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This paper elaborates on the production mechanisms of standing waves during high-speed tire rolling and analyzes the relationship between the change of wavelength of sidewall waves and the vehicle velocity, from an oblique wave point of view. A finite element model for a 195/65R15 radial tire is established with the nonlinear analysis software ABAQUS, based on the tire structure and cord parameters. This paper comparatively analyzes the finite element simulation results and experimental results of the tire load-sinkage relation and the load vs inflatable section width relation and finds little difference between the simulation and experimental results. A similar analysis studies the change in the wavelength of sidewall standing waves at different vehicle velocities during high-speed tire rolling. The calculated value by the oblique wave approach, the value by simulation, and the experimental results demonstrate high consistency, concluding that during high-speed tire rolling, the wavelength of sidewall standing waves increases with vehicle velocity. Thus, the accuracy of the finite element model is verified under both static and dynamic conditions. Under a constant tire pressure and load, the impact of velocity change on tire-cord stress during high-speed tire rolling is studied based on the finite element model so as to identity the relation between the cord stress and standing waves.

Traffic accidents caused by tire bursts occur frequently, and studies have found that the standing wave on high-speed tires is a major cause of tire bursts. The weight of a vehicle causes a slight deformation of a tire where it contacts the ground, and the deformed part tends to regain its original shape after rolling out of ground contact. When a vehicle moves at a high speed, the tire rolls too fast to regain its original shape from deformation, thereby forming standing waves [

Tire standing waves.

High-performance computers, high-speed cameras, and high-power chassis dynamometers have been increasingly used to explore the mechanisms that produce standing waves in tires. Brockman [

This paper analyzes the production mechanisms of standing waves during high-speed tire rolling and the changes of wavelength on the sidewall based on the oblique wave approach. ABAQUS is used to establish a three-dimensional finite element model of the tire and drum tester, and both static and dynamic experiments are carried out to verify the accuracy of the finite element model. Furthermore, the paper analyzes how the cord stress changes with the vehicle velocity during high-speed tire rolling and discusses the mechanical patterns of tire standing waves, providing a mechanical basis for tire design so as to improve tire safety and service life.

Diagonal waves can be considered as waves transmitted in pipes or plane waves transmitted in the waveguide with a certain angle, frequency, and width [

Fundamental wave formed by two intersected plane waves [

On the tire bead, which cannot be displaced, troughs can be reflected as peaks and vice versa. The peaks intersect on the centerline

Therefore,

The wave-group velocity

The wavelength can be expressed as

Substituting

When the tire velocity

Curve of the tire centerline when

The velocity of energy flow from the ground-contact part can be expressed as

The energy per unit length of oblique waves can be expressed as

The tire is subjected to a vertical load and sinks so that an angle

Energy consumption caused by standing waves will not occur until the tire velocity

When building a finite element model of a tire, the geometric, material, and contact nonlinearities during tire rolling may complicate the calculation process, which greatly increases computing time and convergence difficulties [

Diagram of the tire’s sectional structure.

Orthogonal anisotropic materials and embedded rebar elements are used to simulate the belt and carcass layers. For stiffener ribs defined in this way, the behavior of the rubber matrix and rebar elements can be considered independent. The stiffener rib model used to define the rebar elements can better demonstrate the stress-strain status of cords when processing the structure of the belt and the carcass layers [

FEA modeling for the tire and the test rig.

A UP-2092 comprehensive test bench (Figure

Bench test for mechanical properties of the tire.

Curves of load vs sinkage by experiment and simulation.

Section width by simulation and experiment.

Vertical load (kN) | 0 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|---|

Ground-contact section | Simulation | 195.7 | 201.4 | 206.2 | 209.6 | 216.2 | 222.8 |

Width (mm) | Experiment | 194.5 | 198.5 | 201.5 | 210.5 | 213.0 | 218.5 |

Error (%) | 0.61 | 1.46 | 2.33 | 0.43 | 1.5 | 2.0 |

Figure

A tire high-speed uniformity testing machine was used to perform high-speed experiments on a 195/65R15 radial tire, with a tire pressure of 0.2 MPa and a load of 5,018 N. The tire linear velocity was gradually adjusted from 180 km/h to 230 km/h while the tire pressure and load remained unchanged. Measurements were taken at an interval of 10 km/h; images were captured by high-speed cameras and imported into CAD software to analyze standing waves on the tire surface. Since standing waves were concentrated at the rear of the ground-contact area, only the images in the concerned semicircle of the tire were selected, and the wavelengths were measured by CAD software. In addition, ABAQUS software was used for high-speed simulation of the tire with the same velocity range and boundary conditions, generating cloud images of tire deformation [

Figure

Comparison between experimental and simulated results on wavelength of standing waves within the

Figure

Comparison between theoretical calculation, simulation, and experiment results on wavelength of sidewall standing waves.

To sum up, the simulation results are highly consistent with those from experiments under both static and dynamic conditions. In other words, the finite element model established in this paper is accurate and suitable for further simulation analysis.

High-speed tire rolling tends to damage the internal cords, causing tire bursts [

Points of circumferential analysis on cords.

Point A is the turn-up point of the carcass layer. The cord at this point is wrapped around the bead wire; hence, the tire sidewall deformation is constrained by the bead wire. Figures

Circumferential distribution of carcass cord stress at different velocities. (a) Circumferential stress on the turn-up point of the carcass layer (point A). (b) Circumferential stress on the sidewall point of the carcass layer (point B).

As can be seen from Figure

As can be seen from Figure

Figures

Circumferential stress on belt cord ends at different velocities. (a) Circumferential stress on the cord end of the first belt layer (point C). (b) Circumferential stress on the cord end of the second belt layer (point D).

As shown in Figures

Through the analysis of the above four points, the regularity of the cord stress when the tire is rolling at high speed can be inferred, revealing the relationship between the stress of the cord and the standing wave, providing the research basis for the tire test mechanics. From the above four figures, it can be seen that the standing wave phenomenon will occur when the tire is rolling at a high speed. As the rolling speed increases, the amount of deformation of the tire sidewall increases, and the wavelength of the standing wave also increases. The area where the standing wave occurs is mainly concentrated behind the grounding point, and the tire is easily damaged in this area. The higher the speed, the greater the stress of the cord and the greater the fluctuation of the curve. At this time, the tire sidewall deformation reaches the maximum, and it may bulge. Thus, when designing the structure of the tire, it is necessary to improve its shoulder rigidity and prevent the tire from damage due to deformation.

Comparing the above four figures, it can be seen that the stress of the belt cord is significantly greater than that of the ply cord, i.e., the belt cord is the main force-receiving part. Therefore, the design of the tire should aim mainly to strengthen the belt cord. Compared with the circumferential forces of the other three points, the force fluctuation of the ply cord carcass turn-up point (point A) near the ground is less because the ply cords on the sidewall (point B) have already taken most of the force from the tire, so the force transmitted to the turn-up point A will be significantly reduced, the circumferential force at point A will be relatively even and flat, and the force at the three points of BCD will be at the grounding point, which shows greater fluctuations.

Using the oblique wave approach, this paper analyzes the production mechanisms of standing waves during high-speed tire rolling, studies the relations between sidewall standing waves and vehicle velocity, and calculates the theoretical wavelengths of sidewall standing waves of a 195/65R15 radial tire. Based on the tire structure and parameters of the carcass layer and belt layers and accounting for longitudinal tire patterns, a three-dimensional finite element model of the tire was established with ABAQUS software. We compared the experimental and simulation results on the tire load-sinkage relation and load vs inflatable section width relation, and the difference between the two was found to be insignificant. High-speed experiments and simulations were carried out, with the tire load, pressure, and velocity range set to 5 kN, 0.2 Mpa, and 180–230 km/h, respectively. Images were captured at an interval of 10 km/h by CAD software. By comparing the simulation, experiment, and theoretical wavelength of standing waves, it was found that the wavelength increased with vehicle velocity. Static and dynamic simulation results from the finite element model were in good agreement with those of the experiment, which verified the accuracy of the model.

Based on this finite element model, the pattern of cord stress during high-speed tire rolling was studied by simulating the cord stress at different positions. The conclusions are as follows:

The tire rotation velocity has a significant impact on the stress at point A (the turn-up point of the carcass layer). The range of stress fluctuation increases with velocity, and the stress reaches a maximum value around the ground-contact point (circumferential 180 degrees) of the tire.

With the impact from standing waves, the cord stress on the sidewall point of the carcass layer fluctuates wavily at the rear of the ground-contact part. The higher the velocity, the greater the fluctuation amplitude and extreme cord stress. Cord stress at point B reached a minimum (0 N) around the ground-contact point.

The cord ends C and D of the first and second belt layers are subjected to similar stress conditions. As the tire velocity increases, the extreme cord stress increases accordingly, and the circumferential stress at points C and D fluctuates more significantly, particularly at the rear of the ground-contact part.

For each layer of cords inside a tire, it is generally the case that the higher the tire-rotating velocity, the greater the cord stress.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of the article.

This entire study was supported by the National Natural Science Foundation of China (no. 51475399), Education and Scientific Research Projects for Middle and Young-Aged Teachers of Fujian (no. JA15376), and Science & Technology Innovation Project of Fujian Province, China (no. 2016H2003).