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

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.

Heat Build-Up and Rolling Resistance Analysis of a Solid Tire: Experimental Observation and Numerical Simulation with Thermo-Mechanical Coupling Method

“…The adopted flowchart of thermo-mechanical coupling analysis [ 17 ] of the solid tire is shown in Figure 3 . The black part represents the deformation module, the red part represents the thermo-mechanical coupling module of Endurica and Abaqus co-simulation including the dissipation module and thermal module, and the blue part represents the RR calculation module.…”

“…The nominal strain component history results for each element in the solid tire model was obtained. In the co-simulation module, the heat generation rate of each element was calculated based on the Kraus self-heating model [ 17 , 18 ] and strain results computed in the deformation module. Due to the temperature, strain, and strain rate dependent dynamic properties of rubber, the HBU behavior is much more complicated [ 32 , 33 , 34 ].…”

“…Equation (6) shows the Kraus self-heating model including five material parameters , , , ε a,c and M modified by Ulmer [ 38 ]. This model can very accurately describe the functional relation between G’’ and ε a of rubber material [ 17 , 18 ]. The test data of loss modulus vs. strain amplitude at the temperature of 25 °C in Figure 8 was selected and fitted by Equation (6) at a constant frequency of 10 Hz and a constant temperature of 25 °C.…”

“…By using Prony series and parallel rheological framework (PRF) models, Aldhufairi et al [ 16 ] studied the role of linear and nonlinear viscoelastic representation of materials to verify the calculation accuracy of tire RR. With the combination of the improved convergence at high speed of tires in Abaqus and the incremental, critical plane fatigue analysis procedures of Endurica DT, a pioneering work was done by Mars et al [ 17 ]. They studied the standing wave development, self-heating, and fatigue during regulatory high-speed tire testing protocols.…”

Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design

“…More recently, a number of relevant developments in several applications have introduced the CED criterion such as tires, [37][38][39] bushings, [40,41] airsprings, [42] etc. The principle goal of this research is providing a generalized numerical predictive model-based on CED-parameter.…”