Method for predicting rolling resistance performance based on tire body cord deformation characteristics

Abstract

In order to solve the problems that in the prior art, the rolling resistance of a tire is predicted mainly through the strain of a rubber material, and calculation is complex, the invention provides the method for predicting the rolling resistance performance based on the tire body cord thread deformation characteristics, and simulation calculation is carried out by establishing a finite element simulation model of tire loading and free rolling working conditions, so that the rolling resistance performance of the tire is predicted. The method comprises the following steps of: obtaining a rolling resistance value of each tire design scheme, extracting tire body cord node data, selecting a contour highest point D1, a belted layer end point D2, a contour widest point D3 and a contour lowest point D4 to partition a contour, calculating tire body cord deformation characteristic parameters R of different tire design schemes by a method of taking an average value and a maximum value, and the rolling resistance performance of the tire is evaluated. The rolling resistance of the tire is predicted through no more than 24 tire body cord thread deformation characteristic indexes, and calculation is relatively simple.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of tire rolling resistance performance prediction, and particularly relates to a method for predicting rolling resistance performance based on tire carcass cord deformation characteristics. BACKGROUND

[0002] In the process of continuous development of the automobile industry, the performance of the tire has an increasingly important influence on the fuel consumption and the cruising range of the vehicle. The rolling resistance of the tire, as one of the important factors of the performance of the tire, is a key factor affecting the fuel efficiency of the automobile and the cruising ability of the battery of the electric vehicle. The rolling resistance refers to the resistance caused by the deformation, the friction between the tire and the road surface and the energy loss inside the tire during the driving of the vehicle, which directly affects the fuel consumption and the cruising performance of the vehicle. In order to improve the energy-saving effect of the automobile, reducing the rolling resistance of the tire has become a hot spot in the tire manufacturing and automobile industry.

[0003] The method for estimating the rolling resistance of the tire of KR102070335B1 and the method for predicting the rolling resistance of the tire of JP2003118328A are both for predicting the rolling resistance of the tire through the strain of the rubber material, and the calculation is complex.

[0004] A finite element analysis of the load of the cord of the radial tire is disclosed in the Quarterly Journal of Mechanics, Vol. 23, pp. 323-330, which establishes a finite element model of the radial tire according to the finite element software, analyzes the deformation of the tire and the distribution of the cord stress under the inflation state and the load, and obtains the variation characteristics of the cord stress when the static load changes. However, only the mechanical properties of the cord are studied, and the cord is not related to the performance of the tire. The invention patent “A deformation device and a deformation method for high-elongation cord” (201310735790.3) focuses on the deformation device and the deformation method for high-elongation cord, and the purpose is to reduce the influence of the imbalance of the stress of the cord itself on the overall mechanical properties and the geometric structure of the steel cord.

[0005] It can be seen that the mechanical properties and the geometric deformation characteristics of the cord inside the tire have a direct and significant influence on the performance of the tire. In order to reduce the fuel efficiency and the cruising ability of the automobile to a certain extent, under the support of the existing technology and the mathematical method, the mechanical properties and the geometric properties of the tire carcass cord during deformation after being loaded are needed to predict the rolling resistance of different design schemes, which can effectively reduce the test cost and improve the product development efficiency. SUMMARY

[0006] Since the existing technology mainly predicts the rolling resistance of the tire through the strain of the rubber material, the calculation is complex, in order to solve the above problems, the present application provides a method for predicting the rolling resistance performance based on the tire carcass cord deformation characteristics, which predicts the rolling resistance of the tire through no more than 24 tire carcass cord deformation characteristic indexes, and the calculation is relatively simple.

[0007] The purpose of the present application is achieved in the following manner: a method for predicting rolling resistance performance based on tire carcass cord deformation characteristics, comprising the following steps: S1, establishment of a tire finite element simulation model: a finite element simulation model of tire loading and free rolling conditions is established; S2, numerical calculation of tire rolling resistance: based on the finite element simulation model of tire free rolling conditions in step S1, the stress σ, strain ε and volume V of all rubber elements of the tire under free rolling conditions are extracted, the hysteresis energy loss of the tire under free rolling conditions is calculated by Fourier transform and integration of the stress and strain and multiplication by the volume, and the size of the rolling resistance is calculated, and the rolling resistance calculation formula is: wherein, r is the tire free rolling radius, is the hysteresis energy loss of unit volume of rubber material, V i is the volume of unit rubber material; S3, extraction of carcass cord node data: based on the finite element simulation model of tire loading in step S1, the coordinates and stress of each node of the carcass cord before and after loading corresponding to the inflated profile A, the ground end profile B and the off-ground end profile C are extracted, wherein the stress is represented by S11 stress, i.e. the normal stress along the x-axis direction, the inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before tire loading, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground at the horizontal coordinate X=0 of the carcass cord after tire loading, respectively; S4, calculation of carcass cord deformation characteristic parameter R: the carcass cord deformation characteristic parameter R includes two types of deformation mechanical parameters and geometric parameters, wherein the deformation mechanical parameters are the stress difference before and after the deformation of the carcass cord under loading, and the geometric parameters are the geometric difference before and after the deformation of the carcass cord under loading, including cord elongation and radial deformation; the profile key points are defined based on coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4, the carcass cord profile is divided into region 1, region 2 and region 3 according to the profile key points, and the stress difference and geometric difference of the ground end profile B and the off-ground end profile C after loading relative to the inflated profile A before loading are calculated, wherein the stress difference greater than 0 indicates that the carcass cord deforms to stretch, and the stress difference less than 0 indicates that the carcass cord deforms to compress; according to the difference value, the deformation characteristic parameters R of the inflated profile A compared with the ground end profile B and the off-ground end profile C are obtained by taking the average value and the maximum value, and are divided into ground end parameter J and off-ground end parameter L; S5, obtaining the carcass cord deformation characteristic index S: screening all the carcass cord deformation characteristic parameters R obtained in step S4, the screening method is Pearson correlation analysis, according to the data under different tire design schemes, calculating the correlation coefficient of all the carcass cord deformation characteristic parameters R and the rolling resistance value, screening out the significant correlation deformation characteristic parameters, and determining the deformation characteristic parameters with the correlation coefficient greater than 0.5 as the carcass cord deformation characteristic index S; S6, obtaining the regression equation between the carcass cord deformation characteristic index S and the rolling resistance: obtaining the regression equation between the carcass cord deformation characteristic index S and the rolling resistance by applying principal component analysis to the carcass cord deformation characteristic index S obtained by screening; S7, predicting the tire rolling resistance: based on the regression equation between the carcass cord deformation characteristic index S and the rolling resistance, calculating the tire rolling resistance.

[0008] In S1, a tire finite element simulation model is established, the tire CAD design material distribution map is discretized into finite element grid units by HYPERMESH software, the corresponding tire structure rubber material parameters, carcass cord material parameters, and boundary information such as load and contact conditions are assigned, so as to establish the finite element simulation model of the tire under load and free rolling condition; comprising the following steps: S11, using AutoCAD to draw the scanned tire cross-section material distribution map; S12, importing the drawn material distribution map into HYPERMESH for meshing, generating a two-dimensional axisymmetric finite element model, wherein the grid size of the tread area is 3-4mm, and the grid size of the sidewall and bead area is 2.5-3mm; S13, defining the elements of the two-dimensional grid model: wherein the rubber material quadrilateral element is set as CGAX4H, the triangular element is CGAX3H, and the skeleton material element type is defined as SFMGAX1; S14, defining the wheel rim and the road surface as analytical rigid bodies, and applying the boundary conditions to the tire as follows: air pressure 0.21MPa, load 4824N; S15, establishing the finite element simulation model of the tire under load: performing tire 3D modeling and static loading analysis in ABAQUS, the steps of tire 3D modeling and static loading analysis are as follows: applying standard air pressure to the inner liner surface to form a 2D inflation model; using *SYMMETRIC MODEL GENERATION, REVOLVE command to form a 3D inflation model, and realizing tire load loading by applying displacement to the road surface; S16, establishing the finite element simulation model of the tire under free rolling condition: defining the drum radius R, setting the drum angular velocity and the corresponding linear velocity v= X R, according to the drum linear speed v and the tire rolling radius r , calculate the corresponding tire rolling angular velocity , constantly adjust the tire angular velocity, extract the rim center longitudinal force value, and when the rim center longitudinal force value is zero, the tire is in a free rolling state.

[0009] In S2, based on the finite element simulation model of the tire free rolling condition of step S1, the stress, strain and volume of each element of the tire rubber material are extracted by ABAQUS.

[0010] In S3, the extraction of the carcass cord node data includes the following steps: S31, determine the inflated profile A, the ground end profile B and the off-ground end profile C: The inflated profile A refers to the cord profile of the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles of the carcass cord at the horizontal coordinate X=0 after the tire is loaded, which are closest to and farthest from the ground; S32, select all the nodes of the carcass cord by ABAQUS and create a node set; S33, extract the coordinates and stress size of each node of the three-dimensional tire carcass cord before and after loading by ABAQUS post-processing, wherein the stress is represented by S11 stress; S34, store the serial numbers, coordinates and S11 stresses of all nodes, select the node set corresponding to the horizontal coordinate X=0, and the profiles corresponding to the node set are the required inflated profile A, ground end profile B and off-ground end profile C.

[0011] In S4, the calculation of the carcass cord deformation characteristic parameter R includes the following steps: S41, based on the symmetry of the tire, analyze one half of the carcass cord profile, define the profile key points based on the coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4, and divide the carcass cord profile into region 1, region 2 and region 3 according to the profile key points; S42, write a program by MATLAB to calculate the stress difference and geometric difference between the ground end profile B and the off-ground end profile C relative to the inflated profile A before loading, wherein the stress difference is the S11 stress difference before and after loading of each node, and the stress difference > 0 indicates that the cord is stretched when deformed, and the stress difference < 0 indicates that the cord is compressed when deformed; The geometric difference includes radial deformation and cord elongation rate, and the radial deformation is the change of Z coordinate value; S43、According to the difference value, by taking the average value and the maximum value method, for the two comparison schemes AB and AC of the inflated profile A and the ground end profile B and the inflated profile A and the off-ground end profile C, 24 carcass cord deformation characteristic parameters R of the ground end and the off-ground end are calculated; The off-ground end parameters L are: average tensile stress difference, maximum tensile stress difference, profile highest point stress difference, belt end point stress difference, profile widest point stress difference, tensile stress difference skewness value, region one average stress, region two average stress, region three average stress, cord elongation rate, maximum radial deformation amount, average radial deformation amount; The ground end parameters J are: average tensile stress difference, maximum tensile stress difference, profile highest point stress difference, belt end point stress difference, profile widest point stress difference, tensile stress difference skewness value, region one average stress, region two average stress, region three average stress, cord elongation rate, maximum radial deformation amount, average radial deformation amount.

[0012] In the S5, the acquisition of the carcass cord deformation characteristic index S includes the following steps: S51、According to the data under different tire design schemes, the correlation coefficient P of the 24 carcass cord deformation characteristic parameters R and the rolling resistance is calculated, and the Pearson correlation analysis method is adopted, and the calculation formula of the correlation coefficient P is: S52, the carcass cord deformation characteristic parameters R are screened, and the parameters with a correlation coefficient P greater than 0.5 are selected as the carcass cord deformation characteristic index S.

[0013] In the S6, the regression equation between the carcass cord deformation characteristic index S and the rolling resistance is obtained, including the following steps: S61, a total of a indexes S of the carcass cord deformation characteristic index are screened out in S5, and there are b tire design schemes, and a b×a matrix is constructed X : S62, according to the b tire design schemes, the average value and the standard deviation of each cord deformation characteristic index are calculated respectively , the standardization processing is carried out on each variable , and a standardized matrix Y is obtained S63, the correlation coefficient between each group of indexes is calculated, and a correlation matrix R is established S64, according to the correlation matrix R , the characteristic vector matrix EAnd the corresponding ordering eigenvalue λ i , eigenvector matrix E is: S65, calculate the principal component contribution rate γ i And the cumulative principal component contribution rate Σγ i , principal component contribution rate γ i The calculation formula is: S66, when the cumulative contribution rate reaches 85% or more, the principal components are subjected to multiple linear regression with the rolling resistance target amount, and the regression equation between the rolling resistance and each principal component is obtained; S67, through the eigenvector matrix E , the score expression of each principal component is calculated F i = X i e i , wherein X i The normalized each index, e i The score of each index in the corresponding principal component is substituted into the regression equation; S68, the obtained regression equation is restored through the standardization method of S62, and the final relationship is obtained , wherein y is the rolling resistance, x 1- x 10 Respectively, the carcass cord deformation characteristic index S screened out in step S5, that is, the final regression equation.

[0014] Compared with the prior art, the present application provides a method for predicting the rolling resistance performance based on the tire carcass cord deformation characteristics, (1) by establishing a finite element simulation model of the tire under load and free rolling conditions, simulation calculation is carried out, the rolling resistance numerical value of each tire design scheme is obtained, the carcass cord node data is extracted, the highest point D1, the belt end point D2, the widest point D3 and the lowest point D4 of the profile are selected to partition the profile, the carcass cord deformation characteristic parameter R of different tire design schemes is calculated by taking the average value and the maximum value, and the rolling resistance performance of the tire is evaluated. (2) Using Pearson correlation analysis method, the carcass cord deformation characteristic index S significantly related to the rolling resistance performance is screened out, the regression equation of the rolling resistance and the carcass cord deformation characteristic index S is obtained through principal component analysis method, the rolling resistance of the tire is further predicted through not more than 24 carcass cord deformation characteristic indexes, the calculation is relatively simple, so that the rolling resistance performance of different design schemes is predicted when the tire design scheme is optimized, the calculation amount is reduced, the work efficiency is improved, and the rolling resistance test cost is effectively reduced. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The figure is a tire design material distribution map.

[0016] Figure 2 The figure is a two-dimensional grid model of a tire.

[0017] Figure 3 The figure is a three-dimensional grid model of a tire.

[0018] Figure 4 The figure is a schematic diagram of a finite element simulation model of a tire free rolling condition.

[0019] Figure 5 The figure is a stress nephogram of the ground end profile and the off-ground end profile S11.

[0020] Figure 6 The figure is a schematic diagram of a carcass cord node set.

[0021] Figure 7 The figure is a schematic diagram of a carcass cord profile area division. DETAILED DESCRIPTION

[0022] The present application will be described in detail below with specific embodiments, and it is necessary to point out here that the embodiments are only used to further illustrate the present application, and cannot be understood as limiting the protection scope of the present application. Skilled persons in the art can make some non-essential improvements and adjustments according to the content of the present application.

[0023] Taking the original scheme of a 205 / 55R16 size tire as an example A method for predicting the rolling resistance performance based on the carcass cord deformation characteristics of a tire, the method comprising the following steps: S1, establishment of a tire finite element simulation model: discretize the tire design material distribution map into finite element grid units, and establish the finite element simulation model of the tire under load and free rolling condition by assigning the object rubber material parameters, carcass cord material parameters, and boundary information such as load and contact conditions; First, AutoCAD is used to draw the scanned tire cross-sectional material distribution map, as shown in Figure 1The drawn material distribution map is imported into HYPERMESH for meshing to generate a two-dimensional axisymmetric finite element model, wherein the mesh size of the tread area is 3-4 mm, the mesh size of the sidewall and bead area is 2.5-3 mm, and the built two-dimensional mesh model is as shown in Figure 2 The unit of the two-dimensional mesh model is defined, wherein the rubber material four-side element is set as CGAX4H, the triangular element is CGAX3H, the skeleton material element type is defined as SFMGAX1, the total number of elements is 1818, and the total number of nodes is 1996; the rim and the road surface are both defined as analytical rigid bodies, the boundary conditions of the tire are set as follows: air pressure 0.21 MPa, load 4824 N; then, the three-dimensional model of the tire is established: the 3D modeling and static loading analysis of the tire are performed in ABAQUS, and the steps of the 3D modeling and static loading analysis are as follows: a standard air pressure is applied to the inner liner surface to form a 2D inflation model; a 3D inflation model is formed by using the *SYMMETRIC MODEL GENERATION, REVOLVE command, as shown in Figure 3 Finally, the finite element simulation model of the tire in the free rolling condition is established by applying displacement to the road surface to realize tire load loading: the drum radius R is defined as 0.8535 m, the drum angular velocity = 26.04 rad / s and the corresponding linear velocity v= × R = 80 km / h, the corresponding tire rolling angular velocity r is calculated according to the drum linear velocity v and the tire rolling radius , the tire angular velocity is continuously adjusted, and when the longitudinal force value of the rim center is zero, it is determined whether the tire is in the free rolling state, and the obtained finite element simulation model of the tire in the free rolling condition is as shown in Figure 4 .

[0024] S2, numerical calculation of tire rolling resistance: based on the numerical simulation calculation result of step S1, the stress σ, strain ε and volume V of all rubber elements of the tire in the free rolling condition are extracted, the stress and strain are subjected to Fourier transform and integration, and multiplied by the volume to calculate the hysteresis energy loss of the tire in the free rolling condition, and then the size of the rolling resistance is calculated, and the rolling resistance calculation formula is: wherein, r is the tire free rolling radius, is the hysteresis energy loss of unit volume of rubber material, V i is the volume of unit rubber material; Based on the numerical simulation calculation results of step S1, the stress and strain and volume of each element of the tire rubber material are extracted by ABAQUS; the stress and strain are subjected to Fourier transform to obtain the stress and strain of the rubber element at different frequencies , the total hysteresis energy loss is calculated according to formula (2), wherein m is the Fourier series expansion term number, , , delta is the phase difference between stress and strain, which is obtained by loss factor test; the free rolling radius of the tire is extracted and substituted into formula (1) to calculate the tire rolling resistance.

[0025] S3, extraction of carcass cord node data: based on the simulation results of step S1, the coordinates and stress of each node of the carcass cord before and after loading corresponding to the inflated profile A, the ground end profile B and the off-ground end profile C are extracted, wherein the stress is represented by S11 stress, as shown in Table 1; the inflated profile node data is as shown in Table 1; the inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after the tire is loaded; Figure 5 determine the inflated profile A, the ground end profile B and the off-ground end profile C. The inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after the tire is loaded, the nodes of all the carcass cord models are selected by ABAQUS and a node set is created, as shown in Table 1; the coordinates and stress of each node of the three-dimensional tire carcass cord before and after loading are extracted by ABAQUS post-processing, wherein the stress is represented by S11 stress; the serial numbers, coordinates and S11 stresses of all the nodes are stored in an Excel file, as shown in Table 2, the node set corresponding to the horizontal coordinate X=0 is selected, and the profiles corresponding thereto are the required inflated profile A, ground end profile B and off-ground end profile C, as shown in Table 1. determine the inflated profile A, the ground end profile B and the off-ground end profile C. The inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after the tire is loaded, the nodes of all the carcass cord models are selected by ABAQUS and a node set is created, as shown in Table 1; the coordinates and stress of each node of the three-dimensional tire carcass cord before and after loading are extracted by ABAQUS post-processing, wherein the stress is represented by S11 stress; the serial numbers, coordinates and S11 stresses of all the nodes are stored in an Excel file, as shown in Table 2, the node set corresponding to the horizontal coordinate X=0 is selected, and the profiles corresponding thereto are the required inflated profile A, ground end profile B and off-ground end profile C, as shown in Table 1. Figure 6 determine the inflated profile A, the ground end profile B and the off-ground end profile C. The inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after the tire is loaded, the nodes of all the carcass cord models are selected by ABAQUS and a node set is created, as shown in Table 1; the coordinates and stress of each node of the three-dimensional tire carcass cord before and after loading are extracted by ABAQUS post-processing, wherein the stress is represented by S11 stress; the serial numbers, coordinates and S11 stresses of all the nodes are stored in an Excel file, as shown in Table 2, the node set corresponding to the horizontal coordinate X=0 is selected, and the profiles corresponding thereto are the required inflated profile A, ground end profile B and off-ground end profile C, as shown in Table 1. Figure 7 determine the inflated profile A, the ground end profile B and the off-ground end profile C. The inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground end profile B and the off-ground end profile C refer to the cord profiles corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after the tire is loaded, the nodes of all the carcass cord models are selected by ABAQUS and a node set is created, as shown in Table 1; the coordinates and stress of each node of the three-dimensional tire carcass cord before and after loading are extracted by ABAQUS post-processing, wherein the stress is represented by S11 stress; the serial numbers, coordinates and S11 stresses of all the nodes are stored in an Excel file, as shown in Table 2, the node set corresponding to the horizontal coordinate X=0 is selected, and the profiles corresponding thereto are the required inflated profile A, ground end profile B and off-ground end profile C, as shown in Table 1.

[0026] Table 1 Inflated profile node data of original scheme Table 2 Node coordinate and S11 stress data of three-dimensional carcass cord inflated profile S4, Calculation of the carcass cord deformation characteristic parameter R: The carcass cord deformation characteristic parameter R is mainly divided into two categories of deformation mechanical parameters and geometric parameters, wherein the deformation mechanical parameters are the stress difference before and after the deformation of the carcass cord under load, and the geometric parameters are the geometric difference before and after the deformation of the carcass cord under load, including the cord elongation and the radial deformation. The profile key points are defined based on the coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4. According to the profile key points, the carcass cord profile is divided into region 1, region 2 and region 3, and the stress difference and the geometric difference between the loaded end profile B and the off-ground end profile C relative to the inflated profile A before loading are calculated, wherein the stress difference greater than 0 indicates that the carcass cord is stretched during deformation, and the stress difference less than 0 indicates that the carcass cord is compressed during deformation. According to the difference, the deformation characteristic parameters R of the inflated profile A and the loaded end profile B and the inflated profile A and the off-ground end profile C are obtained by taking the average value and the maximum value, which are divided into the loaded end parameter J and the off-ground end parameter L; Based on the symmetry of the tire, one half of the carcass cord profile is analyzed, and the profile key points are defined based on the coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4. According to the profile key points, the carcass cord profile is divided into region 1, region 2 and region 3, as shown in Figure 7 The program is written by MATLAB to calculate the stress difference and the geometric difference between the loaded end profile B and the off-ground end profile C relative to the inflated profile A before loading, wherein the stress difference is the S11 stress difference before and after loading of each node, the stress difference > 0 indicates that the cord is stretched during deformation, and the stress difference < 0 indicates that the cord is compressed during deformation; the geometric difference is divided into radial deformation (i.e. the change of Z coordinate value) and cord elongation; according to the difference, the average tensile stress difference and the maximum tensile stress difference are obtained by taking the average value and the maximum value of the stress difference of the region where the stress difference of all nodes is greater than 0 (i.e. the cord stretching region), the average stress difference of region 1, region 2 and region 3 is obtained by taking the average value of the stress difference of the nodes in the region divided in step S4, the stress difference of the profile highest point, the stress difference of the belt end point and the stress difference of the profile widest point are obtained by taking the stress difference of the first three profile key points in step S4, the average radial deformation and the maximum radial deformation are obtained by taking the average value and the maximum value of the Z coordinate difference of all nodes, the cord elongation is obtained by taking the difference of the arc length of all nodes after profile comparison calculation, the tensile stress difference skewness value is obtained by taking the overall skewness of the stress difference of the region where the stress difference of all nodes is greater than 0; for the two comparison schemes AB and AC of the inflated profile A and the loaded end profile B and the inflated profile A and the off-ground end profile C, 24 carcass cord deformation characteristic parameters R of the loaded end and the off-ground end are calculated, and the size of each parameter of the original scheme is as shown in Table 3: Table 3 Deformation characteristic parameters of the original scheme S5, obtaining the carcass cord deformation characteristic index S: all the carcass cord deformation characteristic parameters R obtained in step S4 are screened, the screening method is Pearson correlation analysis, the correlation coefficient of the carcass cord deformation characteristic parameters R and the rolling resistance value of different tire design schemes is calculated, and the significantly correlated deformation characteristic parameters are screened out, and the deformation characteristic parameters with a correlation coefficient greater than 0.5 are determined as the carcass cord deformation characteristic index S; According to the data of different tire design schemes, the correlation coefficients P of 24 carcass cord deformation characteristic parameters R and rolling resistance are calculated, as shown in Table 4, and the Pearson correlation analysis method is used, and the calculation formula of the correlation coefficient P is: Table 4 Correlation analysis of 24 deformation characteristic parameters and rolling resistance The carcass cord deformation characteristic parameters R are screened, the parameters with a correlation coefficient P greater than 0.5 are selected as the carcass cord deformation characteristic index S, and the finally screened carcass cord deformation characteristic index S is: the average tensile stress difference in the off-ground end parameter L x 1, maximum tensile stress difference x 2, profile highest point stress difference x 3, belt end point stress difference x 4, region 1 average stress difference x 5, region 2 average stress difference x 6 and cord elongation x 7, average tensile stress difference in the ground end parameter J x 8, maximum tensile stress difference x 9 and region 3 average stress difference x 10 .

[0027] S6, obtaining the regression equation of the carcass cord deformation characteristic index S and the rolling resistance: the carcass cord deformation characteristic index S obtained by screening is applied to the principal component analysis method to obtain the regression equation between the carcass cord deformation characteristic index S and the rolling resistance; The carcass cord deformation characteristic index S has a total of 10 indexes, 1 target function y represents the rolling resistance, and there are 20 tire design schemes. A 20x11 matrix X is constructed, and the matrix is constructed X As shown in Table 5: Table 5 Evaluation index and rolling resistance matrix The average value of each group of indexes is calculated and the standard deviation , the standardization of each variable is carried out , get the normalized matrix Y , as shown in Table 6: Table 6 Normalized matrix Remove the rolling resistance, respectively, calculate the correlation coefficient between the 10 indicators, and establish the correlation matrix R , as shown in Table 7: Table 7 Correlation matrix According to the correlation matrix R , calculate the eigenvector matrix E And the corresponding order eigenvalue λ i , as shown in Table 8: Table 8 Eigenvector matrix The eigenvalues are 6.0697, 1.3675, 1.2244, 0.6162, 0.4061, 0.1665, 0.0754, 0.0645, 0.0086 and 0.0011, respectively; Calculate the principal component contribution rate γ i And the cumulative principal component contribution rate Σγ i The contribution rate of each principal component is the eigenvalue of each principal component × 10%, so each principal component F 1 - F 10 The contribution rates are 60.697%, 13.675%, 12.244%, 6.162%, 4.061%, 1.665%, 0.754%, 0.645%, 0.086, 0.011%, respectively. The cumulative contribution rate of the method is required to reach 85% or more, so the F 1 , F 2 , F 3 And the rolling resistance target quantity is subjected to multiple linear regression, and the relationship between the rolling resistance and each principal component is: Among them, Y is the normalized rolling resistance, F 1 - F 3 Indicates the first three principal components selected according to the cumulative contribution rate.

[0028] Through the eigenvector matrix E , calculate the three principal component score expression F i =X i e i , X i For the standardized indicators, e i Substituting the scores of each indicator into the corresponding principal components (i.e., the first three columns in Table 8), the expressions for the scores of each principal component are as follows: The final regression equation obtained by standardization is: In equation (8), y represents rolling resistance. x 1- x 10 The S values ​​are the tire cord deformation characteristic indicators selected in step S5.

[0029] The regression equation is evaluated below. Based on the regression equation, the rolling resistance corresponding to the above 20 schemes was recalculated using 10 tire cord deformation characteristic indicators, and compared with the rolling resistance results of the 20 schemes obtained in step S2 to evaluate the regression equation. The results are shown in Table 9.

[0030] Table 9 Evaluation Results The evaluation results show that the invention provides a method for predicting rolling resistance performance based on the deformation characteristics of tire carcass cords. The maximum relative error in evaluating rolling resistance performance is controlled within 3%, and the evaluation results are good. It can be used to predict tire rolling resistance performance.

[0031] S7. Prediction of tire rolling resistance: The tire rolling resistance is calculated based on the regression equation between the tire carcass cord deformation characteristic index S and the rolling resistance. The result is compared with the rolling resistance obtained from the numerical simulation in step S2 to verify the accuracy of the regression equation and ultimately to predict the rolling resistance of different tire designs.

[0032] Taking three new tire designs with a specification of 205 / 55R16 as examples, a finite element simulation model is established according to the method for establishing the tire finite element simulation model in step S1. Then, the average tensile stress difference in the tire carcass cord deformation characteristic index S—the ground clearance parameter L—is obtained according to the methods in steps S4 and S5 for the three new designs. x 1. Maximum tensile stress difference x 2. Stress difference at the highest point of the profile x 3. Stress difference at the ends of the belt layer x 4. Average stress difference in region 1x 5, average stress difference of zone 2 x 6 and cord elongation x 7, average tensile stress difference in the parameter J of the ground end x 8, maximum tensile stress difference x 9 and average stress difference of zone 3 x 10 Ten tire body cord deformation characteristic indicators S corresponding to the three new schemes respectively are obtained, as shown in Table 10.

[0033] Table 10 tire body cord deformation characteristic indicators S of new schemes The predicted values of the rolling resistance of the three new schemes are obtained by substituting the indicators in Table 10 into the regression equation established in step S6, and the simulation values of the rolling resistance of the three new schemes are calculated according to the numerical simulation calculation method of step S2, and the final results are shown in Table 11.

[0034] Table 11 predicted results It is concluded from the predicted results that the method for predicting the rolling resistance performance based on the tire body cord deformation characteristics of the application controls the maximum relative error of the rolling resistance performance predicted by the three new schemes to 1.89%, and the predicted results are good, which provides a new method for predicting the rolling resistance performance of the type of tire.

[0035] The above only describes the preferred embodiments of the application, but the protection scope of the application is not limited thereto, and it should be noted that for those skilled in the art and any person skilled in the art, under the premise of not departing from the overall concept of the application, according to the technical scheme and the inventive concept of the application, equivalent replacement or change, and several changes and improvements made, these should also be regarded as the protection scope of the application.

Claims

1. A method of predicting rolling resistance performance based on tire carcass cord deformation characteristics, characterized by, Comprise the following steps: S1, the establishment of tire finite element simulation model: the establishment of tire finite element simulation model under the condition of loading and free rolling; S2, tire rolling resistance numerical calculation: based on the finite element simulation model of the tire free rolling condition of step S1, the stress σ, strain ε and volume of all rubber elements of the tire under the free rolling condition are extracted V The hysteresis energy loss of the tire free rolling condition is calculated by Fourier transforming and integrating the stress and strain and multiplying by the volume, and the size of the rolling resistance is calculated, and the rolling resistance calculation formula is: wherein, r Rf is the free rolling radius of the tire, h is the hysteresis energy loss per unit volume of rubber material, V i V is the volume of the unit of rubber material; S3, the extraction of carcass cord node data: based on the finite element simulation model of tire loading in step S1, the coordinates and stress of each node in the carcass cord before and after loading corresponding to the inflated profile A, the ground end profile B and the off-ground end profile C are extracted respectively, wherein the stress adopts S11 stress, that is, the normal stress along the x axis direction, the inflated profile A refers to the cord profile corresponding to the carcass cord at the horizontal coordinate X=0 before tire loading, and the ground end profile B and the off-ground end profile C respectively refer to the cord profile corresponding to the closest and farthest from the ground of the carcass cord at the horizontal coordinate X=0 after tire loading; S4, the calculation of the deformation characteristic parameter R of the carcass cord: the deformation characteristic parameter R of the carcass cord includes two types of deformation mechanical parameters and geometric parameters, wherein the deformation mechanical parameter is the stress difference before and after the deformation of the carcass cord under loading, and the geometric parameter is the geometric difference before and after the deformation of the carcass cord under loading, including the elongation and radial deformation amount; the profile key points are defined based on the coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4, the carcass cord profile is divided into region 1, region 2 and region 3 according to the profile key points, and the stress difference and geometric difference of the ground end profile B and the off-ground end profile C after loading relative to the inflated profile A before loading are calculated respectively, wherein the stress difference greater than 0 indicates that the carcass cord is stretched when deformed, and the stress difference less than 0 indicates that the carcass cord is compressed when deformed; according to the difference value, the deformation characteristic parameters R of the inflated profile A compared with the ground end profile B and the off-ground end profile C are obtained by taking the average value and the maximum value, which are divided into ground end parameter J and off-ground end parameter L; S5, the acquisition of the deformation characteristic index S of the carcass cord: all the deformation characteristic parameters R of the carcass cord obtained in step S4 are screened, the screening method is Pearson correlation analysis, the correlation coefficients of all the deformation characteristic parameters R of the carcass cord and the rolling resistance value are calculated according to the data under different tire design schemes, and the significantly correlated deformation characteristic parameters are screened out, and the deformation characteristic parameters with the correlation coefficient greater than 0.5 are determined as the deformation characteristic index S of the carcass cord; S6, the regression equation of the deformation characteristic index S of the carcass cord and the rolling resistance is obtained: the deformation characteristic index S of the carcass cord obtained by screening is applied to obtain the regression equation between the deformation characteristic index S of the carcass cord and the rolling resistance by principal component analysis method; S7, the prediction of tire rolling resistance: based on the regression equation between the deformation characteristic index S of the carcass cord and the rolling resistance, the tire rolling resistance is calculated.

2. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein: In the S1, the finite element simulation model of tire is established, the tire CAD design material distribution map is discretized into finite element grid units through HYPERMESH software, the rubber material parameters, carcass cord material parameters, loading and contact conditions and other boundary information corresponding to the tire structure are given, so as to establish the finite element simulation model of tire under the condition of loading and free rolling; comprise the following steps: S11, draw the scanned tire cross-section material distribution map using AutoCAD; S12, import the drawn material distribution map into HYPERMESH for meshing, generating a two-dimensional axisymmetric finite element model, wherein the mesh size of the tread area is 3-4 mm, and the mesh size of the sidewall and bead area is 2.5-3 mm; S13, define the elements of the two-dimensional mesh model: the four-sided rubber material elements are set as CGAX4H, the triangular elements are set as CGAX3H, and the skeleton material element type is defined as SFMGAX1; S14, define the rim and the road surface as analytical rigid bodies, and apply the boundary conditions to the tire: air pressure 0.21 MPa, load 4824 N; S15, establish a finite element simulation model of the loaded tire: perform tire 3D modeling and static loading analysis in ABAQUS, and the steps are as follows: apply standard air pressure to the inner liner surface to form a 2D inflation model; use the *SYMMETRIC MODEL GENERATION, REVOLVE command to form a 3D inflation model, and use the road surface to apply displacement to realize tire load loading; S16, Establishing a finite element simulation model of tire free rolling condition: defining the drum radius R, setting the drum angular velocity and the corresponding linear velocity v= x R, according to the drum linear velocity v and the tire rolling radius r , the corresponding tire rolling angular velocity is calculated, the tire angular velocity is constantly adjusted, the rim center longitudinal force value is extracted, and when the rim center longitudinal force value is zero, the tire is in a free rolling state.

3. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein: In S2, based on the finite element simulation model of the tire free rolling condition in S1, the stress, strain and volume of each element of the tire rubber material are extracted by ABAQUS.

4. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein, In S3, the extraction of the carcass cord node data includes the following steps: S31, determine the inflated profile A, the ground contact end profile B and the off-ground end profile C: The inflated profile A refers to the cord profile of the carcass cord at the horizontal coordinate X=0 before the tire is loaded, and the ground contact end profile B and the off-ground end profile C refer to the cord profiles of the carcass cord at the horizontal coordinate X=0 closest to and farthest from the ground after the tire is loaded; S32, select all the nodes of the carcass cord by ABAQUS and create a node set; S33, extract the coordinates and S11 stress of each node of the three-dimensional tire carcass cord before and after loading by ABAQUS post-processing, wherein the stress is represented by S11 stress; S34, store the serial numbers, coordinates and S11 stresses of all nodes, select the node set corresponding to the horizontal coordinate X=0, and the profiles corresponding to the node set are the required inflated profile A, ground contact end profile B and off-ground end profile C.

5. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein, In S4, the calculation of the carcass cord deformation characteristic parameter R includes the following steps: S41, based on the symmetry of the tire, analyze one half of the carcass cord profile, define the profile key points based on the coordinates, including the profile highest point D1, the belt end point D2, the profile widest point D3 and the profile lowest point D4, and divide the carcass cord profile into region 1, region 2 and region 3 according to the profile key points; S42, through MATLAB program, the stress difference and the geometric difference size of the tire loaded end profile B and the ground end profile C relative to the inflated profile A before the tire is loaded are calculated, wherein the stress difference is the S11 stress difference before and after each node is loaded, and the stress difference > 0 indicates that the cord is stretched when deformed, and the stress difference < 0 indicates that the cord is compressed when deformed; the geometric difference includes radial deformation and cord elongation, and the radial deformation is the change of Z coordinate value; S43, according to the difference size, through the average value and the maximum value method, for the inflated profile A and the ground end profile B and the inflated profile A and the ground end profile C two comparison schemes AB, AC, 24 carcass cord deformation characteristic parameters R of the ground end and the ground end are calculated; The ground end parameter L is: average tensile stress difference, maximum tensile stress difference, profile highest point stress difference, belt end point stress difference, profile widest point stress difference, tensile stress difference skewness value, region one average stress, region two average stress, region three average stress, cord elongation, maximum radial deformation, average radial deformation; The ground end parameter J is: average tensile stress difference, maximum tensile stress difference, profile highest point stress difference, belt end point stress difference, profile widest point stress difference, tensile stress difference skewness value, region one average stress, region two average stress, region three average stress, cord elongation, maximum radial deformation, average radial deformation.

6. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein, In the S5, the acquisition of the carcass cord deformation characteristic index S includes the following steps: S51, according to the data under different tire design schemes, the correlation coefficient P of the 24 carcass cord deformation characteristic parameters R and the rolling resistance is calculated, the Pearson correlation analysis method is adopted, and the calculation formula of the correlation coefficient P is: S52, the carcass cord deformation characteristic parameters R are screened, and the parameters with the correlation coefficient P > 0.5 are selected as the carcass cord deformation characteristic index S.

7. The method of predicting rolling resistance performance based on tire carcass cord deformation characteristics of claim 1, wherein, In the S6, the regression equation between the carcass cord deformation characteristic index S and the rolling resistance is obtained, including the following steps: S61, S5 in the screening out carcass cord deformation characteristic index S a total of a index, a total of b tire design scheme, to build a b x a matrix X : S62、According to b tire design schemes, the average value and standard deviation of each cord deformation characteristic index are calculated respectively, and each variable is standardized , to obtain a standardized matrix Y: S63, calculate the correlation coefficient between each group of indicators, and establish a correlation matrix R : S64, the correlation matrix R , the eigenvector matrix E and the corresponding ordered eigenvalues λ i , the eigenvector matrix E is S65, the principal component contribution rate γ i with the cumulative principal component contribution rate Σγ i , the principal component contribution rate γ i The calculation formula is: S66, when the cumulative contribution rate reaches more than 85%, the principal components and the rolling resistance target are subjected to multiple linear regression to obtain the regression equation between the rolling resistance and the principal components; S67, by the eigenvector matrix E , calculate the principal component score expression F i = X i e i , wherein X i each index after normalization, e i the score of each index in the corresponding principal component, substitute into the regression equation; S68, the resulting regression equation By the standardization method of S62, the resulting final relationship is where y is the rolling resistance, x 1- x 10 S, the carcass cord deformation characteristic index screened out in step S5, is the final regression equation.

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