This paper is concerned with the numerical prediction of the burst pressure of a radial truck tire. Even though relatively rare, the tire fracture or failure brings up a big accident. Especially, the tire burst or rupture is a rapid loss of inflation pressure of a truck and bus tire leading to an explosion. The tire burst pressure, under this extreme loading condition, can be predicted by identifying the pressure at which the cord breaking force of the composite materials is attained. Recently, the use of finite element analysis in tire optimal design has become widely popular. In order to determine the burst pressure of a radial truck tire, an axisymmetric finite element model has been developed using a commercial finite element code with rebar element. The numerical result shows that the bead wire among the various layers modeled the rebar element breaks off first in the radial truck tire. The finite element modeling with the rebar element on the bead wire of a radial truck tire is able to well predict the tire burst pressure identifying the pressure at which the breaking force of steel bead wires is reached. The model predictions of tire burst pressure should be correlated with test data, in which case the tire is hydro-tested to destruction. The effect of the design change with the different bead structure on the tire burst pressure is discussed.
In general, a tire must be sufficiently rigid to withstand various loading conditions and ensure different functions such as sufficient traction for driving and braking, steering control and stability or as cushion of road irregularities. Tire durability due to large local loading, stiffness discontinuities, and production flaws is frequently related to the fracture of tire components such as belt edge separation, ply turn-up separation, or lug cracking in radial truck tire [
Bead area separation in passenger tires has been fairly uncommon since the middle to late 1990s. In light truck-type tires, especially load range D and E sizes, bead area separation is unusual but not rare and remains small in number compared to the number of belt separations. Especially, broken beads are uncommon but can fail in the following instances [
Destructive tests such as the application of burst pressure, high-speed free rotation, and plunger energy are sometimes performed on new tires to ascertain their ultimate strengths [
Bolarinwa and Olatunbosun [
More recently, Michel et al. [
The purpose of the present study is to develop the finite element modeling for the prediction of the burst pressure of radial truck tires. The tire burst pressure, under this extreme loading condition, can be predicted by identifying the pressure at which the cord breaking force of the composite materials is attained. In order to determine the burst pressure of a radial truck tire, an axisymmetric finite element model has been developed using a commercial FE code [
A tire usually consists of several rubber components, each of which is designed to contribute to some particular factors for tire performance in addition to several cords and rubber composites. These components play a role in maintaining the stiffness and strength required in a tire.
The material composition of most tires is distinguished largely into the fiber-reinforced rubber (FRR) parts and the remaining pure rubber part. The FRR parts of the tire model considered here are composed of a single-ply polyester carcass, four steel belt layers, and several steel bead cords. Since the FRR parts are in the highly complex structure, their material models are chosen based on the goal of the numerical simulation. When FRR parts are modeled using finite element analysis, the physical properties of the rubber and cords are combined to yield the resulting physical behavior of the FRR [
Rubbers except for the FRR parts are modeled by the penalized first-order Mooney-Rivlin model in which the strain density function is defined [
where Ji are the invariants of the Green-Lagrangian strain tensor and C10 and C01 are the rubber material constants determined from the experiment. On the other hand, K is a sort of penalty parameter controlling the rubber incompressibility. The shear modulus τ and the bulk modulus k of rubber are related as
Structural tire analysis is often performed using the cured tire geometry as the reference configuration for the finite element model. However, the cord geometry is more conveniently specified with respect to the “green” or uncured, tire configuration. The tire lift equation provides mapping from the uncured geometry to the cured geometry as shown
where r is the position of the rebar along the radial direction in the cured geometry, r0 is the position of the rebar in the uncured geometry, s0 is the spacing in the uncured geometry, α0is the angle measured with respect to the projected local 1-direction in the uncured geometry, and e is the cord extension ratio. A local cylindrical coordinate system must be defined for the rebar if the rebar is associated with three-dimensional elements.
In order to predict the tire burst pressure by identifying the pressure at which the cord breaking force of steel bead wires is reached, the rebar element is used.
because it must calculate the cord tension of bead wire as shown in
To simulate the contact between the tire and the rim, the general purpose interface is defined between a tire slave surface and a rigid body surface of the rim. The inner and outer rim profiles are both modeled by axisymmetric rigid surfaces. Contact with friction is considered between the tire and the rim. The coefficient of friction is assumed to be 0.3 or 0.5. No other interface is used to model the contact between the rubber matrix and the beads or between the rubber matrix and the different layers, such as carcass ply, belt, bead wrap and steel chafer. The effect of the change of friction coefficient on the tire burst pressure is discussed.
The tire burst pressure, under this extreme loading condition, can be predicted by identifying the pressure at which the cord breaking force of the composite materials is attained. In addition, the plot of the cord tension of rebar against the inflation pressure reveals their responses to pressure loading leading to tire burst.
The tire model’s response to an extremely large, but progressively applied, inflation pressure is simulated by inflating the tire up to a limit of 400 psi inflation pressure, representing a 333 per cent increase in the tire’s rated inflation pressure (120 psi). The resulting plot of the deformed geometry with the different bead modeling at a pressure of 120 psi is shown in
excessive deformation of tire bead part is generated, but there is no convergence problem.
Cord | Carcass ply | Belt | Chafer | Wrap | Bead |
---|---|---|---|---|---|
Breaking Force (kgf) | 154.0 | 170.0 | 142.0 | 20.5 | 430.0 |
The inflation pressure of about 300 psi, at which the rebar element breaks, is assumed to correspond to the tire model burst pressure. This proves to be reasonably close to the burst pressure of 264.85 psi [
The bead wires undergo plastic deformation until failure. However, this study is not considered the plastic strain of steel cord because the rebar element provided by ABAQUS [
An important feature of the finite element tire model is that it provides a cost-effective means of carrying out parametric studies on the tire so as to optimize desired performance output. As a result of this, the bead properties can be optimized to achieve a target burst pressure. The main effect of changing the cylindrical diameter of bead and the wire number of the bead design on the tire burst pressure will be investigated using an organized approach popularly referred to as the Design of Experiment (DOE) [
Version | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
Diameter | 573.8 mm | 572.8 mm | 571.8 mm | ||||||
Wire No. | 51 | 57 | 60 | 51 | 57 | 60 | 51 | 57 | 60 |
burst pressure can be taken to be dependent on the bead diameter and the wire number. In order to select the optimized design of the bead wire, the structure of bead wire consists of 51 (8 + 9 + 10 + 9 + 8 + 7), 57 (8 + 9 + 10 + 11 + 10 + 9), and 60 (9 + 10 + 11 + 11 + 10 + 9). From this table of properties, a matrix of nine experiments or simulations and a resulting output burst pressure are generated.
The correlation between simulation and test is shown in
The finite element modeling technique is employed for the calculation of the burst pressure of a radial truck tire, based on the static loading analysis. The high internal pressure produces high circumferential tension in the bead wire. The cord tension can no longer be sustained resulting in a chain reaction and consequently leading to the burst. In order to predict of burst pressure of a radial truck tire, an axisymmetric finite element model is used.
The finite element modeling with the rebar element on the bead wire of a radial truck tire is able to well predict the tire burst pressure identifying the pressure at which the breaking force of steel bead wires is reached. Because the simulation results and those obtained experimentally are in good agreement, it offers better understanding of the tire failure mechanism under inflation pressure, revealing the behavior of tire reinforcements leading to failure. Finally, the bead model developed in this study shows significant flexibility in being used as a radial truck tire design sensitivity tool for optimizing design parameters for a severe service condition such as burst pressure. It is found that the prediction of tire burst pressure using a finite element method will be useful for the reliable bead design of a radial truck tire.
The present study was supported by the Center for Environmentally Friendly Vehicles (CEFV) under the project “Development of the eco-friendly tire for reduction of carbon dioxide and tire wear particles” through the Ministry of Environment (ME, Republic of Korea).
Kyoung Moon Jeong, (2016) Prediction of Burst Pressure of a Radial Truck Tire Using Finite Element Analysis. World Journal of Engineering and Technology,04,228-237. doi: 10.4236/wjet.2016.42022