Editorial Type:
Article Category: Other
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Online Publication Date: 01 Apr 2013

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

Page Range: 127 – 151
DOI: 10.2346/tire.13.410203
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ABSTRACT

The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

Keywords: tire; equilibrium profile; mold profile; finite element analysis; tire tests
FIG. 1
FIG. 1

Cross-bias tire [1].

FIG. 2
FIG. 2

Modern radial ply rigid breaker tire.

FIG. 3
FIG. 3

Bead section coordinates.

FIG. 4
FIG. 4

Tread (crown section).

FIG. 5
FIG. 5

Cross section of the tire.

FIG. 6
FIG. 6

Mold and ply profile.

FIG. 7
FIG. 7

Geometric equations for modeling of the tire profile.

FIG. 8
FIG. 8

Geometric equations for modeling of the tire profile (continued).

FIG. 9
FIG. 9

Equation of virtual work.

FIG. 10
FIG. 10

Membrane pressure equation.

FIG. 11
FIG. 11

Pantographing of the cords.

FIG. 12
FIG. 12

Nomenclature for tire design components.

FIG. 13
FIG. 13

An example of fitting the polynomial strain energy function to experimental data for a given rubber compound.

FIG. 14
FIG. 14

Diagram for the transformation of coordinates in the 2D plane.

FIG. 15
FIG. 15

The loading of the inflated tire.

FIG. 16
FIG. 16

The molded “reference” tire showing material placements. (Top) belt edge magnified. (Bottom) bead section magnified.

FIG. 17
FIG. 17

Finite element results for the molded reference tire, inflated at 26 psi (1.79 × 1005 N/m2) on a rim, and subsequently loaded at 1217 lbs (552 kg) (80% of design load).

FIG. 18
FIG. 18

A comparison of FEA and profile calculation results for the centre of the carcass ply line of the inflated tire at 26 psi (1.79 × 105 N/m2).

FIG. 19
FIG. 19

Design 2 tire. shear strain within the tire when it is inflated at 26 psi (1.79 × 105 N/m2) and subsequently loaded at 1217 lbs (552 kg). The apex section is isolated and magnified.

FIG. 20
FIG. 20

Design 2 tire. Shear stress within the tire when it is inflated at 26 psi (1.79 × 105 N/m2) and subsequently loaded at 1217 lbs (552 kg).

FIG. 21
FIG. 21

Calculated maximum shear stress in apex.

FIG. 24
FIG. 24

Calculated maximum shear strain at belt edge.

FIG. 22
FIG. 22

Calculated maximum shear stress at belt edge.

FIG. 23
FIG. 23

Calculated maximum shear strain in apex.

FIG. 25
FIG. 25

Apex cracking in design 2 tires.

Contributor Notes

1 Corresponding author. 468 Copeland Court, Oakville, Ontario L6J 4B9, Canada. Email: rbauer4@cogeco.ca. Phone: 905-815-1530. The work presented here was carried out at Dunlop Tire Inc., Buffalo, New York, USA.
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