Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Mar 2006

Rim Slip and Bead Fitment of Tires: Analysis and Design2

Page Range: 38 – 63
DOI: 10.2346/1.2169829
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Abstract

A tire slips circumferentially on the rim when subjected to a driving or braking torque greater than the maximum tire-rim frictional torque. The balance of the tire-rim assembly achieved with weight attachment at certain circumferential locations in tire mounting is then lost, and vibration or adverse effects on handling may result when the tire is rolled. Bead fitment refers to the fit between a tire and its rim, and in particular, to whether a gap exists between the two.

Rim slip resistance, or the maximum tire-rim frictional torque, is the integral of the product of contact pressure, friction coefficient, and the distance to the wheel center over the entire tire-rim interface. Analytical solutions and finite element analyses were used to study the dependence of the contact pressure distribution on tire design and operating attributes such as mold ring profile, bead bundle construction and diameter, and inflation pressure, etc. The tire-rim contact pressure distribution consists of two parts. The pressure on the ledge and the flange, respectively, comes primarily from tire-rim interference and inflation. Relative contributions of the two to the total rim slip resistance vary with tire types, depending on the magnitudes of ledge interference and inflation pressure. Based on the analyses, general guidelines are established for bead design modification to improve rim slip resistance and mountability, and to reduce the sensitivity to manufacturing variability. An iterative design and analysis procedure is also developed to improve bead fitment.

Keywords: tire; rim slip; bead fitment; bead design; tire-rim interference; contact pressure; concentric ring model; finite element analysis; interference profiling
Copyright: The Tire Society
FIG. 1.
FIG. 1.

A schematic of rim slip.

FIG. 2.
FIG. 2.

Springs-in-series model.

FIG. 3.
FIG. 3.

Concentric ring model.

FIG. 4.
FIG. 4.

Prediction of tire-rim contact pressure as a function of interference by concentric ring model.

FIG. 5.
FIG. 5.

Concentric ring model prediction of tire-rim contact pressure as a function of rubber thickness while keeping mold ring diameter constant.

FIG. 6.
FIG. 6.

Concentric ring model prediction of tire-rim contact pressure as a function of rubber thickness while keeping bead bundle inside diameter constant.

FIG. 7.
FIG. 7.

Overlay of mold cavity profile, scanned image of a cut section, and laser scans of an unmounted, free-hung race tire (only the lower sidewall-to-bead area of one side of the tire is shown).

FIG. 8.
FIG. 8.

Overlay of tire bead and rim profiles for the control model.

FIG. 9.
FIG. 9.

The lower sidewall-to-bead area of the original and deformed meshes of the control model.

FIG. 10.
FIG. 10.

Hoop stress distribution in the smeared bead bundle of the control model.

FIG. 11.
FIG. 11.

Predicted tire-rim contact pressure distribution for the control model.

FIG. 12.
FIG. 12.

The lower sidewall-to-bead area of the original and deformed meshes of the control model. The deformation includes the effect of the centrifugal force associated with a speed of 150 mph.

FIG. 13.
FIG. 13.

Hoop stress distribution in the smeared bead bundle of the control model with centrifugal force effect included.

FIG. 14.
FIG. 14.

Predicted tire-rim contact pressure distribution for the control model with centrifugal force included.

FIG. 15.
FIG. 15.

Predicted tire-rim contact pressure distribution for the control model with inflation pressure increased to 30 psi.

FIG. 16.
FIG. 16.

Overlay of mold cavity, rim, and mold ring profiles. The mold ring profile in cyan has 5∕10.5° dual ledge taper angles. The mold ring profiles in red and green coincide in the ledge region and only the red one shows; the ledge taper angle is 8°.

FIG. 17.
FIG. 17.

Hoop stress distribution in the smeared bead bundle of model v2.

FIG. 18.
FIG. 18.

Predicted tire-rim contact pressure distribution for model v2.

FIG. 19.
FIG. 19.

Hoop stress distribution in the smeared bead bundle of model v1.

FIG. 20.
FIG. 20.

Predicted tire-rim contact pressure distribution for model v1.

FIG. 21.
FIG. 21.

An illustration of the proposed procedure to eliminate tire-rim separation in the heel-to-flange region.

FIG. 22.
FIG. 22.

Hoop stress distribution in the smeared bead bundle of model 2e.

FIG. 23.
FIG. 23.

Predicted tire-rim contact pressure distribution for model 2e.

FIG. 24.
FIG. 24.

Overlay of tire bead and rim profiles. The bead ledge has dual taper angles with the transition under the center of the bead bundle.

FIG. 25.
FIG. 25.

Predicted tire-rim contact pressure distribution for a passenger tire.

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