Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Sept 2007

Validation of a Steady-State Transport Analysis for Rolling Treaded Tires5

,
,
,
,
,
, and
Page Range: 183 – 208
DOI: 10.2346/1.2768974
Save
Download PDF

Abstract

A new computational procedure for the analysis of treaded tires under conditions of steady-state rolling has been recently developed. As with well-known procedures for axisymmetric structures, the new procedure uses a mixed Eulerian/Lagrangian kinematic description in which rigid body rotation is described in an Eulerian manner and the deformation is described in a Lagrangian manner. This work discusses the industrial and historical context of the procedure, provides an overview of the technology, reviews experimental validation targets, and compares against better-established procedures. The new procedure successfully predicts the distributions of normal, lateral, and longitudinal stress in several different cases. A limitation of the new procedure is that solution accuracy can degrade, particularly in the longitudinal stress, when the angular extent of the base pitch sector is too large. When applied in nontreaded cases, the new procedure produces results consistent with established procedures such as Lagrangian rolling and conventional steady-state transport for axisymmetric structures. The main benefits of the new procedure are (1) computational efficiency and (2) the ability to include the full geometry of treaded tires.

Keywords: Eulerian; Lagrangian; steady-state transport; rolling contact; tread pattern; cyclic symmetry
Copyright: The Tire Society
FIG. 1.
FIG. 1.

Local conditions at the footprint of a tire rolling at a slip angle, viewed looking up through the road.

FIG. 2.
FIG. 2.

Comparison of lateral stresses occurring in the footprint of a non-pneumatic tire under conditions of static loading and slow rolling [28].

FIG. 3.
FIG. 3.

Comparison of lateral stresses occurring in the footprint of a pneumatic tire under conditions of static loading and slow rolling [28].

FIG. 4.
FIG. 4.

Effect of tire cornering on extent of slip region in a rolling tire [26].

FIG. 5.
FIG. 5.

Footprint stress components during straight-ahead rolling under constant load for smooth (top row), grooved (middle row), and block (bottom row) tread patterns. From Ref. [21].

FIG. 6.
FIG. 6.

Axisymmetric tire model.

FIG. 7.
FIG. 7.

Tread mesh.

FIG. 8.
FIG. 8.

Sector mesh.

FIG. 9.
FIG. 9.

Periodic and pitched tread patterns.

FIG. 10.
FIG. 10.

Overall modeling strategy.

FIG. 11.
FIG. 11.

Development of footprint shape and slip velocity during rolling at a slip angle, as computed via the new calculation procedure. Color contours show slip velocity.

FIG. 12.
FIG. 12.

Infinite, laterally grooved, solid rubber wheel, full 3D mesh (left), and base pitch sector (right).

FIG. 13.
FIG. 13.

Ratio of computed spindle forces and moments at 2° slip for infinite, laterally grooved, solid rubber wheel (PSST analysis/Lagrangian analysis).

FIG. 14.
FIG. 14.

Comparison of Lagrangian analysis (circles) and PSST analysis (squares) contact stress, plotted as a function of distance in footprint, of infinite, laterally grooved, solid rubber wheel.

FIG. 15.
FIG. 15.

Computed and measured NTMP solid tire load-deflection characteristics under static loading.

FIG. 16.
FIG. 16.

Computed and measured NTMP solid tire footprint contact stresses. Leading edge is on the left, trailing edge on the right.

FIG. 17.
FIG. 17.

Effect of computation method on dynamic footprint stresses. From left to right: SST, PSST with 1° base sector, PSST with 5° base sector. Leading edge is on the left, trailing edge on the right.

FIG. 18.
FIG. 18.

Computed treaded footprint contact stresses (MPa) during rolling.

  • Download PDF