The tire-performance simulation is solved as follows:
A static structural analysis with large-deflection effects enabled (NLGEOM,ON) is performed in two load steps.
In the first load step, contact between the rigid rim and the tire is established. In the second load step, an inflation analysis is performed with air pressure applied on the inner surfaces of the 2D tire model.
| Step | Description | Command | Comments |
|---|---|---|---|
| 2.1 | Initiate the 2D to 3D analysis. | MAP2DTO3D,START,2,12 | Begins the analysis at the last substep (the 12th in this case) of the second load step. |
| 2.2 | Extrude the 3D mesh from the deformed 2D mesh. |
EEXTRUDE,TIRE,30,3,,40 R,5,,,,,,1 (modify PINB) KEYOPT,8,16,1 (enable steady-state rolling) ALLSEL,ALL (select all entities) CM,Etire,elemcomp (create element component for the 3D model) | Revolves the 2D deformed geometry about the global Y axis with
30 elements in the hoop direction. A relatively fine mesh is created for the tire-road contact region. The rigid rim surface is extruded in the hoop direction, and the rigid road surface is extruded in the global Z direction. Both contact pairs are extruded to the 3D model. After extrusion, you can modify some contact settings (if necessary to resolve convergence issues during rebalancing). In this example, the pin ball radius of the tire-rim contact pair is modified to avoid spurious high penetrations during the rebalancing process. Limited preprocessing is possible. You can create a new contact pair or modify element KEYOPT settings. (Use caution when changing KEYOPTs, however, as an inappropriate modification can lead to different 3D model results after rebalancing.)In this example, the following preprocessing occurs during this step:
If necessary, you can also modify the friction coefficient of the tire-road contact pair. |
| 2.3 | Map boundary conditions and loads. | MAP2DTO3D,FINISH | Transfers boundary conditions, pressure loads, and applied nodal displacements from the 2D mesh to the corresponding entities in the extruded 3D model. |
| 2.4 | Map solution variables. | MAP2DTO3D,SOLVE | Transfers nodal and element solutions from the 2D model to the 3D model and initiates rebalancing. |
The analysis continues on the 3D tire model with new loadings via a multiframe restart. As with the rim-mounting and inflation analyses, the footprint analysis is solved in multiple load steps.
| Step | Description | Command | Comments |
|---|---|---|---|
| 3.1 | Restart the analysis. | ANTYPE,,RESTART,2,13 | Performs a multiframe restart at the last converged substep after MAP2DTO3D,SOLVE. (In this case, it is the 13th substep of the second load step.) |
| 3.2 | Change the behavior of the tire-rim contact pair. | CNKMOD,12,12,3 | The behavior of the tire-rim contact pair is changed to the bonded type. |
| 3.3 | Establish contact between road and tire. |
TIME,3 D,2000,UX,-0.006 | The rigid road surface is moved towards the tire via a displacement loading on the pilot node, ensuring that contact between the tire and the rigid road surface is established. |
| 3.4 | Apply the vehicle load. |
TIME,4 DDELE,2000,UX,,,ON F,2000,FX,-3000 SOLVE | The vehicle load is applied on the tire via the same pilot node of the rigid road surface. The pilot node is kept free to move in UX direction by deleting the previously defined displacement loading. |
| 3.5 | Optional: Define the camber angle. |
TIME,5 D,2000,ROTZ,0.03491 |
If desired, add a non-zero camber angle to the tire by rotating the rigid road surface appropriately. This example problem is solved using the following camber angle values: -4°, -2°, 0°, 2°, and 4°. This load step is not needed for the 0° camber-angle case. |
Following the footprint analysis, the steady-state rolling analyses are performed:
| Step | Description | Command | Comments |
|---|---|---|---|
| 4.1 | Steady-state rolling |
TIME,6 (or 5 for 0° camber) SSTATE,DEFINE,Etire,SPIN,50,POINTS,0,0,0,0,1,0 SSTATE,DEFINE,Etire,TRANSLATE,,,20 | A steady-state rolling analysis is performed with defined rotational and translational velocities. In this case, ω1 and Vz are chosen such that the tire is in a braking condition. |
| 4.2 | Determine the free-rolling spin state |
TIME,7 (or 6 for 0° camber) SSTATE,DEFINE,Etire,SPIN,64.1,POINTS,0,0,0,0,1,0 SSTATE,DEFINE,Etire,TRANSLATE,,,20 |
The rotational velocity is increased from ω1 to ωs (free-rolling spin) while translational velocity (Vz) remains constant. The free-rolling spin (FRS) ωs is initially unknown. To find ωs, two additional steady-state rolling analyses are performed in a separate run (as shown in free_rolling_analysis.dat), where the rotational velocity is increased from ω1 to ω2 while keeping the translational velocity (Vz) constant. The real constant for allowable elastic slip (SLTO) is a major factor in determining the free-rolling spin with desired accuracy. (See Using FKT, SLTO, and KEYOPT(13) in the Contact Technology Guide.) |
| 4.3 | Find the cornering force |
TIME,8 (or 7 for 0° camber) SSTATE,DEFINE,Etire,SPIN,64.1,points,0,0,0,0,1,0 SSTATE,DEFINE,Etire,TRANSLATE,,3.473,19.696 | After achieving the free-rolling state, a third steady-state rolling analysis is performed with a slip angle to calculate the cornering force acting on the tire. |