Incremental, Critical Plane Analysis of Standing Wave Development, Self-Heating, and Fatigue during Regulatory High-Speed Tire Testing Protocols

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Abstract
Tire speed ratings derive from regulatory testing in which tire structural integrity is validated over a series of steps with successively increasing speed. For the FMVSS 139 high-speed standard, there are four half-hour duration speed steps at 80, 140, 150, and 160 kph. Speed ratings from Q through Y may be attained through the UN ECE R30 regulation high-speed testing. For either protocol, a tire must demonstrate the ability to operate without crack development at high speed for a specified period. After the test, “there shall be no evidence of tread, sidewall, ply, cord, inner liner, belt or bead separation, chunking, broken cords, cracking, or open splices.” A workflow for simulating regulatory high-speed durability performance has been developed based upon (1) recent improvements to the Abaqus steady-state transport formulation that now permit converged solutions to be obtained at high speed (including after the development of standing waves in the tire) and (2) Endurica DT self-heating and incremental fatigue simulations that account for thermal effects and for damage accumulation occurring due to a schedule of load cases. The self-heating calculation features the Kraus model and accurately captures viscoelastic loss modulus dependence on strain amplitude and temperature. For each step of the high-speed procedure, steady-state structural and thermal solutions are first computed. The deformation history in the presence of standing waves is shown to require rainflow counting due to the occurrence of multiple load cycles per tire revolution. Crack growth is finally integrated for each potential critical plane through each step of the test until failure is indicated. Standing waves at high speed induce significant self-heating and damage, rapidly limiting high-speed performance. The temperature dependence of self-heating and strength properties also plays a major role in limiting high-speed durability. The simulations were executed on both a flat surface and on the regulation specified 1.7 m diameter road wheel. As expected, durability testing on the road wheel is more severe, and the beneficial effect of a nylon overwrap is predicted.

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