# Bias Truck Tire Deformation Analysis with Finite Element Modeling
## 3 Results and Discussion
The stage of mounting the tire on the rim was carried out in ten increments through concurrent displacement of the rim in the axial and the radial directions against the position, which was consistent with the actual rim dimensions of 8.0-20 assumed for this tire. At this stage, small values of internal pressure were also applied (\(0.001p_{\text{n}}\) per increment) to provide for the correct setting of the bead on the rim. A non-deformable rim exerted contact forces on the bead. Forces tangential to the contact surface were calculated according to the [PERSON]'s law of friction. The rubber-steel friction coefficient was assumed at 0.6. The profile of a tire mounted on the rim is presented in Figure 5, item 3. The simulation of tire inflation was divided into stages: (1) ten pressure increments, \(0.01p_{\rm n}\) each, when there was considerable tire profile alteration resulting from the \"lifting\" of a shrunk tire; (2) nine increments, \(0.01p_{\rm n}\) each, when the tire had already reached an adequate initial stiffness. The inflated tire profile is shown in Figure 5, item 4, together with the displacement of internal profile C and S characteristic points, i.e., the tire crown point and sidewall point. The shown profiles indicate the occurrence of large displacements in a tire subject to internal pressure. Axial displacement of the point located on sidewall was of the order of its thickness. Displacements of the said C and S points but referenced to the tire profile in the mold amounted to 4 mm and 13 mm, respectively. The external diameter of the inflated tire and its width, as obtained from the model, amounted to 1080 mm and 286 mm, respectively. The diameter value was consistent with the catalog requirements for this tire, and the width difference was \(-1.7\%\). This shows that the tire profile in the mold was designed correctly, and the model correctly predicted the overall dimensions of the actual tire. It must be noted that this tire--once manufactured in a series--was correctly designed and fulfilled all requirements stipulated in the European Tyre and Rim Technical Organisation (ETRTO) documents. In the case of tire inflation analysis and neglecting cord shrinkage, quite a mild fluctuation in bodyply cord forces from the tire crown to the bead wire area was observed, which was consistent with the results obtained on the tire netting model (cf. [27] (p. 84, Figure 71a)). When considering the stresses generated by cord shrinkage, considerable variations in cord forces were observed. In particular, in the tire crown, there was almost a 60% increase in force value in the first and the second ply cords. It should be assumed that a certain influence on this increase was contributed by the first groove in the tire tread. The highest values of forces were obtained for innermost plies (first and second) cords,  
Figure 5: Bias truck tire; 1—profile in mold and finite element mesh, 2—outside the mold (shrunk), 3—profile after mounting on rim, 4—inflated up to \(p_{\rm n}\); 5—rim. as this was where the internal pressure was applied, and these values decreased for plies located more outwards in the tire, which was consistent with the principles of deformable body mechanics. Figure 6 presents the chart of body ply cord forces in the function of arc coordinate measured along the profile from the tire crown towards the beads. Although the impact of thermal shrinkage on the maximum force values in body ply cords was high, the final displacements of inner tire profile control points (C and S) were less dependent on whether the shrinkage was or was not taken into account (Figure 7). The differences were 15% and 3.5%, respectively. It must be stressed that the control point S was located at the sidewall and, as a result of tire inflation, it moved axially towards the symmetry plane. Finally, the tire width mounted on the rim and inflated was lower than its width in the vulcanization mold. The stable finite element tire model makes it possible to obtain many usable results.