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Establishment and verification of radial truck tire model based on rebar element

with the rapid development of computer technology, computer aided engineering software (CAE software) with finite element method as the core has been rapidly applied in tire design and analysis The world's major tire companies generally use CAE software to establish digital tire models on computers to simulate the static and dynamic processes of tires and the actual service conditions of tires, so as to obtain various static and dynamic characteristics of tires at the design stage

tire is a very complex flexible structure composed of rubber and framework materials Whether the tire model is established accurately or not plays an important role in further analysis, so the modeling method is very important In this paper, the finite element model of radial truck tire 12.00R20 is established based on the rebar element by using the finite element commercial software ABAQUS The feasibility of this modeling method is further confirmed by comparing and analyzing the load settlement curve measured by the test with the curve obtained by the simulation

1 establishment of finite element model

1 1 model simplification

in order to improve the calculation efficiency, the model is simplified as follows:

(1) the scratch line and mark line are ignored

(2) neglecting the influence of transverse pattern

(3) ignore the gap between the 0 degree band layer and the third band layer (see Figure 1)

Figure 1 location diagram of belt layer

(4) since the air tight layer is very thin, if it is also divided into grids, the quality of grids is poor, so this layer and the inner lining layer are combined into one dividing grid

(5) considering that the shoulder pad and crown base are made of the same compound, the two parts are combined for grid division

1. 2 Establishment of cord rubber composite material model

in order to analyze the mechanical properties of cord rubber composite material, this study adopts the method of defining rebar element in the rubber entity element of the host machine, in which the entity element simulates the mechanical properties of rubber and rebar element simulates the mechanical properties of steel cord, which greatly facilitates the establishment of the model

in ABAQUS, there are two methods to define the rebar unit. One is to directly define the rebar unit in the rubber actual rest unit. As shown in Figure 2, the node numbers of the rubber matrix unit in the figure are 1,2,3 and 4 in turn (the solid line in the figure represents the edge of the axisymmetric unit, and the dotted line is the auxiliary line drawn to represent the cord laying direction). The number of the unit edge determined by the node number sequence is edgel, edge2, edge3 and edge4, The intersection position of the cord ply and the rubber matrix unit can be defined. The intersection also specifies the positive direction in order to define the orientation of the rebar, because the intersection always intersects with the two edges of the matrix unit. The positive direction of the intersection is defined according to the number of the unit edge where the intersection is located, that is, the direction from small to large is the positive direction

Figure 3 Establishment of local coordinate system

another method is to first define the rebar unit on the face unit, and then embed the face unit into the corresponding rubber entity unit, as shown in Figure 3. The direction 1 in the figure is obtained from the unit projection of the plane along the X axis of the overall coordinate axis. Carefully check that the fan rotor, blade, electronic universal testing machine and other components meet the right-hand rule. In the model, you can also define the cord angle, cord spacing, cross-sectional area of a single steel wire and the distance between the center of the steel wire section and the middle surface of the face unit if the planned landing steel cord is in the model. As shown in Figure 4, the cord angle is the included angle between the 1 direction and the actual laying position of the steel cord, that is, the rebar angle to be defined

Figure 4 definition of relevant parameters of rebar unit

through comparative analysis, it is found that the biggest advantage of the second method is that it can reduce the difficulty of dividing rubber entity cells, because in dividing rubber entity cells, the position of the ply is accurately simulated by the surface unit. Secondly, the material parameters of rubber matrix unit and steel cord can be defined respectively. Therefore, the second method is used to simulate steel cord in this study, and the material parameters are obtained from the test

1. 3 choice of rubber constitutive model

at present, there are many kinds of rubber constitutive models, which can be roughly divided into two categories, one is the phenomenological theory model, the other is the molecular complex theory model. These models have been adopted by some large-scale commercial software (such as ABAQUS and ANSYS), but there are the following problems when selecting the constitutive model of rubber materials.

(1) some models have a good effect in fitting the test data of small deformation range, while others have a good effect in fitting the large deformation, which shows that different constitutive models have different characterization effects on the mechanical properties of rubber materials

(2) the material parameters obtained by fitting the same material model with the test data of different deformation ranges also have obvious differences, indicating that the characterization effect of the constitutive model is also related to the deformation range

the strain of the rubber in the tire is generally not greater than 50%, but many researchers also attach great importance to the mechanical properties of the rubber within the large deformation range. Therefore, in this study, the uniaxial tensile test of the material is carried out first, and the material parameters obtained from the test are evaluated by using ABAQUS software. After comprehensively considering the curve fitting effect within different deformation ranges, Yeoh model is adopted

1. 4 element selection

use the two-dimensional model to analyze the tire assembly and inflation conditions. The geometric conditions and load conditions are axisymmetric, and the laying form of the cord is also axisymmetric. Therefore, the plane axisymmetric finite element model can be used to simulate. Due to the influence of the cord at the end of belt layer and carcass layer, the tire is twisted and deformed around the rotation axis. Therefore, cgax4h and cgax3h axisymmetric elements are used for quadrilateral elements and triangular elements respectively

1. 5 contact simulation

this study uses the direct constraint method to deal with contact problems. The direct constraint method is to track all seamless steel pipes for mechanical property test to track the motion trajectory of the object. Once contact is detected, the motion constraints and nodes required for contact are directly applied as boundary conditions on the nodes that generate contact. This method has high accuracy and universal adaptability for contact description During the simulation, the wheel vehicle and road surface are defined as analytical rigid bodies. The analytic rigid body can better simulate the shape of the rigid body, so that the simulated surface of the rigid body is smoother and the contact noise is reduced

2 model analysis and verification

2.1 tire finite element analysis model

this model takes 12, oor20 radial truck tire as the prototype and uses 8 5I type standard flat bottom wheeled vehicle has a rated inflation pressure of 840kpa and a single tire rated load of 36554 n. The established two-dimensional and three-dimensional models are shown in figures 5 and 6. The two-dimensional model has 501 units and 560 nodes. The three-dimensional model is divided into 100 equal parts along the circumference, and the total number of units is 50100

Figure 5 two-dimensional tire finite element model

Figure 6 three-dimensional tire finite element model

2.2 model analysis

there are many ways to verify the model. At present, there are mainly methods to test the contact pressure and area between the tire and the road surface and the inflation section width of the tire. In this study, the method of testing the tire load sinking curve is adopted, which is also one of the commonly used verification methods at present

first install the tire on the wheel and inflate it according to the rated pressure, and then install it on the load sinking test machine. Before the test, the inflation outer radius of the tire shall be tested, and then the distance from the wheel center to the grounding center under different loads shall be tested, and the settlement under different loads shall be obtained through conversion. The comparison between finite element analysis and test results is shown in Figure 7. The maximum error is 5.9500 and the minimum error is 3 99, which meets the requirements of engineering research, and it can be considered that the established model is accurate

2. 3 tire deformation

analyze the tire assembly and inflation conditions with a two-dimensional model. The tire produces axisymmetric deformation under the effect of inflation pressure. Therefore, the overall deformation of the tire can be represented by the tire section, as shown in Figure 8 It can be seen from figure 8 that the deformation at the bead is large, which is mainly caused by assembly, and the tire toe is tilted a certain distance from the wheel vehicle; There is a certain radial displacement along the 1 direction at the crown, which is mainly caused by inflation

figure 8 two dimensional model tire deformation

the load on the tire at the contact area is non axisymmetric, and the load influence area is mainly concentrated in the contact area, as shown in Figure 9. It can be seen from Figure 9 that under the rated static load, the contact area between the tire and the road surface is 150 degrees away from both sides of the center of the ground, and the range of obvious non axisymmetric deformation due to the grounding effect is about 30 degrees away from both sides of the center of the ground

Figure 9 three dimensional model tire deformation

3 conclusion

through comparative analysis of the load sink curve obtained from the test and simulation, it is found that the error is within an acceptable range, and the method based on rebar element can be used to establish tire model. Through the simulation of tire loading process, the mechanical properties and changes of various parts of the tire can be observed intuitively, and various adverse factors can be eliminated through improvement. Therefore, the simulation analysis of tire loading process can not only provide a basis for improving tire design quality, but also provide a powerful analysis means for improving tire performance. (end)

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