Calculation method and prediction model for invasion depth of rubber in contact with rough road surface

Abstract

The invention discloses a calculation method and a prediction model for the invasion depth of rubber in contact with a rough road surface. The method comprises the following steps: establishing a rubber block and rough pavement contact model, and defining the surface of the rubber block in contact with the rough pavement as a feature contact surface S; boundary conditions of constraints and loads are applied to the rubber block and rough pavement contact model, and contact between the rubber block and the rough pavement in the loaded state is achieved; on the premise that the rough road surface contour is not changed, model parameters and loads representing rubber attributes are changed respectively, and the corresponding rubber block invasion depth H under the combination of the model parameters and the loads of different rubber attributes is calculated; and constructing a rubber invasion depth prediction model and verifying to predict the invasion depth H when the rubber is in contact with the rough road surface in a loaded state. The method has the advantages that the invasion depth of the rubber block on the rough road surface under the action of different loads can be effectively captured, so that theoretical analysis and numerical analysis of rubber friction characteristics can be better guided and corrected.

Description

Technical Field

[0001] This invention belongs to the field of tire industry and numerical simulation analysis, and in particular relates to a method and prediction model for calculating the penetration depth of rubber when it contacts a rough road surface. Background Technology

[0002] Tires are the only component of a vehicle that directly contacts the ground. Many of a car's performance characteristics, such as steering, braking, and handling stability, are primarily achieved through tire performance. The contact state between the tire and the rough surface directly affects tire driving force, vibration characteristics, rolling resistance, and anti-skid properties. However, the frictional characteristics of tire contact with rough surfaces not only affect the tire contact state but also the tire's driving force and braking force. Therefore, rubber friction characteristics directly impact vehicle safety. When a rubber-based tire comes into contact with a rough surface, the tire load causes the tread rubber to penetrate into the contours of the rough surface, thus affecting the tire's frictional characteristics. However, road surfaces have multi-scale surface roughness, and the tread rubber cannot establish complete contact with all contours of the rough surface. Therefore, the penetration depth of rubber into a rough surface is defined as the ratio of the volume of rubber that penetrates into the contours of the rough surface under a certain load to its projected area. The impact of rough road surfaces on the frictional properties of rubber has become a research topic for technicians and researchers. For example, patent number 202011062061.2 focuses on the modeling methods for the tribological properties of rubber in contact with rough surfaces, mainly involving rubber geometric models, road texture models, and numerical calculations. However, the efficiency of this research process needs improvement. Regarding the construction of frictional properties based on physical models, the main approach is the study of numerical analytical solutions, represented by Persson theory. However, these numerical analytical solutions mostly treat rubber as a linear elastic material and establish theoretical calculation equations for penetration depth by subjecting it to load contact with a two-dimensional rough road surface. These equations are mainly applicable to small load conditions, leading to significant differences between the numerical analytical solutions and physical experimental results under large loads and strong boundary nonlinearities when rubber contacts a rough three-dimensional road surface. Furthermore, theoretical models tend to focus on exploring the relationship between rubber elasticity and penetration depth, while rubber penetration depth prediction models that integrate rubber material properties and load factors are rarely published, resulting in uncertainties between theoretical calculation results and practical applications. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a method and prediction model for calculating the penetration depth of rubber in contact with a rough road surface. A finite element model of the rubber block in contact with the rough road surface is established. By analyzing the deformation characteristics of the rubber penetrating the rough road surface under load, the penetration depth is calculated using the coordinate information of the deformation characteristics. Based on this, a prediction model is constructed with rubber material parameters and load as independent variables and penetration depth as the dependent variable. The accuracy of the prediction model is numerically verified. The implementation of this invention achieves the goal of rapid and accurate prediction of the penetration depth of rubber in contact with a rough road surface. This not only helps improve the accuracy and efficiency of calculating the frictional characteristics of rubber with rough road surfaces but also guides the design and development of new rubber formulations.

[0004] The present invention provides a method and prediction model for calculating the penetration depth of rubber in contact with a rough road surface, comprising the following steps:

[0005] S1: Establish a contact model between the rubber block and the rough road surface, and define the surface of the rubber block in contact with the rough road surface as the characteristic contact surface S;

[0006] S2: Apply boundary conditions of constraints and loads to the contact model between the rubber block and the rough road surface to achieve phase contact between the rubber block and the rough road surface under load.

[0007] S3: Based on the rubber block's intrusion into the rough road surface contour, extract the coordinate information of NA nodes on the characteristic contact surface S of the rubber block. The coordinate information is represented by (X, Y, Z), where X and Y are the positions and Z is the displacement amplitude. Subtract the maximum value Z from each of the NA coordinates in the z-direction of the node set N. max This allows the characteristic contact surface S to be translated below the XY plane under load.

[0008] S4: Interpolate the coordinate information of the NA nodes in the node set N on the feature contact surface S of the rubber block to obtain the node set M, thereby increasing the number of nodes in the node set N on the feature contact surface S from NA to MA.

[0009] S5: Smooth the MA coordinate information of the interpolated node set M to construct the corresponding spatial surface F, and verify the accuracy of the spatial surface F.

[0010] S6: Using the coordinates of the highest point Rz of the road surface profile in the contact area between the rubber block and the rough road surface as a reference, and combining the four boundaries B of the spatial surface F, construct the spatial domain D enclosed by the highest point Rz of the road surface profile, the four boundaries B, and the spatial surface F.

[0011] S7: Based on the number MA of the node set M, divide the spatial surface F and the spatial domain D into MA small units and MA sub-spatial domains d respectively. Calculate the product of the area of ​​each small unit on the spatial surface F and its height Z to the XY plane in turn to calculate the volume of each sub-spatial domain d. Then sum the volumes of MA sub-spatial domains d to obtain the volume corresponding to the spatial domain D, that is, the volume Vr of the rubber block intruding into the rough road surface contour.

[0012] S8: Calculate the projected area Sp of the spatial domain D on the highest point Rz of the vertical road surface profile, and calculate the penetration depth H of the rubber when it contacts the rough road surface under load by dividing the rubber volume Vr by the projected area Sp.

[0013] S9: Based on the process of steps S2-S8, under the premise that the rough road surface profile remains unchanged, the model parameters and loads that characterize the rubber properties are changed respectively to calculate the rubber block intrusion depth H corresponding to different combinations of model parameters and loads for different rubber properties.

[0014] S10: Using the constitutive model parameters of rubber and the load as independent variables and the corresponding penetration depth H as the dependent variable, a rubber penetration depth prediction model with independent and dependent variables is constructed, and the accuracy of the prediction model is verified to obtain the predicted penetration depth H' when rubber contacts a rough road surface under load.

[0015] In step S1, the physical properties of the rubber block are characterized by a hyperelastic constitutive model, and the rough road surface is characterized by an analytical rigid body model. Its rough contour can be constructed by point cloud in three-dimensional space.

[0016] In step S2, in order to achieve contact between the rubber block and the rough road surface, the boundary conditions can be applied by either fixing the rough road surface and subjecting the rubber block to load, or by fixing the rubber block and subjecting the rough road surface to load.

[0017] In step S3, the coordinate information of NA nodes on the characteristic contact surface S of the loaded rubber block is extracted, and the maximum value Z is determined. max The methods for obtaining and translating can be obtained manually or through secondary development.

[0018] In step S4, the natural neighborhood interpolation method is used to adjust the NA coordinate information of the node set N on the feature surface S to the MA coordinate information of the node set M, where MA is at least 5 times NA, and the root mean square error index is used to verify the reliability of the interpolation method.

[0019] In step S5, a spatial surface F formed by MA coordinate information of the node set M is constructed using the cubic smooth spline method, and the reliability of the spatial surface F construction method is verified by the root mean square error index.

[0020] In step S7, the spatial surface F is divided into tiny units corresponding to the number of nodes MA in the node set M. The height Z of each tiny unit to the XY plane is determined by the z-coordinate value of the corresponding node. The volume corresponding to each tiny unit is calculated by definite integral method, and the volumes of MA tiny units are summed to obtain the rubber volume Vr of the loaded rubber block intruding into the rough road surface contour.

[0021] In step S8, the highest point Rz of the road surface profile is the maximum value Z in the MA node coordinate information. max The projected area Sp is obtained by projecting the region bounded by the four boundaries B of the spatial domain D onto the plane parallel to the rough road surface and passing through the highest point Rz of the road surface profile.

[0022] In step S9, the model parameters characterizing the rubber properties are changed by modifying the equation parameters in the rubber hyperelastic constitutive model.

[0023] In step S10, the rubber intrusion depth prediction model constructed by the relationship between independent and dependent variables is realized through a multiple linear regression prediction equation.

[0024] The beneficial effects of this invention are as follows: By establishing a method for calculating the penetration depth when a rubber block contacts a rough road surface, and leveraging the hyperelastic deformation characteristics of rubber, the penetration depth of the rubber block under different loads on a rough road surface can be effectively captured. This better guides and corrects the theoretical analysis and numerical analysis of rubber friction characteristics. Simultaneously, by integrating rubber material parameters and load factors, a precise prediction model for the penetration depth of different types of rubber on rough roads is constructed, which can effectively and accurately determine the friction characteristics of different rubbers on rough roads. The penetration depth calculation method proposed in this invention is more in line with actual conditions and possesses the characteristics of universality and accuracy, providing theoretical and methodological guidance for the research and improvement of tire friction and wear performance. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the technical process of the present invention.

[0026] Figure 2 A simulation model of the contact between a rubber block and a rough road surface;

[0027] Figure 3 The displacement amplitude of the characteristic plane S when the rubber block comes into contact with the rough road surface under four different loads;

[0028] Figure 4 The node coordinates and interpolation of the characteristic plane S under load;

[0029] Figure 5This is a schematic diagram illustrating the changes in the state of a rubber block when it comes into contact with a rough road surface.

[0030] Figure 6 A graph showing the relationship between rubber penetration depth under different rubber material properties and loads;

[0031] Figure 7 This is the predicted penetration depth when a rubber block comes into contact with a rough road surface. Detailed Implementation

[0032] The following, in conjunction with the accompanying drawings and specific embodiments, provides a more detailed description of the method for calculating and predicting the penetration depth of rubber when in contact with a rough road surface according to the present invention. Example:

[0033] like Figure 1 As shown, it includes the following steps:

[0034] S1: Establish a contact model between the rubber block and the rough road surface, and define the surface of the rubber block in contact with the rough road surface as the characteristic contact surface S;

[0035] S2: Apply boundary conditions of constraints and loads to the rubber block and rough road surface contact model to achieve phase contact between the rubber block and the rough road surface under load, so as to achieve the purpose of the rubber block intruding into the rough road surface contour.

[0036] S3: Based on the rubber block intrusion into the rough road surface profile, extract the coordinate information of NA nodes on the characteristic contact surface S of the rubber block. The coordinate information is represented by (X, Y, Z), where X and Y are the position and Z is the displacement amplitude. Subtract the maximum value Z from each of the NA coordinates in the z-direction. max This allows the characteristic contact surface S to be translated below the XY plane under load.

[0037] S4: Interpolate the coordinate information of the NA nodes of the node set N on the feature contact surface S of the rubber block to obtain the node set M, thereby increasing the number of nodes of the node set N on the feature contact surface S to the number of nodes MA of the node set M, so as to accurately and effectively preserve the local features when the rubber block invades the rough road surface contour.

[0038] S5: Smooth the MA coordinate information of the interpolated node set M to construct the corresponding spatial surface F, and verify the accuracy of the spatial surface F.

[0039] S6: Using the coordinates of the highest point Rz of the road surface profile in the contact area between the rubber block and the rough road surface as a reference, and combining the four boundaries B of the spatial surface F, construct the spatial domain D enclosed by the highest point Rz of the road surface profile, the four boundaries B, and the spatial surface F.

[0040] S7: Based on the number MA of the node set M, divide the spatial surface F and the spatial domain D into MA small units and MA sub-spatial domains d respectively. Calculate the product of the area of ​​each small unit on the spatial surface F and its height Z to the XY plane in turn to calculate the volume of each sub-spatial domain d. Then sum the volumes of MA sub-spatial domains d to obtain the volume corresponding to the spatial domain D, that is, the volume Vr of the rubber block intruding into the rough road surface contour.

[0041] S8: Calculate the projected area Sp of the spatial domain D on the highest point Rz of the vertical road surface profile, and calculate the penetration depth H of the rubber when it contacts the rough road surface under load by dividing the rubber volume Vr by the projected area Sp.

[0042] S9: Based on the process of steps S2-S8, under the premise that the rough road surface profile remains unchanged, the model parameters and loads that characterize the rubber properties are changed respectively to calculate the rubber block intrusion depth H corresponding to different combinations of model parameters and loads for different rubber properties.

[0043] S10: Using the constitutive model parameters of rubber and the load as independent variables and the corresponding penetration depth H as the dependent variable, a rubber penetration depth prediction model with independent and dependent variables is constructed, and the accuracy of the prediction model is verified to obtain the predicted penetration depth H' when rubber contacts a rough road surface under load.

[0044] To more clearly illustrate the technical solution of the present invention, the technical solution of this application will be further described below with reference to the accompanying drawings:

[0045] 1) Construction of the contact model between the rubber block and the rough road surface. A contact model between the rubber block and the rough road surface is established in the finite element software ABAQUS, such as... Figure 2 As shown, the length l, width w, and height t of the rubber block are 30mm, 30mm, and 10mm, respectively. The rough road surface adopts an analytical rigid body model, and its length and width are at least three times the corresponding dimensions of the rubber block. In the contact model, the element size of the rubber block is 0.3-0.6mm, and the element size of the rough road surface is 0.2-0.3mm. The physical properties of the rubber block are characterized by the hyperelastic constitutive Yeoh model. The constitutive equation of the Yeoh model is shown in formula (1), and the specific model parameters are shown in Table 1. To avoid problems such as difficulty in numerical calculation convergence due to excessive load during the contact process between the rubber and the rough road surface, the rough road surface is fixedly constrained, the top of the rubber block is loaded, and the contact property between the rubber and the rough road surface is Coulomb friction, with a specific friction coefficient of 0.55.

[0046]

[0047] Among them, C 10 C 20 and C30 These are material parameters. I1 is the first strain tensor invariant, while J... el It is the elastic volume ratio, D i J is the material constant for volumetric deformation. Because rubber is volumetrically incompressible, therefore J... el The value is 1.

[0048] Table 1 Rubber property parameters

[0049]

[0050] 2) Analysis of Rubber Block Extrusion Deformation Characteristics. When the rubber block comes into contact with the rough road surface, due to the fixed constraint of the rough road surface, the rubber block will gradually deform and intrude into the rough road surface as the applied load increases. The degree of rubber deformation can be characterized by the contour map of the displacement amplitude on the characteristic contact surface S of the rubber block in the contact area. The displacement amplitude variation characteristics on the contact surface S when applying four different loads of 50N, 100N, 150N, and 200N to the rubber block are as follows: Figure 3 As shown.

[0051] 3) Obtaining the coordinate information of NA nodes in the feature contact surface S of the rubber block. The coordinates of the node set N of the feature contact surface S after compression deformation are obtained using a Python subroutine method. There are NA = 100 nodes in both the x and y axes. The specific coordinate information of each node is represented by (X, Y, Z), where X and Y are the position and Z is the displacement amplitude. Then, MATLAB software is used to read and process the coordinate information of the NA nodes in the node set N. The specific processing procedure is as follows: First, the maximum value Z in the z-axis is selected from the coordinate information of the NA nodes in the node set N. max Secondly, subtract Z from the Z values ​​of the coordinates of all NA nodes in the node set N. max The purpose of this process is to translate the spatial position of the node set N of the feature contact surface S below the XY plane where the zero value is located, thereby preprocessing the coordinate information of the NA coordinates of the node set N of the feature contact surface S, such as... Figure 4 As shown.

[0052] 4) Interpolation of the coordinate information of the NA nodes in the node set N on the feature contact surface S. To establish a continuous surface model and effectively preserve local features, the natural neighborhood interpolation method is used to interpolate the coordinate information of the NA nodes in the preprocessed node set N, resulting in a node set M. The number of nodes is increased by five times NA in the X and Y axes, increasing the number of nodes in the node set S from NA to MA nodes in the node set M (MA = 500 grid points). The root mean square error (RMSE) is introduced as an evaluation index for the consistency of the coordinate information between the MA and NA node sets. For grid point coordinate information with missing values ​​(NaN) after interpolation, the nearest neighbor interpolation method is used to fill in the missing values, ensuring data integrity.

[0053] 5) Establishment of the spatial surface F corresponding to the feature contact surface S. Based on the MA coordinate information of the node set M, a smooth spatial surface F that retains key features is constructed using the cubic smooth spline method. The root mean square error is introduced to evaluate the accuracy and reliability of the spatial surface F establishment method.

[0054] 6) Method for calculating the volume of a rubber block under load. Based on the coordinate information features of MA nodes in the node set M, the spatial surface F is divided into 500*500 micro-units. Since the coordinate information is preprocessed in step S4, the spatial surface F is located below the XY plane. Using the principle of definite integral, the product of the area of ​​each micro-unit on the spatial surface F and its height Z to the XY plane is calculated in turn to calculate the volume of each sub-space domain d. The volumes of MA sub-space domains d are summed to obtain the volume corresponding to the spatial domain D, that is, the volume Vr of the rubber block intruding into the rough road surface contour under load.

[0055] 7) Calculation of the penetration depth of rubber in contact with a rough road surface. Due to the incompressible nature of rubber, after the rubber block contacts the rough road surface, it will expand outwards under load, resulting in a deformed surface slightly smaller than the original surface. The projected area Sp of the four boundaries B of the characteristic contact surface S of the rubber block on the XY plane is calculated using the convhull function in MATLAB. The penetration depth H when the rubber contacts the rough road surface is obtained by dividing the penetration volume Vr of the rubber block by the projected area Sp. Figure 5 This diagram illustrates the changes in the state of a rubber block when it comes into contact with a rough road surface under load.

[0056] 8) To investigate the influence of rubber block material properties and different loads on the penetration depth of the rubber block, under the premise that the profile of the rough road surface remains unchanged, the model parameters characterizing the rubber properties are changed by modifying the equation parameters in the rubber hyperelastic constitutive model. Seven different rubber materials are set as shown in Table 2. Under the condition that the rubber block is subjected to different loads lnp, the relationship between the penetration depth of the rubber block and the rubber material and the load is obtained, as follows: Figure 6 As shown, where, Figure 6 The elastic modulus E and rubber model parameters C are shown. 10 C 20 C 30 There exists a relationship as shown in equation (2):

[0057]

[0058] Table 2 Properties of Rubber Materials

[0059]

[0060] 9) Construction of a rubber block intrusion depth prediction model. Further modifications were made to the rubber model parameter C based on the rubber material. 10 C 20 C 30 Different applied loads were considered, and the optimal super-Latin method was used to construct the experimental scheme. The rubber penetration depth calculation method of this application was employed to obtain sufficient sample data. Material parameters of the rubber block, rubber model parameters, and rubber model parameters C were used. 10 C 20 C 30 With the applied load p as the independent variable and the intrusion depth H as the dependent variable, a multiple linear regression model is established, and its expression is shown in equation (3), where x1, x2, x3, and x4 are C 10 C 20 C 30 The values ​​of lnp are given, where b0 is the intercept, and b1, b2, b3, and b4 are the regression coefficients.

[0061] H'=b0+b1x1+b2x2+b3x3+b4x4 (3)

[0062] By calculating different sample data, the results of multiple linear regression prediction are obtained, such as... Figure 7 The x-axis and y-axis represent the actual penetration depth in the numerical experiment and the penetration depth predicted by the model, respectively. Blue circles represent the penetration depth corresponding to different sample points, and the black dashed line is the ideal fitting line. The closer the blue circle is to the black dashed line, the more accurate the prediction model. Figure 7As can be seen, the blue circles are mostly next to the black dotted line, and the root mean square error of the coefficient of determination (RMSE) is 0.0096, which indicates that the constructed prediction model is excellent. The specific expression of the regression prediction model is shown in equation (4).

[0063] H' = -0.39963 - 0.056962C 10 +0.14713C 20 +0.40186C 30 +0.062605lnp (4)

[0064] To verify the accuracy of formula (4), the penetration depth method of this invention was used to recalculate the other three sets of rubber properties in ABAQUS software. The penetration depth data (denoted as H) obtained by numerical simulation under different applied loads were obtained. 实 ), and the depth of intrusion predicted by formula (4) (denoted as H') 预 The results are shown in Table 3. As can be seen from Table 3, the relative errors between the numerically calculated penetration depths of the three different rubbers and the penetration depths estimated by formula (4) are all below 6%, which indicates that the penetration depth prediction model proposed in this invention has high reliability and accuracy.

[0065] Table 3 Comparison of calculated and predicted values ​​of rubber penetration depth

[0066]

[0067]

Claims

1. A method and prediction model for calculating the penetration depth of rubber in contact with a rough road surface, characterized in that, Includes the following steps: S1: Establish a contact model between the rubber block and the rough road surface, and define the surface of the rubber block in contact with the rough road surface as the characteristic contact surface S; S2: Apply boundary conditions of constraints and loads to the contact model between the rubber block and the rough road surface to achieve phase contact between the rubber block and the rough road surface under load. S3: Based on the rubber block's intrusion into the rough road surface contour, extract the coordinate information of NA nodes on the characteristic contact surface S of the rubber block. The coordinate information is represented by (X, Y, Z), where X and Y are the positions and Z is the displacement amplitude. Subtract the maximum value Z from each of the NA coordinates in the z-direction of the node set N. max This allows the characteristic contact surface S to be translated below the XY plane under load. S4: Interpolate the coordinate information of the NA nodes in the node set N on the feature contact surface S of the rubber block to obtain the node set M, thereby increasing the number of nodes in the node set N on the feature contact surface S to the number of nodes MA in the node set M. S5: Smooth the MA coordinate information of the interpolated node set M to construct the corresponding spatial surface F, and verify the accuracy of the spatial surface F. S6: Using the coordinates of the highest point Rz of the road surface profile in the contact area between the rubber block and the rough road surface as a reference, and combining the four boundaries B of the spatial surface F, construct the spatial domain D enclosed by the highest point Rz of the road surface profile, the four boundaries B, and the spatial surface F. S7: Based on the number MA of the node set M, divide the spatial surface F and the spatial domain D into MA small units and MA sub-spatial domains d respectively. Calculate the product of the area of ​​each small unit on the spatial surface F and its height Z to the XY plane in turn to calculate the volume of each sub-spatial domain d. Then sum the volumes of MA sub-spatial domains d to obtain the volume corresponding to the spatial domain D, that is, the volume Vr of the rubber block intruding into the rough road surface contour. S8: Calculate the projected area Sp of the spatial domain D on the highest point Rz of the vertical road surface profile, and calculate the penetration depth H of the rubber when it contacts the rough road surface under load by dividing the rubber volume Vr by the projected area Sp. S9: Based on the process of steps S2-S8, under the premise that the rough road surface profile remains unchanged, the model parameters and loads that characterize the rubber properties are changed respectively to calculate the rubber block intrusion depth H corresponding to different combinations of model parameters and loads for different rubber properties. S10: Using the constitutive model parameters of rubber and the load as independent variables and the corresponding penetration depth H as the dependent variable, a rubber penetration depth prediction model with independent and dependent variables is constructed, and the accuracy of the prediction model is verified to obtain the predicted penetration depth H' when rubber contacts a rough road surface under load.

2. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S1, the physical properties of the rubber block are characterized by a hyperelastic constitutive model, and the rough road surface is characterized by an analytical rigid body model. Its rough contour can be constructed by point cloud in three-dimensional space.

3. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S2, in order to achieve contact between the rubber block and the rough road surface, the boundary conditions can be applied by either fixing the rough road surface and subjecting the rubber block to load, or by fixing the rubber block and subjecting the rough road surface to load.

4. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S3, the coordinate information of NA nodes on the characteristic contact surface S of the loaded rubber block is extracted, and the maximum value Z is determined. max The methods for obtaining and translating can be obtained manually or through secondary development.

5. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S4, the natural neighborhood interpolation method is used to adjust the NA coordinate information of the node set N on the feature surface S to the MA coordinate information of the node set M, where MA is at least 5 times NA, and the root mean square error index is used to verify the reliability of the interpolation method.

6. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S5, a spatial surface F formed by MA coordinate information of the node set M is constructed using the cubic smooth spline method, and the reliability of the spatial surface F construction method is verified by the root mean square error index.

7. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S7, the spatial surface F is divided into tiny units corresponding to the number of nodes MA in the node set M. The height Z of each tiny unit to the XY plane is determined by the z-coordinate value of the corresponding node. The volume corresponding to each tiny unit is calculated by definite integral method, and the volumes of MA tiny units are summed to obtain the rubber volume Vr of the loaded rubber block intruding into the rough road surface contour.

8. The method for calculating and predicting the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S8, the highest point Rz of the road surface profile is the maximum value Z in the MA node coordinate information. max The projected area Sp is obtained by projecting the region bounded by the four boundaries B of the spatial domain D onto the plane parallel to the rough road surface and passing through the highest point Rz of the road surface profile.

9. The method and prediction model for calculating the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that, In step S9, the model parameters characterizing the rubber properties are changed by modifying the equation parameters in the rubber hyperelastic constitutive model.

10. The method and prediction model for calculating the penetration depth of rubber in contact with a rough road surface according to claim 1, characterized in that: In step S10, the rubber intrusion depth prediction model constructed by the relationship between independent and dependent variables is realized through a multiple linear regression prediction equation.

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