additional ground resistance obtained in step one and As a correction term, it is combined with the linearized tire model to obtain a tire model suitable for fitting tire forces on soft roads.

[0055] 2.1 Derivation of a linearized tire model

[0056] First, the formula for the linear tire model needs to be derived. On soft surfaces, vehicles will not travel at excessively high speeds, meaning the tire slip angle will not be too large; therefore, a linearized tire model can be used as a reference.

[0057] The linearized tire model assumes that when a vehicle is in motion, the actual direction of the wheel deviates from the wheel's center plane, resulting in a tire slip angle. When the tire slip angle is small, the lateral force on the tire can be approximated as a linear function of the tire slip angle.

[0058] F y =C α ·α

[0059] Where: C α Let α be the tire lateral stiffness and α be the tire lateral angle.

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

[0061] F x =C s ·S

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

[0063] This invention ignores axle load transfer and suspension deformation, and considers the four-wheeled vehicle model as being composed of two bicycle models.

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

[0065] The longitudinal slippage of a wheel can be described as:

[0066]

[0067] Among them, V xR is 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 a wheel has lateral elasticity, its direction of travel will deviate from the direction of the wheel plane. The angle between the displacement direction of the center of the tire contact patch and the X-axis is defined as the tire slip angle. According to theoretical mechanics, the tire slip angle can be expressed as:

[0069]

[0070] Among them, V y Let denot be the lateral velocity of the vehicle, δ be the front wheel steering angle, and a and b be the distances from the vehicle's center of gravity to the front and rear axles, respectively. Let yaw rate be the vehicle's angular velocity.

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

[0072]

[0073] Where f represents the front wheel related parameters and r represents the rear wheel related parameters.

[0074] 2.2 Combined Bekker and Linearized Tire Model

[0075] Based on 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 road surfaces is constructed. Due to its unique surface characteristics, soft ground often causes tire slippage, resulting in less friction than on typical roads. Therefore, the linear tire model can be proportionally modified to suit soft ground. Combining the additional ground resistance formula and the linear tire model obtained in steps 1.2 and 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] Where the subscripts f and r represent the relevant parameters of the front and rear wheels, respectively, and k yf k xf The scaling factor is used to linearize the tire model. Since the rear wheel's trajectory is basically the same as the front wheel's, additional ground resistance is ignored.

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

[0081] Step 3: Building a simulation environment for soft road surfaces

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

[0083] This embodiment utilizes Chrono software to define the experimental environment, establishing a Chrono-Simulink co-simulation environment to acquire model parameters in real time and output true and calculated tire force values. Soft road surfaces represent the working conditions faced by off-road vehicles. To ensure the rationality of the experiment, this embodiment redefines key parameters such as the test vehicle's mass, wheelbase, track width, and tire lateral stiffness. 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 model parameter accuracy.

[0084] Double lane change is a common operating condition for evaluating vehicle driving performance. This embodiment uses this as the vehicle's trajectory to observe whether the model can fit the tire force. The process involves the vehicle moving from its original lane to an adjacent parallel lane within a certain distance through the driver's steering wheel operation, and then returning to the original lane. During this process, the vehicle should not cross the lane boundary line.

[0085] Step 4: Collect co-simulation data, adjust and validate the model.

[0086] Based on the experimental conditions established in step three, including the vehicle, ground, and operating conditions, a joint simulation experiment was conducted. The Chrono-Simulink joint simulation environment can acquire various signals during vehicle operation in real time, and by adjusting the weighting coefficients, the calculated values ​​of tire force model are obtained through fitting.

[0087] 4.1 Joint Simulation Experiment

[0088] Initiating a Chrono-Simulink co-simulation, in this embodiment, the vehicle travels at a speed v on a soft road surface. ref =At 40km / h, perform a single double lane change, and during the process, while the road conditions remain unchanged, collect signals such as vehicle speed, wheel slip ratio, tire slip angle, axle position, and tire force.

[0089] 4.2 Data Post-processing and Parameter Adjustment

[0090] Based on the simulation results obtained in step 4.1, extract the effective segments of the acquired signals and adjust the model parameter k. x ,k y ,k xf ,k yf The tire force calculation values ​​based on the wheel-ground contact model are obtained.

[0091] 4.3 Error Calculation

[0092] Based on the tire force calculation value obtained in step 4.2, and referring to the normalized root mean square error calculation formula, the percentage error between the calculated value and the measured tire force value is calculated:

[0093]

[0094] The above description is merely a description of preferred embodiments of this application and is not intended to limit the scope of this application in any way. Any changes or modifications made by those skilled in the art based on the above-disclosed technical content should be considered as equivalent and valid embodiments and fall within the scope of protection of the technical solution of this application.

Claims

1. A method for establishing a wheel-ground contact model suitable for soft road surfaces, characterized in that, Includes the following steps: Step 1: Analyze and simplify the Bekker model; Step 1.1 Derive the integral form of the Bekker model First, based on Coulomb's equation, the relationship between soil shear stress and normal stress is obtained: in, It is the maximum shear stress on the contact surface. It is the maximum normal stress on the contact surface. and These are soil cohesion and internal friction angle, which are inherent parameters of the soil. When a vehicle drives on soft ground, the soil deforms, causing the tires to sink. This results in geometric quantities such as wheel sinkage, wheel contact angle, and wheel lift-off angle. Based on geometry, the wheel sinkage can be calculated using the following formula: in, Indicates the effective radius of the wheel. This represents the angle from the initial contact point with the terrain to the point of maximum stress, and correspondingly... This represents the angle from the point of maximum stress to the point where the terrain breaks off from the contact point. According to the Bekker model, the normal pressure between the tire and the soil is related to the tire's sinkage and the soil's inherent parameters. The pressure-sinkage relationship is as follows: in , and These are the subsidence index, soil cohesion coefficient, and soil friction coefficient, which are determined through plate subsidence tests. Furthermore, according to Bekker, the soil shear stress is calculated as follows: in, Shear modulus Soil deformation is represented by the following formula: Based on Coulomb's formula, Bekker's theory, and the geometric relationship of wheel sinking, the integral form of the soil force acting on the tire is derived: Step 1.2 Derive the formula for additional ground resistance The additional force from the soft ground is calculated in real time as a correction term to improve the linear tire model; Assumption 1: , This is the angle from the point of maximum stress to the point where the terrain breaks off from the contact point. This angle is small and can be ignored. Assumption 2: The maximum shear stress and normal stress occur at the same point, located at... place, that is ; Assumption 3: The shear and normal stress distribution curves are approximately linear, meaning that in actual calculations, the stress at each point is obtained through linear calculations of the maximum stress. Assumption 4: The forces on the left and right wheels are the same; Based on the above assumptions, the following derivation can be made: Therefore, the expression for the additional soil resistance experienced by the tires due to wheel sinking when a vehicle is driving on a soft road surface is as follows: in , The additional lateral and longitudinal soil resistance experienced by the tires. The stress coefficient is given by 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: Combine the Bekker model with the linearized tire model to establish a wheel-ground contact model suitable for soft road surfaces: The additional ground resistance obtained in step one and As a correction term, it is combined with the linearized tire model to obtain a tire model suitable for fitting tire forces on soft roads. Step 2.1 Derive the linearized tire model First, the formula for the linear tire model is derived. On soft surfaces, the linearized tire model is referenced. Based on the linearized tire model, when a vehicle is in motion, the actual direction of the wheel deviates from the wheel's center plane, resulting in a tire slip angle. When the tire slip angle is small, the lateral force on the tire can be approximated as a linear function of the tire slip angle. in: For tire lateral stiffness, This refers to the tire slip angle; Similarly, when the slip ratio is small, the linearized tire model confirms that the tire longitudinal force is proportional to the slip ratio: in: For tire longitudinal stiffness, Wheel slip ratio; Ignoring axle load transfer and suspension deformation, the four-wheeled vehicle model is considered to be composed of two bicycle models; From the linear tire model formula, we can see that the tire longitudinal force Lateral force The solution requires longitudinal stiffness Lateral stiffness Tire slip angle and wheel slip ratio Among them, the longitudinal and lateral stiffness are fixed parameters of the vehicle and are known; The longitudinal slip of a wheel is described as follows: in, The longitudinal speed of the vehicle. The effective radius of the wheel, The wheel's angular velocity; When a wheel has lateral elasticity, its direction of travel will deviate from the plane of the wheel. The angle between the displacement direction of the center of the tire contact patch and the X-axis is defined as the tire slip angle. According to theoretical mechanics, the tire slip angle is expressed as: in, The lateral speed of the vehicle, For the front wheel steering angle, and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. The vehicle's yaw rate; Through the above derivation, all the parameters for calculating tire forces are obtained. Therefore, under the assumption of a linear tire model, the lateral and longitudinal forces acting on the tire are expressed as follows: in, Indicates front wheel related parameters, Indicates parameters related to the rear wheels; Step 2.2 Combine Bekker and linearized tire model Based on the derivation of additional ground resistance and linear tire model in steps 1.2 and 2.1, a tire model suitable for soft road surfaces is built. Due to their unique surface characteristics, soft surfaces often cause tire slippage, resulting in less friction than on typical roads. Therefore, the linear tire model is modified proportionally to suit soft surfaces. 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: in, Subscript , These represent the relevant parameters for the front and rear wheels, respectively. , To linearize the tire model scaling factor, since the rear wheel's trajectory is basically the same as the front wheel's, additional ground resistance is ignored; Since the formula is a linear combination of the linear tire model and the additional soil resistance, the coefficients are obtained by the least squares method.

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