Analysis of the Effect of Wear on Tire Cornering Characteristics Based on Grounding Characteristics

Abstract

Electric vehicles can lead to accelerated tire wear, an inevitable phenomenon during tire usage that can affect the cornering characteristics determining handling stability. In order to simulate tire wear, a finite element model for tire wear was established using the UMESHMOTION subroutine and Arbitrary Lagrangian–Eulerian (ALE) adaptive meshing in ABAQUS, which is based on the Archard theory. The tire’s cornering characteristics were analyzed based on the obtained worn tire. The research results demonstrate that as the wear amount increases, the cornering stiffness and aligning stiffness of the tire also increase. When there are differences in wear on both tire shoulders with the same global wear, the change in cornering stiffness is not significant, while the aligning stiffness exhibits noticeable differences. To explain the above phenomenon, grounding characteristics were incorporated as mediator variables. The analysis results indicate that wear has an impact on the grounding characteristics. Additionally, statistically significant correlations exist between grounding parameters and cornering characteristics. In conclusion, wear affects the tire’s cornering characteristics by changing the grounding characteristics.

1. Introduction

New energy vehicles are environmentally friendly vehicles that can alleviate energy shortages and reduce greenhouse gas emissions. With countries around the world announcing the cessation of production and sales of fuel powered vehicles, new energy vehicles have gradually become the mainstream. Among them, electric vehicles are currently the most popular type. It is worth considering that the special power system of electric vehicles can also bring some new problems. For tires, electric vehicles of the same specification are heavier than fuel vehicles, which can lead to faster tire wear [1].

Tire wear refers to the destruction of macromolecular chains or chemical bond between molecular chains of rubber layer caused by the sliding between tire and road. Wear can be divided into uniform wear and abnormal wear, with abnormal wear including uneven wear in the width direction and irregular wear in the circumferential direction [2].

So far, research on wear has mainly focused on two aspects: predicting wear and controlling wear. There are three main methods for predicting wear. One is the theoretical analysis method, which predicts wear by establishing a mathematical model. Li et al. [3] employed a combination of theoretical analysis and numerical simulation to develop a tire wear formula that incorporates temperature effects and vehicle dynamic characteristics. Huang et al. [4] established a three-dimensional tire wear model based on the brush model as a function of road roughness and vehicle dynamic characteristics under the condition of camber angle. Wang et al. [5] combined an improved ring model with the brush model to develop the tire wear model and analyzed the quantitative relationship between contact characteristics and wear. Chen et al. [6] proposed a new three degree of freedom nonlinear vehicle dynamics model for multi axle steering vehicles, and calculated tire wear considering suspension, steering system, and toe in angle. Nguyen et al. [7] considered the historical dependence and directionality of wear and established a rubber wear model, which was introduced into finite element analysis and verified through experimental data. Lepine et al. [8] proposed an empirical tire wear model for heavy-duty multi axle vehicles based on route data and vehicle models. Nakajima et al. [9] introduced a two-dimensional contact patch in the wear calculation, expanded the width direction, and predicted the wear process of tires under pure slip and combined slip conditions. Building upon the magic formula, Sakhnevych et al. [10] extended its applicability by incorporating the effects of thermodynamics and wear state on tire mechanical properties. They developed a multiphysical magic formula.

The second is the experimental method. Stalnaker et al. [11] obtained good consistency by comparing indoor drum measurement data with outdoor vehicle wear results. Runge et al. [12] proposed a deeper understanding of the friction and wear mechanisms of tire tread based on micro-tread block wear experiments, emphasizing the importance of considering the real-time dynamic contact between the tire and the road surface.

The third method is finite element analysis (FEA). FEA is a numerical method used to obtain approximate solutions for engineering problems, which owes its development to the rapid advancement of computer technology and computer-aided engineering (CAE) techniques. Cho et al. [13] considered the influence of contact pressure on the friction coefficient and used explicit finite element method to simulate tread wear of tires with complex patterns. Dionisio et al. [14] and Li et al. [15] used a finite element model to calculate the tread wear of tires containing only longitudinal groove patterns. Tamada et al. [16] used the LS-DYNA to simulate wear on tires with complex tread patterns, taking into account uneven wear.

Controlling tire wear can be tackled from two angles: one is to consider the tire itself, while the other is to look at other parts of the vehicle such as the suspension. Implementing effective wear control measures can help to prolong the lifespan of tires and also minimize the impact of tire wear particles on the environment. Liang et al. [17] used the skewness value of friction work in the grounding area to evaluate the tire’s uneven wear, and through FEA, optimized the running surface width and arc height, which effectively reduces the uneven wear of tires. Papaioannou et al. [18] aimed to reduce tire wear and improve driving comfort and vehicle handling stability. The tire and suspension parameters have been optimized. Wang et al. [19] adopted a virtual camber and optimal curved running surface method, effectively reducing the total wear of straddle-type monorail trains’ running wheel tires. Waquier et al. [20] and Zhang et al. [21] proposed improving the rubber material of the tire, which can increase the wear resistance of the tire.

Currently, there are two main methods for onboard evaluation of tire wear: machine vision and smart tires.

Due to the continuous advancement of machine vision technology, numerous efficient and accurate methods for calculating tire wear have emerged. Wang et al. [22] processed the radial section image of the tire tread obtained from the laser plane to extract a single pixel centerline. The pixel coordinates of the centerline were then converted into world coordinates using calibration information. Contour curves of the tire’s radial section were obtained. Finally, an algorithm was developed to identify and locate tread grooves on the profile curve and calculate the depth of each groove. Zhu et al. [23] proposed a method for image feature extraction and representation. They employed preprocessing and texture feature extraction techniques to analyze tire pattern wear images from a small sample database. They also utilized machine learning technology to establish mathematical models for wear degree estimation and develop a wear feature vector.

Smart tires utilize optical, strain, and acceleration sensors to capture dynamic response information from tires, enabling real-time wear detection. Zhang et al. [24] proposed an intelligent tire information system that utilizes triaxial accelerometer data and strain gauge data to estimate tire wear. Li et al. [25] presented an intelligent algorithm for predicting tire wear using an artificial neural network. The algorithm is based on the relationship among tire inflation pressure, load, tire wear, speed, and radial vibration frequency. In the above studies the research on tire wear mostly focuses on itself. However, in recent years, there has been a growing interest among researchers in exploring the impact of wear on the mechanical properties of tires. The most direct impact of tire wear is the change in tread height, which, as the only component of the vehicle that comes into contact with the ground, affects the mechanical properties of the tire. Todoroff et al. [26] compared the wet grip performance of worn tires of the same model with new tires and explained the decrease in wet grip ability of worn tires through two aspects: rubber friction and water sliding mechanism. Wright et al. [27] found that wear has an impact of approximately 10% on the longitudinal friction of tires. Becker et al. [28] studied agricultural large lug tire and found that wear significantly affects the stiffness of the tires. Nantapuk et al. [29] conducted a study comparing new tires with tires that had covered a distance of 50,000 km and observed an increase in the stiffness and energy absorption of the used tires.

Cornering characteristics are one of the important mechanical properties that seriously affect the handling stability. Lu et al. [30] extended the wear conditions of the UniTire tire model and examined how different wear conditions affected cornering stiffness and aligning stiffness. The analysis was then compared with experimental data to validate the model’s accuracy. This research is important because it helps us better understand the impact of tire wear on tire performance, especially in terms of handling stability. Inspired by this study, this paper investigates the cornering properties of worn tires.

In this paper, a finite element model of the tire is first established for wear simulation, followed by secondary simulation of different worn tires obtained to obtain the lateral force and aligning torque for fitting cornering stiffness and aligning stiffness. Finally, a qualitative explanation is provided for the changes in the cornering characteristics of uneven wear tires from grounding characteristics. During the analysis, grounding characteristics are employed as intermediate variables to elucidate the impact of wear on cornering characteristics.

2. Finite Element Model of the Tire

2.1. Finite Element Structural Model

Taking 205/55R16 radial tire as the research object, the cross-sectional profile of the tire was established using AutoCAD. In order to reduce calculation costs, only the longitudinal grooves of the tire were considered, while the small transverse groove patterns were ignored.

Import the geometric modeling into HyperMesh for geometric cleaning and mesh generation. Immediately afterwards, an “INP” file containing all information about tire models is exported. The rubber materials are represented in the simulation using CGAX3H (3-node generalized linear axisymmetric triangle element) and CGAX4H (4-node generalized bilinear axisymmetric quadrilateral element) elements, while the reinforcement is modeled using SFMGAX1 (2-node linear axisymmetric surface element) elements that carry rebar layers [31]. To embed the reinforcement layers in the rubber matrix, an embedded element constraint is utilized.

Subsequently, corresponding material properties are assigned to the cross-section of each component of the tire. Neo-Hookean constitutive model is used to describe the stress-strain relationship of rubber material, and Rebar model is used to simulate fiber-reinforced material. The specific material parameters can be found in [32]. The two-dimensional finite element model is shown in Figure 1a.

In ABAQUS/Standard, the keyword * SYMMETRIC MODEL GENERALATION is used to obtain the three-dimensional finite element model of the tire. In order to accelerate the calculation speed and ensure accuracy, the mesh needs to be refined only in the contact region, as shown in Figure 1b. The wheel rim and road surface are set as analytical rigid bodies. The relative motion between the tire and rim is ignored. Finally, the friction model between the tire and the road surface adopts Coulomb friction.

2.2. Verification of Finite Element Model

2.2.1. Grounding Footprint Verification

Grounding footprint verification is one of the commonly methods to validate the accuracy of tire finite element models. In this study, the verification was performed using the Tire Multifunction Testing Machine-2 (MTM-2). During the testing, the tire was loaded to its rated load of 4821 N, and the inflation pressure was set to the rated pressure of 0.24 MPa. The grounding footprint of the tire was obtained through ink printing, and the relevant geometric parameters of the footprint were extracted. It is important to note that the tire remained stationary during the testing process.

The footprints obtained by the experimental method and FEA are shown in Figure 2.

The comparison of detailed geometric parameters is shown in

Table 1. Area characteristic parameters.

Solution	FEA	Experiment	Error
contact length/mm	144	147	2.04%
contact width/mm	162	161	0.62%

.

The finite element simulation results show good agreement with the experimental data in terms of the footprint, and the maximum relative error between the experimental and simulated values for the contact length and width is only 2.04%. This shows that the established finite element model can accurately reflect the tire grounding footprint.

2.2.2. Stiffness Verification

According to the test method specified in national standards (GB/T 23663-2020), the tire stiffness was evaluated using the MTM-2. Concurrently, a stiffness simulation of the tire finite element model was conducted in ABAQUS, replicating the identical working conditions. The test results and simulation data are presented in

Table 2. Comparison between simulation value and experiment value of tire stiffness.

Stiffness	FEA	Experiment	Error
radial stiffness/(N/mm)	214.50	206.28	3.98%
lateral stiffness/(N/mm)	154.06	148.37	3.84%
longitudinal stiffness/(N/mm)	161.13	168.56	4.40%

.

By comparing the tire stiffness obtained through the experiment with the tire stiffness obtained through FEA, a high level of agreement between the two is observed. This indicates that the established tire finite element model possesses a high degree of accuracy in terms of tire stiffness. The verification results obtained from both the grounding footprint and stiffness analysis provide compelling evidence supporting the high validity of the tire finite element model established in this paper.

3. Wear Simulation

After establishing the finite element tire model, the subsequent step involves simulating wear. The tire wear simulation in ABAQUS utilizes the UMESHMOTION subroutine and ALE adaptive meshing. Specifically, the wear amount is calculated using the Archard model. Figure 3 outlines the step-by-step procedure for conducting the simulation.

3.1. Archard’s Wear Law

This study exclusively focuses on the simulation of abrasive wear, which is widely recognized as the primary mechanism responsible for tire wear. Archard’s wear law, known as the most prevalent model for describing abrasive wear, is extensively employed by researchers investigating tire wear using ABAQUS. The Archard model, as a classical and well-established approach, provides a robust framework for understanding and analyzing wear on tires. Its main concept is to assume that wear is a linear function of the normal force and sliding distance at the contact interface [31,33].

$$V=K\frac{F}{H}s$$

(1)

where $V$ is the wear volume of the tire tread material, $s$ is the sliding distance, $K$ is a nondimensional wear coefficient, $F$ is the normal reaction force acting at the contact patch of the tire with the ground, and $H$ is the material hardness.

The wear volume is a function of time and taking the derivative of Formula (1) with respect to time yields Formula (2).

$$\dot{q}=\frac{K}{H}F\dot{\gamma }=\frac{K}{H}PS\dot{\gamma }$$

(2)

where $\dot{q}$ is the volumetric material loss rate, $P$ is the interface normal pressure, $S$ is the interface area, and $\dot{\gamma }$ is the interface slip rate.

Assuming that the wear of the tire is uniformly distributed and continuous in the circumferential direction, the expression for the wear volume of the tread per unit time is

$$\dot{q}(\mathrm{t})=\frac{K}{H}{{\displaystyle \int }}_{\mathrm{ribbon}}P(x,t)\dot{\gamma }(x,t)dS$$

(3)

where $t$ is the time, and $x$ is the current configuration position.

Due to the use of the Eulerian steady-state transport procedure, the above equation can be written as a time independent expression:

$$\dot{q}=\frac{K}{H}{{\displaystyle \int }}_{G}P(G)\dot{\gamma }(G)T(G)dG$$

(4)

where $G$ is a position along the streamline, and $T(G)$ is the width of the stream ribbon at position.

According to the physical meaning of material volume wear rate, the volume wear rate can also be represented by the wear rate $\dot{h}$ of the node material:

$$\dot{q}={{\displaystyle \int }}_G\dot{h}(G)T(G)dG$$

(5)

Equating Formulas (4) and (5) in a discrete form results in the following expression:

$${\displaystyle \sum _{i=1}^N{\dot{h}}_i{S}_i}=\frac{K}{H}{\displaystyle \sum _{i=1}^N{P}_i{\dot{\gamma }}_i{S}_i}$$

(6)

Assuming that the circumferential node wear rate on the tread is constant, the expression for wear rate can be obtained.

$$\dot{h}=\frac{K{\displaystyle \sum _{i=1}^N{P}_i\dot{\gamma }{S}_i}}{H{\displaystyle \sum _{i=1}^N{S}_i}}$$

(7)

3.2. ALE and UMESHMOTION Subroutine

The ALE technique combines the advantages of pure Lagrangian and pure Eulerian analysis, which can maintain high-quality mesh during the simulation without changing the topology of the mesh. This reduces the possibility of non-convergence in the tire wear simulation process. The UMESHMOTION is an ABAQUS subroutine developed based on Fortran language, which can call utility routines (GetVRN, GetNODETOELEMCONN, GetVRMAVGATNODE) to obtain node information for calculating wear rate. The wear rate calculation is based on the Archard wear model, and the wear direction of internal nodes is determined by the average of the element facet normals near the node, while the node at the tread corners is directly defined by the vector along the edge of the tread [31].

3.3. Simulation Operating Condition

The wear results are determined by the operating conditions of the tire. Different wear conditions can be generated by setting different inflation pressure, loads, time, and loading angles. Tire operating conditions exhibit significant variability in real-world scenarios. In this study, our objective was to simulate wear under various typical operating conditions, while considering the influence of the time factor. The specific operating conditions are shown in

Table 3. Operating conditions.

Number	Inflation Pressure/MPa	Load/N	Velocity/km/h	Slip Angle/deg	Camber Angle/deg	Longitudinal Slip/%	Time/h
1	240	4821	70	2	0	0	110
2	240	4821	70	0	5	0	110
3	240	4821	70	2	0	0	220
4	240	6000	70	0	0	60%	220
5	240	4821	70	0	5	0	220

. Conditions 1 and 3 are similar, except for the difference in operating time, and they represent pure lateral slip conditions. Conditions 2 and 5 are also similar, except for the difference in operating time, and they represent pure camber conditions. The purpose of including different operating times is to capture the varying degrees of wear under specific operating conditions. As for condition 4, it was intentionally designed to represent a scenario of high load and pure longitudinal slip. The coefficient of friction between the tire and the road is consistently set to 0.95, irrespective of the operating conditions. Modifying the key words in the INP file allows for changes in the operating conditions.

Based on these five operating conditions, five wear simulations were carried out on an un-worn 205/55R16 radial tire.

3.4. Result

To obtain accurate wear results, a path was created along the y-direction at the center of the contact area in the ABAQUS visualization to obtain the coordinates of the tread nodes before and after wear, and the wear depth was calculated. The wear category obtained from condition 1 is A, and so on, a total of five wear categories A, B, C, D, and E were obtained. The specific wear amounts for each level are shown in the Figure 4.

The non-uniformity of the wear depth at the tread nodes is evident. Comparing the wear caused by different working conditions reveals that the wear amount of A and B are relatively lower, while the wear amount of C, D, and E are significantly higher. Moreover, the impact of different working conditions on tire wear varies greatly. However, regardless of the operating conditions, the wear peak of the tire tread nodes is located at the shoulder due to the peak of the contact pressure in that region.

In the measurement of tire wear, researchers commonly utilize the method of measuring tire groove depth and calculating its average value. This approach is adopted because it is challenging to obtain wear data from areas other than the grooves during physical tire wear evaluation. One limitation of this method is the limited number of data points available for measurement.

Finite element analysis can provide the wear amount for each tread node, which can then be used to assess the overall wear level by calculating the average of all node wear values. Although this method appears reasonable, it has certain limitations. In particular, tire grooves divide the tread into distinct zones, and each zone may exhibit varying wear patterns. The conventional approach of utilizing the overall average fails to consider these differences, necessitating a more precise evaluation method.

In this paper, a new tire wear evaluation system is presented, drawing inspiration from the methodology proposed by Wang et al. [34]. The method involves dividing the tire tread into three distinct areas: the outer shoulder, crown, and inner shoulder, as shown in the Figure 5. Subsequently, the wear in each area is analyzed.

The wear amounts of the tire were processed based on the division of the tread. Several indicators were calculated to evaluate the wear distribution of the tire, which include: the outer shoulder wear ($w_{os}$), representing the average wear amount of the outer shoulder nodes; the inner shoulder wear ($w_{is}$), indicating the average wear amount of the inner shoulder nodes; the crown wear ($w_c$), showing the average wear amount of the crown nodes; and the global wear ($w_g$), which is the average wear amount of all tread nodes.

Furthermore, an evaluation indicator $w_d$ was proposed to quantify the difference in wear between the two shoulder regions. The calculation method of this evaluation index is given by Formula (8). W_cd is used to differentiate between crown wear and global wear. Equation (9) is used for its calculation.

$$w_d=\frac{\left|w_{os}-w_{is}\right|}{(w_{os}+w_{is})}\times 100\%$$

(8)

$$w_{cd}=\frac{\left|w_c-w_g\right|}{(w_c+w_g)}\times 100\%$$

(9)

By utilizing the above indicators, the wear condition of the tire can be evaluated from multiple perspectives. The specific wear indicators are shown in

Table 4. Wear indicators.

Group	Wear Category	wg/mm	wc/mm	wos/mm	wis/mm	wd	wcd
Ⅰ	A	1.1	1.3	0.9	1.1	10%	8.33%
	B	1.0	1.3	0.2	1.6	77.78%	13.04%
Ⅱ	C	2.1	2.4	1.6	2.2	15.79%	6.67%
	D	2.0	2.4	1.8	1.8	0	9.09%
	E	2.0	2.3	0.3	3.2	82.86%	6.98%

.

According to previous research, wear test results on 205/55R16 tires installed in real vehicles indicate an average wear of 1.41 mm per 10,000 km. In this paper, the wear rate is about 1.30 mm per 10,000 km. Hence, it is demonstrated that the wear results fall within the range of reliability. This result further validates the accuracy of the wear simulation process described in this paper.

The calculation methods for each wear indicator indicate that w_g, w_d, and w_cd are derived as secondary calculations from w_c, w_os, and w_is. Additionally, the small value of w_cd suggests a relatively minor discrepancy between crown wear and global wear. Therefore, w_g and w_d can effectively capture the majority of wear information.

Based on the analysis of wear amounts, two groups were formed: Group I consists of samples A and B, while Group II consists of samples C, D, and E. The global wear in Group I is smaller than that in Group II. The difference in the global wear and wear in the crown within each group is relatively small and can be considered as equal. However, there is a significant difference in wear between the outer and inner shoulders, with the maximum difference being 82.86%. The reason for this phenomenon is that under the selected working conditions, there is no significant difference in the distribution of contact pressure in the crown, but there is a significant difference in the tire shoulders. At the same time, the wear amount calculated by the Archard model is directly proportional to the contact pressure, leading to a difference in wear between the two shoulders of a tire, commonly known as uneven wear.

4. Cornering Characteristics of Worn Tires

To investigate the impact of wear on cornering characteristics, a simulation analysis was conducted using ABAQUS/Standard on five types of worn tires (A–E) and one unworn tire (F). The simulation involved varying the slip angle within the range of −2 to 2 degrees, while maintaining a constant speed of 70 km/h and applying different loads of 2410.5 N, 4821 N, and 7231.5 N. Meanwhile, the effects of camber and longitudinal slip were not considered. The coefficient of friction between the tire and the road was specified as 0.95. The simulation results were then visualized using the ABAQUS Visualization module to generate plots of the lateral force and aligning torque curves. The detailed simulation results are shown in Figure 6.

In order to provide a clearer description of the changes in lateral force and aligning torque under different wear states, fitting is performed for the lateral force and slip angle, as well as the aligning torque and slip angle. This allows for the extraction of parameters that represent the curve’s stiffness, namely the cornering stiffness and aligning stiffness.

The cornering stiffness is the lateral force generated by a unit slip angle, and the calculation formula is

$$C_{\alpha }=\underset{\alpha \to 0}{\lim }\frac{\mathsf{\partial }{F}_y}{\mathsf{\partial }\alpha }$$

(10)

The aligning stiffness is defined as the aligning torque generated by the unit slip angle, and the calculation formula is

$$C_M=\underset{\alpha \to 0}{\lim }\frac{\mathsf{\partial }{M}_z}{\mathsf{\partial }\alpha }$$

(11)

The cornering stiffness and aligning stiffness of each tire under different loads are shown in the Figure 7.

By comparing the cornering stiffness and aligning stiffness under different loads, we not only confirmed the conclusion similar to that in [30], which indicates that both cornering stiffness and aligning stiffness increase proportionally with tire wear, but also found that the magnitude of the changes varies under different loads. Furthermore, an even more interesting observation was made. When the load is consistent and the $w_g$ is the same, the effect of $w_d$ on cornering stiffness is relatively small, while it has a significant impact on the aligning stiffness. The trend of this effect is that $w_d$ is inversely proportional to the aligning stiffness. At low loads, the aligning stiffness exhibits a maximum difference of 8.0%, and even tire E shows a slightly lower aligning stiffness than the unworn tire. When subjected to rated load, the maximum difference of the aligning stiffness increases to 8.6%. Finally, at high loads, the maximum difference of the aligning stiffness decreases to 7.6%.

5. Analysis of the Impact of Wear on Cornering Characteristics

The tire–ground interaction is a result of the combined effect of tire structure and rubber compound, reflecting the comprehensive performance of the tire. It has always been the focus of tire mechanics modeling and can be described by both geometric and mechanical parameters. Based on studies in references [35,36], the grounding characteristics are closely related to tire forces. Therefore, it can be inferred that the cornering stiffness and aligning stiffness of the tire are also related to the grounding characteristics.

5.1. Impact of Grounding Parameters on Cornering Characteristics

In ABAQUS, the tire was first inflated to 0.24 MPa, and all degrees of freedom of the wheel rim were constrained. Then, the road surface was moved into contact with the tire, and finally, a concentrated force of 4821 N was applied on the road surface to obtain the geometric parameters reflecting the shape of each contact zone and the mechanical characteristic parameters representing the pressure distribution in each zone. The acquisition of contact parameters was indeed performed under static conditions, so the speed, slip angle, camber angle, and longitudinal slip were zero.

The definition of contact state parameters refers to references [36,37]. A total of 45 grounding characteristic parameters describing the tire’s geometric and pressure properties were employed in this study.

Firstly, in SPSS (Statistical Package for the Social Sciences), normality tests were performed on the cornering stiffness, aligning stiffness, and various contact characteristic parameters. Due to the small sample size, the significance of the data was assessed using the Shapiro–Wilk method. Some results are presented in

Table 5. Normality tests of parameters.

Parameters	Statistics	p Value
cornering stiffness	0.882	0.279
aligning stiffness	0.938	0.641
contact area	0.99	0.989
footprint area	0.99	0.989
contact area ratio	0.914	0.466

.

The p-values are all greater than 0.005, indicating that all variables follow a normal distribution. Therefore, the Pearson correlation coefficient can be used to measure the strength of linear correlation between two variables. The calculation formula is

$$r=\frac{{\displaystyle {\sum }_{i=1}^n(a_i-\overline{a})(s_i-\overline{s})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(a_i-\overline{a})}^2{\displaystyle {\sum }_{i=1}^n{(s_i-\overline{s})}^2}}}}$$

(12)

where $n$ represents the sample size; $s_i$, $\overline{s}$, $a_i$ and $\overline{a}$ respectively, represent the value of cornering or aligning stiffness of each tire, the average value of cornering or aligning stiffness of each tire, the value of grounding parameter, and the average value of the grounding parameters for tires.

The statistical test of the Pearson correlation coefficient involves calculating the $t$ statistic, which is defined as

$$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$

(13)

where the $t$ statistics follows the $t$ distribution of $n-2$ degrees of freedom.

Through correlation analysis, the ground contact characteristic parameters that exhibit a significant correlation with tire cornering stiffness and aligning stiffness were identified and presented in

Table 6. Normality tests of parameters.

Parameters	Cornering Stiffness	Aligning Stiffness
contact area	0.961	0.968
footprint area	0.947	0.981
contact area ratio	0.924
contact length	−0.996	−0.925
contact width	0.94	0.95
contact length to width ratio	−0.952	−0.95
contact sea-to-land ratio	−0.925
average contact pressure	−0.97	−0.964
skewness of contact pressure		−0.869
contact area of the outer shoulder	0.97	0.923
contact width of the outer shoulder		0.967
contact length to width ratio of the outer shoulder		−0.852
average contact pressure of the outer shoulder		−0.952
average contact pressure of the inner shoulder	−0.861
contact area of the inner shoulder		0.931
contact length of the crown	−0.996	−0.925
contact length to width ratio of the crown	−0.815

.

A significant correlation exists between grounding parameters and both cornering stiffness and aligning stiffness. Therefore, by analyzing specific grounding parameters, it is possible to explore the impact of tire wear on cornering characteristics. Moreover, the definition indicates a correlation between grounding parameters. Hence, selected grounding parameters from Table 6 are chosen for further analysis.

5.2. Influence of Wear on Grounding Parameters

5.2.1. Contact length

The contact length of tires in various wear states is depicted in Figure 8. The data presented in the graph indicates that the wear state has minimal impact on the contact length.

5.2.2. Contact Width

Figure 9a illustrates the contact width variation in tires under different wear conditions. Figure 9b displays the contact width across different tread partitions.

Based on the observations, the contact width exhibits the following trends: an increase in the global wear leads to an increase in the contact width. When the global wear remains constant, a smaller wear difference between the shoulders results in a larger contact width. The contact width of outer shoulder increases with an increase in the global wear, and for the same global wear, a larger difference in tire shoulder wear results in a smaller value. The contact width in the inner tire shoulder area exhibits a close relationship with the global wear, meaning that an increase in the global wear leads to an increase in the contact width of the inner shoulder. However, the relationship with the difference in tire shoulder wear is not significant. In the crown, wear has a negligible effect on the contact width.

5.2.3. Contact Area

Figure 10a displays the contact area and footprint area of tires under various wear conditions. Figure 10b illustrates the contact area of each tread partition of a tire across different wear conditions.

Based on the simulation data in Figure 10a, both the contact area and the footprint area exhibit a similar pattern of change. Therefore, only the contact area was analyzed. The observed pattern is as follows: as the global wear amount increases, the contact area also increases. Moreover, when the global wear amount is consistent, a smaller difference in shoulder wear on both sides corresponds to a larger contact area.

Based on the simulation data presented in Figure 10b, the contact area of different regions of tread under a load of 4821 N for various wear states was examined. The results of the analysis lead to the following conclusions.

In the outer shoulder, the contact area increases with the increase in the $w_g$. Even if there are differences in shoulder wear, it has almost no effect on the contact area of the outer shoulder when $w_g$ is the same. In the crown, there is little difference in the contact area of the five worn tires, but it has increased compared to the unworn tire. In the inner shoulder, the contact area increases with the increase in $w_g$. When $w_g$ is the same, the smaller $w_d$, the larger the contact area of the inner shoulder. Moreover, the greater the difference in wear between the two shoulders, the greater the discrepancy of the contact area of the shoulder.

5.2.4. Distribution of Contact Pressure

The distribution of contact pressure for tires A, B, C, D, E, and F at a static load of 4821 N can indicate the different distribution states of the contact pressure of the tire under different wear states, as shown in Figure 11. The influence of wear on the contact pressure distribution in the crown is minimal, while it has a significant impact on the contact pressure distribution in the two sides of the shoulder. For A, C, D, and F, the contact pressure amplitude of the two sides of the shoulder is almost equal. As wear increases, the maximum contact pressure decreases, resulting in a smaller overall amplitude and a more even distribution of the contact pressure. However, for B and E, the contact pressure amplitude of the two sides of the shoulder differs significantly. The contact pressure amplitude of the shoulder of the B and E worn tires differs noticeably, and as the global wear increases, the maximum contact pressure increases, and the non-uniformity of the contact pressure distribution increases.

In order to obtain a more detailed observation of the distribution of contact pressure, an analysis of the contact pressure at a load of 4821 N was conducted according to different regions. The results of the analysis are presented in Figure 12.

For the unworn tire, the distribution of the contact pressure on both tire shoulders is equal. After wear occurs, the distribution becomes different, with the outer shoulder bearing a greater proportion of the contact pressure compared to the inner shoulder. At the same time, the difference between the two shoulders increases with the difference in wear between them. The maximum difference is 15.06% for the worn tire E.

The data shows that tires with higher degrees of uneven wear exhibit greater contact pressure in the outer shoulder region. In the crown, wear increases the contact pressure, but when the global wear is consistent and there are differences in shoulder wear, the greater the difference, the greater the contact pressure. In the inner shoulder region, when the wear on both sides of the shoulder is consistent, the contact pressure slightly increases. However, when the wear is inconsistent, the greater the difference, the smaller the contact pressure.

To further evaluate the distribution of contact pressure, the average contact pressure and the skewness of contact pressure were calculated using the formulas (14) and (15), respectively [37].

$$\overline{p}=\frac{load}{contactarea}$$

(14)

$$\alpha =\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{\left(p_i-\overline{p}\right)}^2}}$$

(15)

where, $n$ is the total number of nodes, and $p_i$ is the contact pressure of any node $i$.

The results are presented in Figure 13.

As observed, wear leads to a decrease in both the mean and skewness of the contact pressure. Under the same global wear conditions, as the wear difference of the shoulders increases, the mean and skewness values of the contact pressure gradually increase.

In conclusion, by analyzing the parameters of grounding characteristics, it becomes evident that both the global wear amount and the difference in tire shoulder wear have a notable impact on the grounding characteristics. This finding indirectly verifies the comprehensiveness and accuracy of the proposed wear evaluation system in this study.

6. Conclusions

To summarize, this study conducts finite element simulations to analyze the cornering characteristics of tires in various wear states. It qualitatively examines the impact of wear on the cornering characteristics using grounding characteristics as intermediaries. The conclusions drawn are as follows.

• Wear can significantly affect a tire’s cornering characteristics by modifying its grounding characteristics.
• The lateral force and aligning torque are directly proportional to the overall wear amount, while the variation in tire shoulder wear minimally affects the lateral force but significantly impacts the aligning torque.
• Among the grounding parameters, five parameters including contact area exhibited a significant positive correlation with cornering stiffness. Additionally, seven parameters such as contact length displayed a significant negative correlation with cornering stiffness. Moreover, six parameters including footprint area showed a significant positive correlation with aligning stiffness. Furthermore, seven grounding characteristic parameters, such as the skewness of contact pressure, were significantly negatively correlated with aligning stiffness.

The obtained conclusions provide a new method for analyzing the relationship between wear and cornering characteristics.