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Article

Study on the Effect of Different Design Parameters of Sidewall Insert Rubber on the Mechanical Characteristics of Self-Supporting Run-Flat Tires

by
Tian Lv
1,
Liguo Zang
1,2,*,
Cheng Xue
1,
Yaowei Li
1,
Yulin Mao
1 and
Xingyu Wang
3
1
School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China
2
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, China
3
School of Automotive Studies, Tongji University, Shanghai 200092, China
*
Author to whom correspondence should be addressed.
Lubricants 2023, 11(11), 458; https://doi.org/10.3390/lubricants11110458
Submission received: 28 September 2023 / Revised: 22 October 2023 / Accepted: 24 October 2023 / Published: 26 October 2023
Browse Figures
Review Reports Versions Notes

Abstract

:
Self-supporting run-flat tires (SSRFTs) achieve good zero-pressure driving ability by reinforcing the sidewalls, and the structural shape of sidewall insert rubber (SIR) is critical in influencing the mechanical characteristics of SSRFTs. In this paper, an SSRFT contour model is established by combining the radial tire contour theory and the design elements of SIR. The influence of two design parameters (maximum width L and maximum thickness H) of SIR on the tire stiffness characteristics and the contact characteristics is analyzed in depth, and the accuracy of the model is verified by the tire mechanics bench test. The results show that the radial stiffness of SSRFTs is positively correlated with two design parameters; an increase in L affects the stress concentration at the end of SIR, while a change in H has a more drastic effect on the stress distribution of SIR, leading to a large change in both the location of the deformation of SIR and the maximum equivalent stress; under rated pressure conditions, when L is less than 100 mm, the overlap between SIR and the tread decreases, which in turn makes the contact characteristics of SSRFTs closer to that of a normal tire, and obtains better comfort and abrasion resistance; under zero-pressure conditions, the maximum contact stress of the tread is the smallest when the H is 8 mm, but when H is less than 6 mm, the contact characteristics appear to deteriorate uniformly, and the maximum contact stress continues to rise. The results of the research provide a reference value for the selection of the design parameters for SIR and the optimization of the dynamic performance of SSRFTs.

1. Introduction

Tires are the only medium of contact between a vehicle and the ground, in addition to supporting the weight of the whole vehicle. They are also responsible for transmitting driving and braking torque, and providing vibration damping and envelope capacity for the vehicle to ensure the stability of driving and steering [1,2,3,4]. Through continuous iterative upgrades, radial tires, which are widely used in vehicles today, can give vehicles good controllability, driving comfort, smoothness, and other dynamic characteristics. However, due to the structural form of pneumatic tires, there is a potential risk of blowout under some special working conditions, so in order to solve such safety hazards, the concept of safety tires has been proposed and has received widespread attention in the industry [5,6]. The self-supporting run-flat tire (SSRFT) belongs to the category of pneumatic safety tires, which can still support the weight of the vehicle after tire blowout by strengthening the sidewalls (the working mode of an SSRFT is shown in Figure 1), and can continue to drive for 150 km at a speed of 80 km/h [7]. Since the SSRFT does not require any other accessory and is compatible with most current rims, it has a significant cost advantage and is widely used in passenger cars.
Over the past half century, scholars in various countries have successively proposed tire models with different functions from different perspectives. The brush-type tire friction model treats the tread as an elastic body with brush deformation characteristics and the carcass as an inelastic rigid body [8]. Gipser proposed the flexible ring tire model (FTire), where the tire bead, sidewall and belt ply are viewed as a whole and divided into a number of belt units. There are springs and damping in the radial, tangential, and transverse directions that are nonlinear and vary with tire pressure between the belt units and between the belt units and the rim [9,10]. Mavros et al. proposed a model consisting of a discrete flexible belt with damping and inertia and connected to the rim by a viscoelastic unit representing the body. The behavior of tires under transient handling maneuvers was investigated by taking into account the velocity of tread elements, the normal force, and the unequal coefficients of friction in the lateral and longitudinal directions [11]. The magic formula proposed by Pacejka is currently the most widely used tire model and has a good ability to express the mechanical properties of tires under various working conditions [12]. The SWIFT tire model uses rigid ring theory for the carcass part, the magic formula for the tread part to calculate the lateral force and the return torque, and the rigid ring theory to calculate the longitudinal force and the vertical force [13]. Guo first proposed the Unitire model in 1986, and gradually formed a complete semi-empirical model based on the theoretical model, which not only has good expressive ability for various working conditions, but also has a concise model with outstanding predictive and extrapolation ability [14]. Based on the above tire model, many scholars at home and abroad have carried out a large amount of extrapolation and optimization research on the model after considering the friction coefficient, tire stiffness, contact dynamics, and other factors [15,16,17,18,19].
Based on the tire model mentioned above, scholars in foreign countries have carried out a lot of research on tire mechanical characteristics. Zhang et al. used FEM to study the deformation characteristics of tires during contraction and inflation, and the authors also analyzed the contact characteristics of tires under vertical loading conditions [20]. Lu et al. used the steady state transport analysis method to analyze the relationship between tire sidewall deflection and cord angle [21]. Ku et al. carried out steady-state mechanical simulations under multiple working conditions in order to comprehensively explore the steady-state mechanical characteristics of a new flexible spoke non-pneumatic tire (FSNPT) [22]. Zang et al. derived a mechanical model of rhombic porous structure based on the theory of the hexagonal honeycomb structure and studied the difference of mechanical characteristics for rhombic NPT tread on horizontal pavement as well as complex pavement [23]. Zang et al. analyzed the change rule of radial stiffness and lateral stiffness of tires under different load conditions using the tire mechanical characteristics test bench for inserts supporting run-flat tires [24].
According to the results of our previous research [25], SSRFTs can provide better load-carrying performance under zero-pressure conditions, but at the same time, the radial stiffness of SSRFTs increases significantly. Therefore, under normal driving conditions, the rolling resistance, wear resistance, and driving comfort of SSRFTs are inferior to normal tires. Therefore, to address the above problems, some scholars have optimized the structural design of SSRFTs. J. R. Cho et al. designed a generalized multi-objective optimization algorithm to optimize the shape of SIR with different weights [26]. Liu et al. analyzed the effect of tire temperature and stress on the zero-pressure driving ability of SSRFTs, by taking into account the material properties of SIR and the shape and dimensions of SIR [27]. Other scholars and tire companies tried new rubber materials for SIR by adding ZnO-treated aramid pulp (AP), TBIR (trans-butadiene-isoprene rubber) material, neodymium-based butadiene rubber, carbon black modified low cis-polybutadiene rubber (LCBR), and so on, to the compound of SIR can enhance the performance of SSRFTs in terms of fatigue resistance, wear resistance, and also improve the rolling resistance, deformation heat generation, and riding comfort [28,29,30,31].
SSRFTs have the advantages of a simple structure and easy assembly and can also provide good zero-pressure driving ability for vehicles. However, due to the large stiffness of SIR, the unsprung mass, driving comfort, and abrasion resistance will be negatively impacted. Therefore, specific adjustments to the vehicle suspension based on the mechanical characteristics of the SSRFTs are necessary. In addition, due to the relatively single structure of SIR, there are some limitations to the optimization method. How to quantify the design parameters of SIR, establish a suitable contour model for SSRFTs, and select the appropriate material and design parameters of SIR according to demand is an urgent problem to be solved.
In the open literature, most scholars focus on the optimization of the rubber materials of SIR, while there are relatively few studies on the influence and optimization of the design of SIR. In our previous research [25], we tried to investigate the effect of the different structures of SIR on the mechanical characteristics of SSRFTs under zero-pressure conditions. This paper will be based on the radial tire contour theory, combine SIR contour design, establish a SSRFT contour model, further refine the design parameters of SIR, and systematically analyze the influence of different design parameters on the mechanical characteristics of SSRFT under rated pressure and zero-pressure conditions. At the same time, the accuracy of the research will be verified by the tire mechanics bench test.

2. Establishment and Accuracy Verification of the Finite Element Model of SSRFTs

2.1. Establishment and Pre-Processing of Finite the Element Model of SSRFTs

The tire is a complex composite product, containing complex geometrical contours and multiple materials [32]. The finite element method (FEM), as a widely used technical tool in engineering, can be used by tire designers to shorten the development time and reduce the development cost. As shown in Figure 2, a 3D model of an SSRFT (225/50RF17 98W) is established and simplified based on the cross-section contour of the actual tire. The influence of tread pattern is not considered, and the specific internal structure of the SSRFT is shown in Figure 3.
The mesh of the tire in Hypermesh. The model uses the C3D8H mesh to define the rubber material and the SFM3D4R mesh to define the cord layer. C3D8H is an 8-node hexahedral cell, which can reflect the incompressibility of the rubber material well, and SFM3D4R is a 4-node thin-film cell, which does not have internal stiffness and thickness. As shown in Figure 4, the tire finite element model has a total of 128,402 cells and 225,402 nodes. In the finite element analysis of SSRFTs, in order to reduce the computation time, the center of the tire is bound to the tire toe and is completely fixed without considering the influence of the rim, which is shown in Figure 5.
The material of the tire mainly consists of a rubber ply and a cord ply. The cord is described using linear elastic material properties. The constitutive behavior of rubber materials is often defined by a polynomial model based on the mechanical theory of continuous media. The study of run-flat tires involves zero-pressure conditions, when the tire produces a large deflection phenomenon, showing strong nonlinear characteristics, and the strain of the rubber material is close to 25%. The Yeoh constitutive model [33] is a better fit for the large deformation of the rubber material, so in this paper, the Yeoh constitutive model was selected to describe the tire rubber. According to a large amount of experimental data, the Yeoh constitutive model can be summarized in the following cubic function form:
W = C 10 ( I 1 − 3 ) + C 20 ( I 1 − 3 ) 2 + C 30 ( I 1 − 3 ) 3
where I 1 is the first invariant of the right Cauchy–Green deformation tensor; C 10 , C 20 , C 30 are material constants, and they can be obtained through the tensile testing of rubber materials. The concrete parameters of rubber and cord materials are shown in the Table 1 [34].

2.2. Accuracy Validation of the Finite Element Model of SSRFTs

Due to the simplification of the 3D model of SSRFTs in this paper, and the differences in the fitting effect of the constitutive model compared to the actual rubber material parameters, mechanical tests under the same conditions are conducted based on the tire mechanical characteristics test bench to verify the accuracy of the model and make corresponding adjustments.
The tire mechanical characteristics test bench (shown in Figure 6) can apply radial and lateral loads to the tire through the vertical loading cylinder and horizontal loading cylinder, respectively, and the PLC control cabinet can be used to see the trend of the change between the loads and tire radial displacements. In addition, the tire mechanical characteristics test bench can also achieve different working conditions by adjusting the tire pressure and camber angle [35]. In this paper, the rated load (750 kg/7350 N) is applied to the test tire (225/50RF17 98 W) for different tire pressures (250 kPa~0 kPa, 250 kPa is the rated tire pressure), and the test data of the radial displacement is compared with the simulation results to ensure the accuracy of the model, as shown in Table 2. The error between the finite element model of SSRFT and the actual tire is 4.96% at maximum, 2.55% at minimum, and 3.5% at average, and the errors are kept within 5%, so the model has good reliability and can be used for subsequent simulation studies.

3. Contour Design of SSRFTs

In the early days of tire development and production, the design relied solely on human experience [36]. The earliest tire contour design was primarily based on the theory of the natural balanced tire contour proposed by Day and Purdy [37,38], which later evolved into the theory of radial tire design. With the refinement of the theory of the mechanical analysis of tires, Bridgestone Corporation of Japan proposed unbalanced contour theories that take into account the deformation of tires, such as the optimal rolling contour theory (RCOT) and the improved optimal tension control theory (TCOT). With the popularity of the FEM in the field of tire mechanics characteristics research, Nakajima K et al. combined the natural balanced contour theory and unbalanced contour theory based on RCOT and TCOT. They proposed the geometrically unified tire technology (GUTT) contour optimization theory, which combines the FEM and optimization method for iterative cycles to find the optimal solution [39]. In Section 2 of this paper, based on the natural balanced contour theory of radial tires, the cross-section model of SSRFTs is established by incorporating SIR structure. In this section, the design of SIR will be further optimized by combining the GUTT optimization theory.

Section Contour and Design Parameters of SIR

Based on the design points for the structure of SIR, currently, the upper and lower parts of SIR should be axisymmetric as much as possible. One end of SIR, connected to the tire shoulder, generally extends to about 80% of the half-width of the belt layer [40]. The other end, connected to the tire bead, generally extends to about 15 mm away from the bottom of the bead filler. The maximum thickness is located at the middle position of the structure, as shown in Figure 7. Where L is the maximum width of SIR, H is the maximum thickness, and the two points a and b are the contour design transition points and also the neighboring nodes in the design scheme. By adjusting the spacing between points a and b, contour curves with different accuracies can be obtained. After SIR contour is determined, the thickness of the SIR contour is refined through the differential method. The thickness at each location (h1~hN) is equivalently fitted into the cross-section contour of a conventional tire to achieve the cross-section design of SIR, as shown in Figure 8.
Through the measurement of the initial model of SIR, it can be obtained that the maximum width (L) of the actual SIR is 105 mm, and the maximum thickness (H) is 7 mm. In order to investigate the effect of the section design of SIR on the mechanical characteristics of SSRFT, L and H are selected as the design parameters for the study. In this paper, the range of the L is 90 mm~120 mm (every 5 mm as a variable) (shown in Figure 9) and the range of the H is 7 mm~9 mm (every 1 mm as a variable) (shown in Figure 10). The static analyses of SSRFTs are carried out under different design parameters.

4. Effect of SIR Design Parameters on the Mechanical Characteristics of SSRFTs

The stiffness characteristics and contact characteristics are important aspects in the study of the mechanical characteristics of tires, which have direct effects on vehicle controllability, driving comfort, and rolling resistance. The analysis of the mechanical characteristics of the tire is the basis of tire dynamics research and design optimization [41,42]. According to the introduction of SIR cross-section design parameters, the mechanical characteristics of different design schemes are investigated. A radial rated load (7350 N) is applied to the tire under rated pressure (250 kPa) and zero-pressure (0 kPa) conditions, respectively, and the stiffness characteristics and contact characteristics of SSRFTs are evaluated and investigated. The effect trend of the design parameters on the mechanical characteristics of SSRFTs is expounded by extracting radial displacement, tread stress, and other indicators.

4.1. Effect of SIR Design Parameters on the Stiffness Characteristics of SSRFTs

The radial stiffness of a tire can be considered as the ratio of the radial load to the radial displacement of the tire [43]:
k p = F a
where k p is the radial stiffness of the tire (N/mm), F is the radial load of the tire (N), and a is the radial displacement of the tire under the radial load (mm).
Figure 11 shows the trend of the influence of the maximum width (L) and maximum thickness (H) on the radial stiffness of SSRFTs under rated pressure and zero-pressure conditions. It can be found that with the increase of L and H, the radial stiffness of SSRFTs under the two conditions is generally in an upward trend, where the increase of L has a more significant impact on the radial stiffness of SSRFTs, while the influence of H is relatively smaller. Under rated pressure conditions, the radial stiffness of SSRFTs has a relatively large increase (about 0.5%) when L is in the range of 95 mm and 100 mm, and then it tends to gently increase. It can be seen that when the L of SIR is shorter, it has less overlap with the tread and belt, resulting in less involvement in the tire load. This reduces the radial stiffness and improves comfort to a certain extent. Under zero-pressure conditions, the longer L of SIR does not bring significant radial stiffness gain, and the increase in zero-pressure driving ability of SSRFTs is limited. The radial stiffness of SSRFTs varies linearly with H. Although the increase of H can significantly improve the zero-pressure driving ability and radial stiffness (under rated pressure conditions) of SSRFT, comfort is affected.
Since SIR is relatively rigid, the deformation and stress distribution of SIR directly determines the stiffness characteristics of SSRFTs, so the analysis of the stress distribution of SIR is essential. The stress concentration location of SIR is relatively uniform (all are on the inner side of SIR bending deformation). In order to visualize the stress distribution of SIR, we select the inner side of the SIR bend as path1—width of SIR (shown in Figure 12) and extract the Mises stress of the nodes on path1 by the direction of the arrows in the figure. These extracted Mises stress data will be used to compare the stress distribution of SIR with the design parameters under rated pressure and zero-pressure conditions.
The trend of Mises stress on path1 changes with the maximum width (L) of SIR under rated pressure and zero-pressure conditions is shown in Figure 13. It can be found that the stress distribution of different L of SIR is basically the same, the maximum near the 20 mm width of SIR is mainly due to the extrusion of the bead and SIR, and the maximum near the 50 mm of width of SIR is a stress concentration due to the bending deformation of the SIR involved in the loading. Through local magnification, it is found that there is a stress increase trend at the end of SIR (80–120 mm of width of SIR) under both tire pressure conditions with the increase of L. An additional stress concentration area is formed, and a more obvious maximum occurs under rated pressure conditions. This is because under rated pressure conditions, the end of the SIR extends too far into the tread, resulting in a higher overlap with the tread. As a result, the stiffness of the tread area increases, and there is greater stress at the end of the SIR. Under zero-pressure conditions, the central area of the tread depresses and warps into the inside of the tire, no longer making direct contact with the ground. The end of the SIR warps inward with the tread, resulting in a relative decrease in stress values. In summary, the change in L has a small effect on the load carrying performance of SSRFTs as well as on the stress distribution of SIR. However, as L increases, the stress at the end of the SIR rises, which is more pronounced under rated pressure conditions. Therefore, a longer L of SIR may lead to larger cyclic stress changes in SIR under normal driving, thus increasing the risk of the fatigue failure of SIR.
The trend of Mises stress on path1 with the maximum thickness H of SIR under rated pressure and zero-pressure conditions is shown in Figure 14. Overall, compared with L, H has a more significant effect on the stress distribution of SIR. Under rated pressure conditions, the maximum stress near the 20 mm width of SIR and at the end of the SIR decreases as H increases. But the maximum stress near the 50 mm width of SIR increases. All of them have a maximum migration phenomenon, which is caused by the change in radial stiffness. Under zero-pressure conditions, the larger H of the SIR can reduce the radial displacement of SSRFTs, increasing the radial stiffness of SSRFTs. Furthermore, the stress value of SIR is also decreased, which can comprehensively improve the zero-pressure driving ability of SSRFTs. In addition, when the H is less than 6 mm, a very obvious stress concentration occurs at the end of the SIR. This is because the H of the SIR is too small, resulting in the excessive deformation of the tire and more severe tread warpage. Therefore, the selection of as small as possible H should be avoided, so as to prevent the deterioration of the zero-pressure driving ability of SSRFTs.

4.2. Influence of SIR Design Parameters on Tire Contact Characteristics

Figure 15 and Figure 16 are the tread contact stress cloud diagrams of SSRFTs with different maximum widths L under rated pressure and zero-pressure conditions, respectively.
Under static loading conditions and rated pressure conditions, the contact stress of the tread is uniformly distributed in a quasi-elliptical shape, and the maximum contact stress is concentrated in the shoulder area on both sides. However, under zero-pressure conditions, the radial displacement of the tire is obvious, the center of the tread area is buckled, and the contact stress is concentrated only in the shoulders on both sides. Combined with the analysis of the contact stress cloud diagram and Figure 17 (Trend of maximum contact stress of tread with maximum width L), it can be seen that as the maximum width L increases overall, both the radial stiffness and the maximum contact stress of the tread are on an upward trend, but the trends of the two have a certain irregularity. The changes in radial stiffness under both pressure conditions and maximum tread contact stress under rated pressure are not significant, with a fluctuation range of about 1%. However, the maximum tread contact stress under zero-pressure conditions fluctuates up and down by about 15%, which indicates that the larger L of SIR is detrimental to tread wear and travel distance under zero-pressure conditions.
In addition, in order to reflect the differences between SSRFTs with different SIR design parameters and normal tires under rated pressure conditions, this paper introduces a new quantitative index of correlation. It extracts the contact stress and the equivalent stress of nodes in the same area on the tread, and compares them based on the same node ID, representing the degree of the correlation between their stress distribution trends in percentage form. The effect of L on the correlation of equivalent stress and contact stress between SSRFTs and normal tires under rated pressure conditions is shown in Figure 18. The black curve in the figure is the correlation of equivalent stress, which corresponds to the left-axis scale; the red bolded curve is the correlation of contact stress, which corresponds to the right-axis scale.
It can be found that before L is 90 mm~95 mm, the correlation of equivalent stress and contact stress is higher. This is because the L of SIR is relatively short, and under rated pressure conditions, SIR is less involved in load bearing, resulting in the stress distribution of the tread being similar to that of radial tires. When L reaches 100 mm, SIR with a longer L is more involved in tire load bearing. At this point, there is a cliff-like decrease in the correlation between the two stress indicators, and as L continues to increase, the correlation further gently decreases. Obviously, the longer L of SIR will increase the radial stiffness under rated pressure conditions, which in turn affects vehicle comfort.
Figure 19 and Figure 20 are the tread contact stress cloud diagrams of SSRFTs with different maximum thicknesses H under rated pressure and zero-pressure conditions, respectively.
Combining the trends of the maximum tread contact stress with the maximum thickness H under the two tire pressure static loading conditions shown in Figure 21, it can be seen that H has a more significant effect on the contact characteristics of SSRFTs compared to L. Due to the increase in the H of SIR, the radial stiffness of SSRFTs is increased resulting in the lower radial displacement of SSRFTs and a smaller contact area between the tread and the ground. Under zero-pressure conditions, when H is less than 6 mm, the end of the contact marks on both sides of the tire shoulder separates outward, forming a smaller stress concentration. This leads to the deterioration of the contact stress distribution in a uniform manner, thereby affecting the zero-pressure driving performance of SSRFTs. Under rated pressure conditions, the maximum contact stress shows a linear increase with the increase of H. However, under zero-pressure conditions, the maximum contact stress shows an irregular phenomenon. When H is less than 8 mm, it initially decreases and then increases. The minimum value of the maximum contact stress is observed at 8 mm. Clearly, the zero-pressure driving performance of SSRFTs is better at an L of 8 mm.
The effect of H on the correlation of equivalent stress and contact stress between SSRFTs and normal tires under rated pressure conditions is shown in Figure 22. It can be observed that H has a relatively linear impact on the correlation of the two stresses. As H decreases, the correlation tends to decrease. Therefore, an appropriate reduction in the H of SIR can improve the driving comfort of SSRFTs.

5. Conclusions

  • This paper establishes an SSRFT contour model, which is obtained by the equivalent fitting of SIR cross-section design on the basis of the natural balanced tire contour theory. The accuracy of the model is verified by tire mechanical test bench data. Through the SIR cross-section design model, the required design parameters can be introduced to control the variables of the SSRFT contour model. In this paper, the maximum width L and thickness H of SIR are regarded as design parameters, and 14 different SIR design schemes are constructed to conduct a quantitative study on the mechanical characteristics of SSRFTs by design parameters.
  • The radial stiffness of SSRFTs is positively correlated with the two design parameters of SIR. Larger widths have limited enhancement of the stiffness characteristics and instead lead to a small increase in stress at the end of the SIR. The variation of the maximum thickness H directly affects the flexural deformation position of SSRFTs and the stress distribution of the SIR. A smaller thickness not only leads to a decrease in the radial stiffness, but also results in a significant increase in the structural stress of the SIR. Therefore, the thickness of SIR is a key parameter to improve the radial stiffness characteristics of SSRFTs.
  • Under rated pressure conditions, when the maximum width L of SIR is less than 100 mm, the size and distribution trend of the contact stress of SSRFTs will be closer to that of a radial tire with the same specifications, thus providing better driving comfort and wear resistance. Under zero-pressure conditions, when the maximum thickness H of SIR is less than 6 mm, the radial stiffness of SSRFTs decreases and the contact stress distribution deteriorates, which seriously affects the zero-pressure driving ability of SSRFTs. Therefore, while appropriately reducing the maximum width L of SIR to obtain more desirable rated tire pressure characteristics, it is also possible to appropriately increase the maximum thickness H of SIR to ensure good zero-pressure driving ability of SSRFT.

Author Contributions

Conceptualization, L.Z. and T.L.; data curation, C.X.; formal analysis, Y.L.; funding acquisition, L.Z.; investigation, T.L.; methodology, T.L. and C.X.; project administration, L.Z. and Y.M.; resources, L.Z.; software, T.L.; supervision, Y.L., C.X. and Y.M.; validation, X.W. and C.X.; visualization, X.W.; writing—original draft, T.L.; writing—review and editing, L.Z. and T.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (grant number 51605215; 52372357), the Open Fund for State Key Laboratory of Automotive Simulation and Control (grant number 20210205), the Key Research and Development Program of Jiangsu Province (grant number BE2022146), Research Foundation of Nanjing Institute of Technology (grant number. CKJA202205).

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The contours after tire blowout: (a) normal tires; (b) SSRFTs.
Figure 1. The contours after tire blowout: (a) normal tires; (b) SSRFTs.
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Figure 2. Actual contour of an SSRFT.
Figure 2. Actual contour of an SSRFT.
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Figure 3. Internal structure of an SSRFT.
Figure 3. Internal structure of an SSRFT.
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Figure 4. Finite element model of SSRFTs.
Figure 4. Finite element model of SSRFTs.
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Figure 5. Boundary conditions of static load.
Figure 5. Boundary conditions of static load.
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Figure 6. Tire mechanical characteristics test bench.
Figure 6. Tire mechanical characteristics test bench.
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Figure 7. Section design of SIR.
Figure 7. Section design of SIR.
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Figure 8. Fitting process of the section contour of SIR.
Figure 8. Fitting process of the section contour of SIR.
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Figure 9. Design schemes of maximum width L of SIR.
Figure 9. Design schemes of maximum width L of SIR.
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Figure 10. Design schemes of maximum thickness H of SIR.
Figure 10. Design schemes of maximum thickness H of SIR.
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Figure 11. Trend of tire radial stiffness with design parameters: (a) trend of radial stiffness with maximum width L; (b) trend of radial stiffness with maximum thickness H.
Figure 11. Trend of tire radial stiffness with design parameters: (a) trend of radial stiffness with maximum width L; (b) trend of radial stiffness with maximum thickness H.
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Figure 12. Path1—Width of SIR.
Figure 12. Path1—Width of SIR.
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Figure 13. Trend of SIR stress (path1) with maximum width L: (a) rated pressure conditions; (b) zero-pressure conditions.
Figure 13. Trend of SIR stress (path1) with maximum width L: (a) rated pressure conditions; (b) zero-pressure conditions.
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Figure 14. Trend of SIR stress (path1) with maximum thickness H: (a) rated pressure conditions; (b) zero-pressure conditions.
Figure 14. Trend of SIR stress (path1) with maximum thickness H: (a) rated pressure conditions; (b) zero-pressure conditions.
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Figure 15. Trend of tire contact stress cloud diagram with maximum width L (250 kPa).
Figure 15. Trend of tire contact stress cloud diagram with maximum width L (250 kPa).
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Figure 16. Trend of tread contact stress cloud diagram with maximum width L (0 kPa).
Figure 16. Trend of tread contact stress cloud diagram with maximum width L (0 kPa).
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Figure 17. Trend of maximum contact stress of tread with maximum width L.
Figure 17. Trend of maximum contact stress of tread with maximum width L.
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Figure 18. Trend of correlation with a normal tire with maximum width L.
Figure 18. Trend of correlation with a normal tire with maximum width L.
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Figure 19. Trend of tire contact stress cloud diagram with maximum thickness H (250 kPa).
Figure 19. Trend of tire contact stress cloud diagram with maximum thickness H (250 kPa).
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Figure 20. Trend of tire contact stress cloud diagram with maximum thickness H (0 kPa).
Figure 20. Trend of tire contact stress cloud diagram with maximum thickness H (0 kPa).
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Figure 21. Trend of maximum tread contact stress with maximum thickness H.
Figure 21. Trend of maximum tread contact stress with maximum thickness H.
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Figure 22. Trend of correlation with a normal tire with maximum thickness H.
Figure 22. Trend of correlation with a normal tire with maximum thickness H.
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Table 1. Tire rubber material and skeleton material parameters.
Table 1. Tire rubber material and skeleton material parameters.
Parameters of Yeoh Constitutive ModelParameters of Linear Elastic MaterialDensity
(t/mm3)		Ply Angle
(deg)
C 10 C 20 C 30 Young’s Modulus
(MPa)		Poisson’s Ratio
Tread0.755224−0.2149690.068268//1.160 × 10−9/
Carcass0.930771−0.2373150.091423//1.147 × 10−9/
Sidewall0.644826−0.1733950.056512//1.127 × 10−9/
Belt1.139369−0.2729870.105123//1.203 × 10−9/
Bead filler2.258663−0.733306−0.733306//1.245 × 10−9/
SIR2.965836−0.1646920.010994//1.2 × 10−9/
Belt ply 1///205,3510.37.8 × 10−967
Belt ply 2///205,3510.37.8 × 10−9113
Carcass ply///10,5490.41.5 × 10−90
Bead///210,0000.47.8 × 10−9/
Table 2. Comparison of the tire radial displacement between bench test data and simulation results.
Table 2. Comparison of the tire radial displacement between bench test data and simulation results.
Tire Pressure (kPa)Bench Test Data (mm)Simulation Result (mm)Error (%)
046.5647.8492.77
5038.536.9444.04
10029.430.4863.63
15028.1226.7254.96
20024.5623.9332.55
25022.4821.7943.05
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MDPI and ACS Style

Lv, T.; Zang, L.; Xue, C.; Li, Y.; Mao, Y.; Wang, X. Study on the Effect of Different Design Parameters of Sidewall Insert Rubber on the Mechanical Characteristics of Self-Supporting Run-Flat Tires. Lubricants 2023, 11, 458. https://doi.org/10.3390/lubricants11110458

AMA Style

Lv T, Zang L, Xue C, Li Y, Mao Y, Wang X. Study on the Effect of Different Design Parameters of Sidewall Insert Rubber on the Mechanical Characteristics of Self-Supporting Run-Flat Tires. Lubricants. 2023; 11(11):458. https://doi.org/10.3390/lubricants11110458

Chicago/Turabian Style

Lv, Tian, Liguo Zang, Cheng Xue, Yaowei Li, Yulin Mao, and Xingyu Wang. 2023. "Study on the Effect of Different Design Parameters of Sidewall Insert Rubber on the Mechanical Characteristics of Self-Supporting Run-Flat Tires" Lubricants 11, no. 11: 458. https://doi.org/10.3390/lubricants11110458

APA Style

Lv, T., Zang, L., Xue, C., Li, Y., Mao, Y., & Wang, X. (2023). Study on the Effect of Different Design Parameters of Sidewall Insert Rubber on the Mechanical Characteristics of Self-Supporting Run-Flat Tires. Lubricants, 11(11), 458. https://doi.org/10.3390/lubricants11110458

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