## 3 The Finite Element Model of the Tire Established in ABAQUS
### Global Sensitivity Analysis of Tire Forces  
During the rolling of tire, the magnitude of the vertical force can be adjusted by applying a specific vertical load, whereas the longitudinal and lateral forces are difficult to control precisely. The longitudinal and lateral tire forces are significantly related to the slip ratio and slip angle within a certain range. Therefore, varying these parameters can effectively reflect the force conditions experienced by the tire during actual movement [27]. Accordingly, in the global sensitivity analysis of tire forces, the slip ratio and slip angle are used as the actual input variables, while the acceleration, strain, and displacement response variables at each node within the ground deformation area of the rolling tire inner liner are taken as the output variables. Through finite element simulation analysis, the relationships between the longitudinal force and slip ratio, as well as the lateral force and slip angle, under standard loading conditions during pure longitudinal slip and pure lateral slip scenarios are obtained, as shown in Figure 6a,b. From the figures, it can be observed that under each single scenario, the slip ratio and slip angle vary within ranges of 10% and 8\({}^{\circ}\), respectively. Both variables exhibit a one-to-one correspondence with the longitudinal and lateral forces. The variation trends of the longitudinal and lateral forces are consistent with the predictive force curves from the Pacejka magic formula and the Brush tire model, both of which effectively describe the mechanical characteristics of tires. Therefore, these ranges are adopted as the variation intervals for the input variables slip ratio and slip angle in the global sensitivity analysis of tire forces, with the assumption that these input variables are uniformly distributed. Figure 5: Planar unfolding and detailed partitioning of the ground deformation area of the tire inner liner. Figure 6: (**a**) Tire longitudinal force versus slip ratio. (**b**) Tire lateral force versus slip angle. Based on the five-point Gaussian numerical integration rule [28], the specific values of each input variable are determined, as listed in Table 3, to establish the global sensitivity analysis scheme for tire forces. The Abaqus/Standard solver is used to simulate the rolling process of tire under combined slip angle and longitudinal slip conditions. The tire is configured with a nominal inflation pressure of 0.24 MPa, a vertical load of 4821 N, a road adhesion coefficient of 0.8, and a rolling speed of 70 km/h. The global sensitivity analysis of tire forces based on the scheme shown in Table 3 is conducted using the finite element method. The acceleration (\(A\)), strain (\(LE\)), and displacement (\(U\)) components in three directions are extracted at each node within the ground deformation area of the rolling tire inner liner, resulting in nine output response variables. (\(A_{1}\), \(A_{2}\), and \(A_{3}\) represent the radial, circumferential, and lateral accelerations, respectively, while other strain and displacement components follow the same directional notation). These response values are calculated for 21 sub-areas, and the moments of various orders are determined to obtain 189 output response variables in different areas under varying input variables, thereby enabling the calculation of the global sensitivity main index \(S_{i}\). When \(S_{i}\geq 0.8\), the input variable is considered to show high sensitivity to the output response variable; when \(0.6<S_{i}<0.8\), it indicates moderate sensitivity; and when \(S_{i}\leq 0.6\), it indicates low sensitivity.