Study on the Influence of Temperature on Tire Cornering Stiffness and Aligning Stiffness

 Abstract: Based on the results of tire handling test, the cornering properties of the tire at a small range of steer angles under different temperature are obtained, and the variation law of the tire cornering characteristic parameters with the tire temperature is obtained. By establishing a tread temperature model and finite element tire model considering temperature, the mechanism of tire mechanical properties with temperature is clarified, and the expression of tread stiffness and aligning stiffness considering temperature is obtained. Then, based on the above expression and the tire brush model considering the tire temperature state, a complex brush model is established. Through the model derivation, the relationship between the temperature and the tire cornering stiffness is obtained. The relationship is used as the basic expression formula to establish the UniTire cornering model considering tire temperature. In order to verify the correctness of the model, four kinds of temperature state cornering data are used for parameter identification, and the tire cornering properties in the other two temperature states is predicted. The error between the simulation results of the prediction model and the experimental results is very small, which effectively proves the predictive ability of the UniTire cornering model considering tire temperature. This research is helpful to improve the application of UniTire model, and provide theoretical and technical support for UniTire model indoor and outdoor expansion applications


Introduction
Tire is a rubber product, and the rubber material   [11].
The frictional heat generation of the tire is based on the tangential force friction work in the tire footprint, and the internal heat generation of the tire is calculated based on the viscoelastic of the tire.
In summary, the current research on tire temperature is mainly divided into two aspects:

Tire Cornering Test under Different Temperatures
In this paper, the tire is first placed in an incubator equipment for several hours. After the tire temperature is completely stabilized to the set temperature, the tire corner stiffness test is carried out to obtain the mechanical characteristics of the tire corner stiffness at different temperatures.

Test Condition
The test tire type is Hankook 225 55 R17. The tire cornering mechanical properties are tested under 6 different temperature conditions. In order to control the temperature of the tire during the test, this test uses a low speed test to ensure that the tire temperature does not change more than 3 ° C during the test. The specific test content is as shown in the table 1.

Test Result
The tire incubator equipment is shown in Figure 1    As is shown in the curve of corner stiffness and aligning stiffness with temperature, the corner stiffness and the aligning stiffness of the tire gradually decreases with the increase of tire temperature under the same vertical load.

Mechanism of temperature influence on tire mechanical properties
Firstly, the rubber is subjected to dynamic mechanical analysis test and tensile test at different temperatures to obtain the variation law of rubber mechanical properties with temperature. The finite element analysis method is used to analyze the lateral and torsional deformation of the carcass at different temperatures. After that, the tire is simplified into tread and carcass parts, and the influence of temperature on the mechanical characteristics of tire tread and carcass is studied.

Rubber dynamic mechanical analysis test under different temperatures
A cylindrical rubber block with a diameter of 25mm and a height of 13mm is used for dynamic mechanical analysis and testing on a DMA testing rig. The DMA test rig is shown in Figure 8. The test result is shown in Figure 9.  Figure 9 The elastic modulus at different temperatures It can be seen from the test results that the elastic modulus of rubber is decreasing with increasing temperature.
It is known that the shear modulus and elastic modulus of rubber have a strong correlation [9], so the expression of the shear modulus of rubber with temperature can be approximated as shown in equation (1): lim it G is the high temperature critical modulus of rubber material.
According to the formula (1), the relationship between the shear modulus of rubber with the temperature is obtained. Therefore, the lateral uniform stiffness of the tire tread can be obtained as shown in (2) 01 ty tread k p G  (2) Where: 1 p is the geometric parameter of rubber.

Effect of temperature on the mechanical properties of tire carcass
It can be seen from the previous section that the influence of temperature on the elastic modulus of rubber, and the temperature characteristics of the tire carcass cannot be directly measured from the test, so the tire carcass characteristics with temperature are analyzed with the help of the finite element analysis method Changes with temperature.
Based on the tire finite element model used in paper [12], the tire lateral translation stiffness and torsional stiffness simulation at different temperatures are carried out respectively, and then the variation law of the translational stiffness and torsional stiffness of the carcass with temperature is obtained. The specific simulation conditions are shown in Table 2. After that, the deformation of the carcass is extracted. The method of extracting the carcass deformation is to take the displacement of the point on the midline (red dotted line) of the tire inner surface in the footprint (between the red solid lines) as the carcass deformation, as shown in Figure 10.
Taking a load of 3000N as an example, the deformation of the carcass is shown in Figure 11-12. From the simulation results of lateral stiffness simulation, it can be seen that the deformation of the carcass is mainly translational deformation, and the bending deformation of the tire is not particularly significant; from the simulation results of torsional stiffness simulation, it can be seen that the deformation of the tire is mainly torsional deformation.  It can be seen from the above results that the lateral force of the carcass gradually decreases with increasing temperature under the same load and the same lateral deformation; the aligning torque of the carcass gradually decreases with increasing temperature too. From the above results, extract the characteristic parameters of the lateral stiffness and torsional stiffness of the carcass as a function of temperature. As shown in Figure 15 The brush model is a simplified tire physical model [13][14], which can reflect the basic mechanical characteristics of the tire. Combining the results of the above test and finite element simulation, this paper establishes a brush model considering the elasticity of the carcass [15], which includes the lateral translation deformation and the torsional deformation of the carcass as is shown in Figure 17. Define: According to formula (9) Where: Pneumatic trail is the ratio of aligning torque and lateral force. The change law of lateral force and aligning torque with temperature in the small slip zone is in the form of E exponential, so the relationship between pneumatic trail with temperature can also be set as the E exponential function relationship, and an empirical model is built based on this relationship. In the UniTire semi-empirical model, the pneumatic trail expression is as shown in equation (14), and multiplied by _ x tempe D on the basis of the formula, the expression is shown in (15), and the UniTire model pneumatic trail expression (16) considering the influence of temperature is obtained.  Figure 27 The comparison results of the aligning torque between identification results and test results under different tire temperature at 10kN loads From the above identification results, it can be seen that the UniTire model has higher accuracy for the tire mechanical characteristics at different temperatures, and the simulationg accuracy of UniTire model is 99%.

2 Prediction results of UniTire cornering model at different temperatures
The UniTire model considering temperature is obtained based on the test results at temperatures of 0°C, 10°C, 32°C, and 43°C. In order to verify the accuracy of the UniTire steady-state model considering temperature, the tire lateral force and aligning torque are predicted at temperatures of 18°C and 53°C, the lateral force prediction results are shown in Figure 28-30, and the aligning torque prediction results are shown in Figure 31-33. From the simulation results and prediction results of the UniTire model, the prediction accuracy of the UniTire lateral force is more than 99%. The accuracy of the UniTire aligning torque model is more than 96%.

Conclusions
Based on the test results, the mechanical properties of tires are studied at different temperatures in this paper.