Sand grain contact parameter calibration method under sand-wheel contact and tire performance parameter estimation method under sand-wheel contact
By combining the angle of repose test and the steepest climb test with the Box-Behnken test, a second-order regression model was constructed to optimize the sand contact parameters. This solved the error problem in the calibration of sand-wheel contact parameters in the existing technology and improved the accuracy and reliability of tire performance analysis under sand-wheel contact.
Patent Information
- Application Number
- CN202511032029.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-25
- Publication Date
- 2025-10-31
AI Technical Summary
In existing technologies, the calibration of sand particle contact parameters under sand-wheel contact relies on empirical values, resulting in large errors in the simulation angle of repose, which affects the accuracy of tire structure optimization and performance prediction of vehicles in sandy terrain, and lacks systematic quantitative analysis of the tread structure.
The measured angle of repose was obtained through the angle of repose test, and a discrete element contact model was established to obtain the coarse screening feasible range of the intrinsic parameters of sand grains. Combined with the steepest slope test and the Box-Behnken test, a second-order regression model between the angle of repose and the sand grain contact parameters was constructed to optimize the sand grain contact parameters.
It achieves precise optimization of sand particle contact parameters, with small errors between the simulated angle of repose and the measured angle, improving the reliability of the discrete element model and the reliability of subsequent mechanical property analysis under sand-wheel contact, and providing a theoretical basis for tire structure optimization.
Smart Images
Figure CN120874503A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of vehicle engineering and ground mechanics, and particularly relates to a method for calibrating sand particle contact parameters under sand-wheel contact and a method for estimating tire performance parameters under sand-wheel contact. Background Technology
[0002] In the fields of vehicle engineering and ground mechanics, accurate analysis of the contact mechanics between tires and sand is crucial for improving vehicle passability on soft surfaces. While the Discrete Element Method (DEM) has been used to study wheel-sand interactions, existing techniques have significant limitations: the calibration of sand particle contact parameters in traditional methods often relies on empirical values, such as directly using parameters recommended by the GEMM database (coefficient of restitution 0.6, static friction coefficient 0.85), leading to large errors in the simulation's angle of repose and severely reducing the reliability of the model and subsequent analysis; traditional methods lack systematic quantitative analysis of tire tread structure, and existing research mostly focuses on single tire types, failing to establish a comparative mechanism between smooth tires and patterned tires in key indicators such as traction and sinkage.
[0003] The problems existing in the above-mentioned technologies restrict the accuracy of tire structure optimization and performance prediction of vehicles in sandy conditions. There is an urgent need to develop a method for calibrating sand particle contact parameters and a method for estimating tire performance parameters under sand-wheel contact to achieve high-precision parameter calibration and quantitative analysis of multi-tread performance. Summary of the Invention
[0004] To address the problems existing in the prior art, this invention proposes a method for calibrating sand particle contact parameters under sand-wheel contact and a method for estimating tire performance parameters under sand-wheel contact.
[0005] The technical solution of the present invention is as follows:
[0006] A method for calibrating sand grain contact parameters under sand-wheel contact conditions, wherein the sand grain contact parameters include the coefficient of restitution, the static friction coefficient, and the rolling friction coefficient, the method comprising:
[0007] The measured angle of repose of the target sand grains was obtained through an angle of repose test.
[0008] A discrete element contact model for wheel-sand contact is established, and based on the discrete element contact model, the coarse screening feasible range of each sand grain contact parameter corresponding to the intrinsic parameters of sand grains is obtained. A sand grain contact parameter scheme is formed by combining several sets of discrete values in different coarse screening feasible ranges.
[0009] By conducting the steepest climbing test, the simulated angle of repose for each group of sand grain contact parameter schemes is obtained. The k groups of sand grain contact parameter schemes with the smallest relative error between the simulated angle of repose and the measured angle of repose are searched. The maximum and minimum values of the sand grain contact parameters in these k groups of sand grain contact parameter schemes are used to form the fine screening feasible range for each sand grain contact parameter.
[0010] A Box-Behnkens test was conducted using the feasible range of each sand grain contact parameter. A second-order regression model between the angle of repose and the sand grain contact parameter was constructed using a combination of several discrete values within the feasible range of each sand grain contact parameter.
[0011] Based on the second-order regression model, the sand grain contact parameters corresponding to the measured angle of repose are obtained and used as the calibrated sand grain contact parameters.
[0012] Furthermore, the specific method for forming a sand particle contact parameter scheme by combining several sets of discrete values within different feasible ranges of coarse screening includes:
[0013] The feasible range of coarse screening parameters for each sand grain is divided according to the preset coarse screening resolution.
[0014] Several discrete values within the coarse screening feasible range of each sand grain contact parameter are taken, and the discrete values in different coarse screening feasible ranges are combined to form several sets of sand grain contact parameter schemes.
[0015] Furthermore, the specific method for constructing a second-order regression model between the angle of repose and the sand grain contact parameter by conducting Box-Behnkens experiments using a feasible interval for each sand grain contact parameter and combining several sets of discrete values within that interval includes:
[0016] The range of independent variables was determined, with the simulated angle of repose of the target sand grains as the response variable of the Box-Behnken test, and the coefficient of restitution, static friction coefficient and rolling friction coefficient as the three independent variables. The feasible interval of the independent variables was used as the optimization interval, i.e. the range of factor levels.
[0017] Parameter encoding converts the actual values into encoded values, and standardizes and encodes the three independent variables respectively;
[0018] The formula for generating test points and the total number of test points is: 12 are the factorial points. The number of repetitions at the center point;
[0019] Simulation experiments were conducted for each test point to obtain the simulated angle of repose for each test point, thereby constructing a dataset.
[0020] Construct a design matrix based on the dataset, which includes constant terms, linear terms of independent variables, quadratic terms, and interaction terms;
[0021] Estimate the coefficients of the second-order regression model to obtain the second-order regression model between the angle of repose and the sand grain contact parameters.
[0022] Furthermore, the coefficients of the second-order regression model are estimated using the least squares method.
[0023] Furthermore, the expression for the second-order regression model is:
[0024]
[0025] In the formula, The angle of repose, i.e., the response variable; , and These are the coefficient of restitution, the coefficient of static friction, and the coefficient of rolling friction, i.e., the first, second, and third independent variables; For the intercept term, , , The linear effect coefficient, , , This is the secondary effect coefficient. , , This is the interaction effect coefficient; This is the random error term.
[0026] Furthermore, the number of sand grain contact parameter schemes k being searched ranges from 3 to 5.
[0027] Furthermore, the sand contact parameter calibration method further includes: conducting multiple tests with the calibrated sand contact parameters, calculating the standard deviation of the multiple test results and the measured angle of repose, and comparing the calculated standard deviation with a set standard deviation threshold to verify the accuracy of the calibrated sand contact parameters.
[0028] A method for estimating tire performance parameters under sand-wheel contact, wherein the performance parameters include traction force, indentation data, and sand particle flow vector, including:
[0029] Obtain the sand contact parameters calibrated by any of the sand-wheel contact parameter calibration methods described above, and use this to construct a sandy road surface model;
[0030] The sandy road surface model is combined with a pre-constructed radial tire model containing a smooth surface and a tread pattern to form a wheel-sand contact digital model.
[0031] Based on the set working parameters, the traction force and subsidence data are output using the wheel-sand contact digital model.
[0032] Furthermore, the set operating parameters include: tire vertical load, tire center of gravity loading horizontal speed, and corresponding angular velocity and slip ratio.
[0033] Furthermore, the method for estimating tire performance parameters under sand-wheel contact also includes: plotting traction force, sinking data, and sand flow vector variation curves for smooth and patterned radial tires under different set operating conditions, and analyzing the mechanical properties of smooth and patterned radial tires.
[0034] Compared with the prior art, the present invention has the following beneficial effects:
[0035] This invention proposes a method for calibrating sand grain contact parameters under sand-wheel contact conditions. The method first obtains a coarse-screening feasible interval for each sand grain contact parameter based on its intrinsic parameters. Then, based on the relative error between the simulated and measured angles of repose of multiple sand grain contact parameter schemes within the coarse-screening feasible interval, a fine-screening feasible interval is formed. Finally, based on the combination of discrete values within the fine-screening feasible interval, a second-order regression model is constructed between the angle of repose and the sand grain contact parameters. The second-order regression model outputs the sand grain contact parameters corresponding to the measured angle of repose. This method combines a metaphysical model with experimental data, using a combination of angle-of-pack experiments and response surface methodology to achieve precise optimization of sand grain contact parameters. It minimizes the error between the simulated and measured angles of repose, significantly improving the reliability of the discrete element model and subsequent analysis of the mechanical properties under sand-wheel contact conditions.
[0036] This invention proposes a method for estimating tire performance parameters under sand-wheel contact. Based on the sand contact parameter calibration method of this invention, the method establishes a wheel-sand contact model including smooth and patterned tires, and quantitatively analyzes the influence of slip ratio and tread structure on traction and sinking, providing a theoretical basis for tire structure optimization.
[0037] By combining discrete element method (DEM) physical models with experimental data, the intrinsic relationship between sand flow patterns and tire traction performance is revealed, overcoming the black-box nature of traditional methods and improving the interpretability of the analysis results. Attached Figure Description
[0038] Figure 1 A flowchart illustrating the method for calibrating sand particle contact parameters under sand-wheel contact conditions;
[0039] Figure 2 This is a basic schematic diagram of the contact model;
[0040] Figure 3(a) is one of the schematic diagrams of the angle of accumulation test;
[0041] Figure 3(b) is the second schematic diagram of the angle of accumulation test;
[0042] Figure 4(a) is one of the schematic diagrams of the angle of accumulation simulation test;
[0043] Figure 4(b) is the second schematic diagram of the angle of accumulation simulation test;
[0044] Figure 5 This is a schematic diagram of the road surface simulation model;
[0045] Figure 6 A schematic diagram of the tire modeling process;
[0046] Figure 7 This is a schematic diagram of the structure of a patterned tire model;
[0047] Figure 8 This is a schematic diagram of the motion trajectory of a smooth tire under a 30% slip condition.
[0048] Figure 9 This is a schematic diagram illustrating the trend of traction force as a function of slip ratio.
[0049] Figure 10 This is a schematic diagram illustrating the flow trend of sand particles.
[0050] Figure 11 This is a schematic diagram showing the change of the normal reaction force from the road surface on two types of tires at a 30% slip rate over time.
[0051] Figure 12 This is a schematic diagram showing the change of traction force over time for two types of tires at a 30% slip rate.
[0052] Figure 13 This is a schematic diagram showing the change in the sinking amount of two types of tires over time at a 30% slip rate. Detailed Implementation
[0053] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0054] Example 1:
[0055] This invention provides a method for calibrating sand grain contact parameters under sand-wheel contact conditions, used for mechanical property analysis under sand-wheel contact conditions. The sand grain contact parameters include the coefficient of restitution, the static friction coefficient, and the rolling friction coefficient. The method includes:
[0056] The measured angle of repose of the target sand grains was obtained through an angle of repose test.
[0057] A discrete element contact model for wheel-sand contact is established, and based on the discrete element contact model, the coarse screening feasible intervals of each sand grain contact parameter corresponding to the intrinsic parameters of sand grains are obtained. A sand grain contact parameter scheme is formed by combining several sets of discrete values in different coarse screening feasible intervals.
[0058] By conducting the steepest climbing test, the simulated angle of repose for each group of sand grain contact parameter schemes is obtained. The k groups of sand grain contact parameter schemes with the smallest relative error between the simulated angle of repose and the measured angle of repose are searched. The maximum and minimum values of the sand grain contact parameters in these k groups of sand grain contact parameter schemes are used to form the fine screening feasible range for each sand grain contact parameter.
[0059] Box-Behnkens experiments were conducted using the feasible range of each sand grain contact parameter. A second-order regression model between the angle of repose and the sand grain contact parameter was constructed using a combination of several discrete values within the feasible range of each sand grain contact parameter.
[0060] Based on the second-order regression model, the sand grain contact parameters corresponding to the measured angle of repose are obtained and used as the calibrated sand grain contact parameters.
[0061] Furthermore, the specific methods for forming sand particle contact parameter schemes by combining several sets of discrete values within different feasible ranges of coarse screening include:
[0062] The feasible range of coarse screening parameters for each sand grain is divided according to the preset coarse screening resolution.
[0063] Several discrete values within the coarse screening feasible range of each sand grain contact parameter are taken, and the discrete values in different coarse screening feasible ranges are combined to form several sets of sand grain contact parameter schemes.
[0064] Furthermore, the specific method for constructing a second-order regression model between the angle of repose and the sand grain contact parameter by conducting Box-Behnkens experiments with a finely screened feasible interval for each sand grain contact parameter, and by combining several sets of discrete values within the finely screened feasible interval for each sand grain contact parameter, includes:
[0065] The range of independent variables was determined, with the simulated angle of repose of the target sand grains as the response variable of the Box-Behnken test, and the coefficient of restitution, static friction coefficient and rolling friction coefficient as the three independent variables. The feasible interval of the independent variables was used as the optimization interval, i.e. the range of factor levels.
[0066] Parameter encoding converts actual values into encoded values, and standardizes the three independent variables into encodings (-1, 0, 1).
[0067] The formula for generating test points and the total number of test points is: 12 are the factorial points. The number of repetitions at the center point;
[0068] Simulation experiments were conducted for each test point to obtain the simulated angle of repose for each test point, thereby constructing a dataset.
[0069] Construct a design matrix based on the dataset, which includes constant terms, linear terms of independent variables, quadratic terms, and interaction terms;
[0070] Estimate the coefficients of the second-order regression model to obtain the second-order regression model between the angle of repose and the sand grain contact parameters.
[0071] Furthermore, the coefficients of the second-order regression model are estimated using the least squares method.
[0072] Furthermore, the expression for the second-order regression model is:
[0073]
[0074] In the formula, The angle of repose, i.e., the response variable; , and These are the coefficient of restitution, the coefficient of static friction, and the coefficient of rolling friction, i.e., the first, second, and third independent variables; For the intercept term, , , The linear effect coefficient, , , This is the secondary effect coefficient. , , This is the interaction effect coefficient; The random error term follows a normal distribution. .
[0075] Furthermore, specific methods for obtaining the measured angle of repose of sand grains through the angle of repose test include:
[0076] Sample preparation involves selecting representative target sand (composed of target sand particles), removing impurities, and ensuring that its condition (such as dryness) meets the experimental requirements.
[0077] Method selection depends on the characteristics of the sand particles. The funnel method is suitable for fine particles, the cylinder method is suitable for medium-sized sand particles, and the plate-breaking method can be used for larger particles.
[0078] The setup involves adjusting device parameters based on sand characteristics. For example, in the cylindrical method, the inner diameter needs to be 5-10 times larger than the maximum sand particle size to reduce boundary effects. The initial filling height is related to the dry density of the sand: the higher the dry density, the greater the mass of sand particles in the same volume, and the initial height can be appropriately reduced to avoid over-compaction. The stacking height (initial filling height) is directly related to the dry density of the sand: the higher the dry density (the higher the compaction of the sand particles), the greater the mass of sand particles in the same volume, and the initial stacking height needs to be adapted to ensure a stable slope angle can be formed during natural stacking. The device dimensions (such as the inner diameter of the cylinder) are related to the sand particle size; the larger the particle size, the larger the inner diameter is required to avoid the cylinder wall hindering the flow of sand particles and reduce the impact of boundary effects on the angle of repose.
[0079] During the experiment, slowly remove the constraints (such as lifting the cylinder, opening the funnel valve, or removing the baffle) to allow the sand to accumulate naturally.
[0080] Measurement and repetition: After the accumulation pattern stabilizes, measure the slope angle from multiple angles, repeat 3-5 times and take the average value.
[0081] The angle of repose is mainly related to the contact parameters of the sand grains (coefficient of restitution, static friction coefficient, and rolling friction coefficient). These parameters reflect the surface roughness (the higher the static friction coefficient, the rougher the surface), elasticity (the higher the coefficient of restitution, the better the elasticity), and shape regularity (the higher the rolling friction coefficient, the more irregular the particles).
[0082] Furthermore, the number of sand grain contact parameter schemes k being searched ranges from 3 to 5.
[0083] Furthermore, the sand contact parameter calibration method also includes: conducting multiple tests (4-5 times) with the calibrated sand contact parameters, calculating the standard deviation between the results of the multiple tests and the measured angle of repose, and comparing the calculated standard deviation with the set standard deviation threshold to verify the accuracy of the calibrated sand contact parameters.
[0084] Example 2:
[0085] This invention provides a method for estimating tire performance parameters under sand-wheel contact conditions. The performance parameters include traction force, indentation data, and sand flow vectors.
[0086] The sand contact parameters calibrated by the sand-wheel contact parameter calibration method described in any of the above embodiments are obtained, and a sandy road surface model is constructed accordingly.
[0087] The sand road surface model is combined with a pre-built radial tire model that includes a smooth surface and a tread pattern to form a wheel-sand contact digital model.
[0088] Based on the set working parameters, the system outputs traction force and subsidence data using a wheel-sand contact digital model.
[0089] Furthermore, the set operating parameters include: tire vertical load, tire center of gravity loading horizontal speed, and corresponding angular velocity and slip ratio.
[0090] Furthermore, the method for estimating tire performance parameters under sand-wheel contact also includes: plotting the traction force, sinking data, and sand flow vector variation curves of smooth and treaded radial tires under different set operating conditions, and analyzing the mechanical properties of smooth and treaded radial tires.
[0091] Example 3:
[0092] An electronic device according to the present invention includes a memory and a processor. The memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to perform the method as described in any of the above embodiments.
[0093] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the above embodiments.
[0094] Application Examples:
[0095] The present invention simulates the estimation of tire performance parameters under sand-wheel contact conditions, and the specific process is as follows:
[0096] 1) First, analyze the contact principle of the grinding wheel contact, such as... Figure 2 As shown, elastic force, damping force, and rolling friction exist between the two particles. A spring simulates the elastic effect between the particles, a damper simulates the damping effect, and a slider is used to describe the relative sliding between two contacting discrete particles. When two adjacent particles come into contact, they are subjected to interaction forces obtained by a penalty-based contact algorithm. These interaction forces are decomposed into normal contact forces and tangential contact forces. , , , , These are the spring normal stiffness coefficient, spring tangential stiffness coefficient, normal damping coefficient, tangential damping coefficient, and static friction coefficient, respectively.
[0097] 2) The cylindrical method was used to conduct the angle of repose test, as shown in Figures 3(a), 3(b), 4(a), and 4(b). The specific experimental procedure was as follows: Sand was filled into a cylinder with an inner diameter of 50 mm and a height of 250 mm to a height of 150 mm. Then the cylinder was slowly lifted, and the sand naturally accumulated and formed a slope angle. The foot of this slope is the angle of repose. After the foot of the slope stabilized, a vertical photo was taken and the image was imported into the image processing software to measure the angle of repose.
[0098] 3) A discrete element model of wheel-sand interaction was constructed using EDEM software. The Hertz-Mindlin-Deresiewicz no-slip contact model was selected to describe the normal and tangential interactions between sand grains. The model includes elastic force, damping force and rolling friction.
[0099] The intrinsic parameters of sand grains are defined, including particle radius, material density, Young's modulus, and Poisson's ratio, where the particle radius is set to 2 mm, the material density to 2650 kg / m³, and the Young's modulus to 2 × 10⁻⁶. 8 Pa, Poisson's ratio is 0.21.
[0100] There is an elastic force between the two particles Damping force Rolling friction Among them, elastic force and damping force It can be further divided into normal elastic force. Tangential elastic force Normal damping force Tangential damping force . , , , , These are the spring normal stiffness coefficient, spring tangential stiffness coefficient, normal damping coefficient, tangential damping coefficient, and static friction coefficient, respectively.
[0101]
[0102]
[0103]
[0104] In the formula, It is the equivalent Young's modulus; Equivalent radius; This is the normal overlap. , Young's modulus; , Poisson's ratio; , The radius of the contact sphere;
[0105]
[0106]
[0107] In the formula, For normal damping; Equivalent mass; The normal component of the relative velocity;
[0108]
[0109]
[0110] In the formula, The damping ratio; Normal stiffness; The coefficient of recovery;
[0111]
[0112]
[0113] In the formula, It is a tangential force; Tangential stiffness; This is the tangential overlap. Equivalent shear modulus;
[0114]
[0115] In the formula, For tangential damping force; This represents the tangential component of the relative velocity;
[0116] For discrete element method (DEM) simulations, rolling friction between particles is very important, and it is often necessary to apply a torque to the contact surface. In the formula, The coefficient of rolling friction; The distance from the point of contact to the center of mass; This is the vector of the unit angular velocity of the object at the point of contact.
[0117] The coarse screening feasible range of each sand grain contact parameter corresponding to the intrinsic parameters of the sand grain is used, and the sand grain contact parameter scheme is formed by combining several sets of discrete values in different coarse screening feasible ranges (as shown in Table 1). In Table 1, parameter A represents the coefficient of restitution, parameter B represents the static friction coefficient, and parameter C represents the rolling friction coefficient.
[0118] Table 1
[0119]
[0120] Then, through the steepest climbing test, the simulated angle of repose of each group of sand contact parameter schemes is obtained. The three groups of sand contact parameter schemes with the smallest relative error between the simulated angle of repose and the measured angle of repose are searched, as shown in Table 2. The maximum and minimum values of the sand contact parameters in these three groups of sand contact parameter schemes are used to form the fine screening feasible range of each sand contact parameter.
[0121] Table 2
[0122]
[0123] Then construct a second-order regression model using the following procedure:
[0124] Determine the core parameters (inputs):
[0125] Independent variable: coefficient of recovery static friction coefficient Rolling friction coefficient (From the range determined by the steepest climb test).
[0126] Response variable: Angle of repose of sand grains .
[0127] 2. Generate test site dataset
[0128] 1) Encoding the independent variables
[0129] 2) Generate 17 test points (12 factorial points + 5 center points) according to the Box-Behnken design rules.
[0130] 3) For each test point, the angle of repose y is calculated using EDEM software to form a dataset.
[0131] 3. Fitting the second-order regression model
[0132] 1) Construct the design matrix X: containing constant terms, linear terms of independent variables, quadratic terms, and interaction terms, corresponding to the values of 17 experimental points;
[0133]
[0134] 2) Estimating coefficients using the least squares method: Least squares coefficients are estimated through matrix operations. That is, calculation , … ;
[0135] 3) Obtain the specific regression equation
[0136] 4. Model Validation and Optimization
[0137] 1) Analysis of variance (ANOVA): Calculate the regression sum of squares and the residual sum of squares, and verify the significance of the model through the F test;
[0138] 2) Goodness-of-fit evaluation: Calculation Correction The model was confirmed to fit well.
[0139] 3) Parameter optimization: With the objective of minimizing the relative error of the angle of repose, the optimal solution is obtained through stationary point analysis. , , .
[0140] The generated test points are shown in Table 3:
[0141] Table 3
[0142]
[0143] The specific regression equation obtained is as follows
[0144] Based on the aforementioned second-order regression model, model testing and optimization are performed as follows:
[0145] 1) Analysis of variance (ANOVA): Calculate the regression sum of squares and the residual sum of squares, and verify the significance of the model through the F test;
[0146] 2) Goodness-of-fit evaluation: Calculation Correction The model was confirmed to fit well, as shown in Table 4:
[0147] Table 4
[0148]
[0149] 3) Parameter optimization: With the objective of minimizing the relative error of the angle of repose, the optimal solution is obtained through stationary point analysis. , , The final values obtained were a coefficient of restitution of 0.638, a static friction coefficient of 1.89, and a rolling friction coefficient of 0.283. The relative error between the simulated angle of repose and the measured angle of repose was 1.2%.
[0150] Obtain the calibrated sand grain contact parameters to construct a sandy road surface model, such as... Figure 5 As shown, the road surface dimensions are set to 5m in length, 0.4m in width, and 0.15m in thickness. The sand particles reach a stable state under their own weight through discrete element kinetic energy analysis.
[0151] A model of a 205 / 55 R16 radial tire is established, including both smooth and patterned tires. The tire is assumed to be a rigid, homogeneous model, and tire deformation is ignored. The tire material parameters are defined as follows: density 1800 kg / m³, Young's modulus 2 × 10⁻⁶. 6 Pa, Poisson's ratio 0.49. A three-dimensional tire model is generated by rotating a two-dimensional cross-section, such as... Figure 6 As shown, patterned tires require the addition of grooved tread structures to the tread, such as... Figure 7 As shown.
[0152] Combine the sandy road surface model with the radial tire model, such as Figure 8 As shown, a digital model of wheel-sand contact is formed;
[0153] Simulation conditions were set up, including a vertical load of 1000N and a horizontal speed of 5m / s. The tire angular velocity was adjusted to control the slip ratio (0-60%). Data on tire traction, settlement, and sand flow vectors were collected to analyze the mechanical properties under different slip ratios.
[0154] Figure 9 The traction force is taken as the average value after the tires have stabilized on the sand. As shown in the figure, there is a large difference between the simulation results and the experimental values, which is due to the different tire models and loads, but the overall trend is consistent. Before the slip ratio is less than 30%, the traction force increases significantly with the increase of the slip ratio; after it is greater than 30%, the traction force tends to stabilize.
[0155] Figure 10 (a) is a vector diagram of sand flow under a 30% slip condition. The diagram shows that the sand flow can be divided into two regions: the front region flows clockwise, and the rear region flows counterclockwise. This phenomenon is related to... Figure 10 The experimental results shown in (b) are consistent.
[0156] Figure 11 The figure shows the trend of the normal reaction force from the road surface on two types of tires with the same slip rate over time. As can be seen from the figure, when the tires are traveling on sand, the normal reaction force from the road surface on both types of tires fluctuates significantly, and then fluctuates around 1000N.
[0157] Figure 12 The graph shows the change in traction force of the two types of tires over time. As can be seen, after the tires contact the sand, the traction force initially fluctuates significantly, then decreases rapidly and enters a relatively stable state. The traction force of the patterned tire is approximately 116 N, greater than the 73 N of the smooth tire. The tire tread grooves increase the contact area between the tire and the sand, leading to an increase in driving force, which is consistent with general patterns.
[0158] Figure 13 The graph shows the change in sinking amount of the two types of tires over time. As can be seen, the sinking amount increases rapidly after the tires contact the sand, and then quickly stabilizes. The sinking amount of the patterned tires is approximately 21 mm, which is greater than the 18 mm of the smooth tires. This is because the tangential force of the patterned tires pushes the sand particles to both sides, resulting in a larger sinking amount.
[0159] The simulation results of smooth tires and patterned tires were compared to verify the mechanism by which tire tread pattern affects contact area, traction, and sinkage. When the slip ratio is 30%, the traction of the patterned tire is significantly greater than that of the smooth tire, and the sinkage is also greater, indicating that the tread pattern improves traction performance by increasing the contact area.
[0160] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for calibrating sand grain contact parameters under sand-wheel contact conditions, wherein the sand grain contact parameters include the coefficient of restitution, the coefficient of static friction, and the coefficient of rolling friction, characterized in that, The method includes: The measured angle of repose of the target sand grains was obtained through an angle of repose test. A discrete element contact model for wheel-sand contact is established, and based on the discrete element contact model, the coarse screening feasible range of each sand grain contact parameter corresponding to the intrinsic parameters of sand grains is obtained. A sand grain contact parameter scheme is formed by combining several sets of discrete values in different coarse screening feasible ranges. By conducting the steepest climbing test, the simulated angle of repose for each group of sand grain contact parameter schemes is obtained. The k groups of sand grain contact parameter schemes with the smallest relative error between the simulated angle of repose and the measured angle of repose are searched. The maximum and minimum values of the sand grain contact parameters in these k groups of sand grain contact parameter schemes are used to form the fine screening feasible range for each sand grain contact parameter. A Box-Behnkens test was conducted using the feasible range of each sand grain contact parameter. A second-order regression model between the angle of repose and the sand grain contact parameter was constructed using a combination of several discrete values within the feasible range of each sand grain contact parameter. Based on the second-order regression model, the sand grain contact parameters corresponding to the measured angle of repose are obtained and used as the calibrated sand grain contact parameters.
2. The method for calibrating sand grain contact parameters under sand-wheel contact according to claim 1, characterized in that, The specific method for forming a sand particle contact parameter scheme by combining several sets of discrete values within different feasible ranges of coarse screening includes: The feasible range of coarse screening parameters for each sand grain is divided according to the preset coarse screening resolution. Several discrete values within the coarse screening feasible range of each sand grain contact parameter are taken, and the discrete values in different coarse screening feasible ranges are combined to form several sets of sand grain contact parameter schemes.
3. The method for calibrating sand grain contact parameters under sand-wheel contact according to claim 1, characterized in that, The specific method for conducting Box-Behnkens experiments using a feasible interval for each sand grain contact parameter, and constructing a second-order regression model between the angle of repose and the sand grain contact parameter using a combination of several discrete values within the feasible interval for each sand grain contact parameter, includes: The range of independent variables was determined, with the simulated angle of repose of the target sand grains as the response variable of the Box-Behnken test, and the coefficient of restitution, static friction coefficient and rolling friction coefficient as the three independent variables. The feasible interval of the independent variables was used as the optimization interval, i.e. the range of factor levels. Parameter encoding converts the actual values into encoded values, and standardizes and encodes the three independent variables respectively; The formula for generating test points and the total number of test points is: 12 are the factorial points. The number of repetitions at the center point; Simulation experiments were conducted for each test point to obtain the simulated angle of repose for each test point, thereby constructing a dataset. Construct a design matrix based on the dataset, which includes constant terms, linear terms of independent variables, quadratic terms, and interaction terms; Estimate the coefficients of the second-order regression model to obtain the second-order regression model between the angle of repose and the sand grain contact parameters.
4. The method for calibrating sand particle contact parameters under sand-wheel contact according to claim 3, characterized in that, The coefficients of the second-order regression model are estimated using the least squares method.
5. The method for calibrating sand particle contact parameters under sand-wheel contact according to claim 3, characterized in that, The expression for the second-order regression model is: In the formula, The angle of repose, i.e., the response variable; , and These are the coefficient of restitution, the coefficient of static friction, and the coefficient of rolling friction, i.e., the first, second, and third independent variables; For the intercept term, , , The linear effect coefficient, , , This is the secondary effect coefficient. , , This is the interaction effect coefficient; This is the random error term.
6. The method for calibrating sand grain contact parameters under sand-wheel contact according to claim 1, characterized in that, The number of sand grain contact parameter schemes to be searched, k, ranges from 3 to 5.
7. The method for calibrating sand grain contact parameters under sand-wheel contact according to claim 1, characterized in that, The method for calibrating sand grain contact parameters further includes: conducting multiple tests with the calibrated sand grain contact parameters, calculating the standard deviation of the multiple test results and the measured angle of repose, and comparing the calculated standard deviation with a set standard deviation threshold to verify the accuracy of the calibrated sand grain contact parameters.
8. A method for estimating tire performance parameters under sand-wheel contact, wherein the performance parameters include traction force, sinkage data, and sand flow vector, characterized in that, include: Obtain the sand grain contact parameters calibrated by the sand-wheel contact parameter calibration method according to any one of claims 1 to 7, and use this to construct a sandy road surface model; The sandy road surface model is combined with a pre-constructed radial tire model containing a smooth surface and a tread pattern to form a wheel-sand contact digital model. Based on the set working parameters, the traction force and subsidence data are output according to the wheel-sand contact digital model.
9. The method for estimating tire performance parameters under sand-wheel contact as described in claim 8, characterized in that, The set operating parameters include: tire vertical load, tire center of gravity loading horizontal speed, and corresponding angular velocity and slip ratio.
10. The method for estimating tire performance parameters under sand-wheel contact according to claim 7, characterized in that, The method for estimating tire performance parameters under sand-wheel contact further includes: plotting traction force, sinking data, and sand flow vector variation curves for smooth and treaded radial tires under different set operating conditions, and analyzing the mechanical properties of smooth and treaded radial tires.