Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment

Behnke, Ronny; Kaliske, Michael

doi:10.1016/j.ijnonlinmec.2014.06.014

Cited by 62 publications

(22 citation statements)

References 34 publications

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“…However, according to thermal finite element simulations reported in Behnke and Kaliske (2015), , the sidewall component, despite having larger deformations, dissipates less energy than the tread. This is mainly due to the difference in the material properties between the compounds in these two components.…”

Section: Non-uniform Deformationmentioning

confidence: 97%

“…Regarding tire forces and moments which affect tire handling and ride comfort, empirical tire models such as the Magic Formula (Pacejka, 2005), semi-physical tire models such as F-Tire (Gipser, 2007), and physical tire models using finite element models (Ghoreishy, 2008) have been proposed and widely used. However, for the free rolling tire force, specifically the rolling resistance, there are few precise physical tire models (Shida et al, 1999;Behnke and Kaliske, 2015) in existence, due to limited knowledge of the fundamental mechanisms of rolling resistance. The rolling resistance is defined as the energy dissipation per unit distance travelled for a free rolling tire moving in a straight direction.…”

Section: Introductionmentioning

confidence: 99%

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Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Xiong

Tuononen

2015

Journal of Terramechanics

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Section: Non-uniform Deformationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Xiong

Tuononen

2015

Journal of Terramechanics

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“…The introduction of the moving reference frame leads to a flow of the material particles (e.g., P 1 and P 2 in Figure 1) through the moving finite element mesh, which has to be considered in case of inelastic material properties, where the material history has to be collected along the material streamlines. Approaches for the consideration of inelastic tire materials in the steady state ALE frame for rolling bodies are given, for example, by the authors in [15][16][17][18][19] and for the pavement/subground by the authors in [14,20]. A sequentially coupled ALE tire-pavement model, which considers inelastic tire and pavement materials, is described in [21].…”

Section: Introductionmentioning

confidence: 99%

A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

Wollny

Sun

Kaliske

2017

Numerical Meth Engineering

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This paper introduces a hierarchical sequential arbitrary Lagrangian-Eulerian (ALE) model for predicting the tire-soil-water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid-infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two-phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator-split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire-soil-water interaction both close to the contact and in the far field. The presented ALE model for tire-soil-water interaction provides the essential basis for future applications, for example, to a path-dependent frictional-cohesive response of the consolidating soil and unsaturated soil, respectively. HIERARCHICAL SEQUENTIAL ALE MODEL FOR TIRE-SOIL-WATER INTERACTION 913 With x = ALE + and ∇ ALE = 0, Equation (9) reads v (x, t) = ALE t P = J ·F −T andŜ =F −1 ·P,For two-phase porous media composed of incompressible solid constituents, Biot's coefficient becomes B = 1, and Biot's modulus M tends to infinity. Then, the material time derivative of the pore fluid density can be expressed aṡf = fJ ∕J, and the mass balance reads fJ J + ∇ ·̂= 0.In [6], the time derivative of the apparent fluid density f in case of compressible solids and fluids isIF ||r (k+1) || ⩾ Tolerance THEN k = k + 1 GO TO 1. Solid step ENDIF In the hierarchical sequential scheme, there are two major interaction mechanisms captured, that is, (1) tire and soil at the contact surface and (2) interaction between the solid skeleton and the pore fluid within the soil. To the best knowledge of the authors, this is the first time in which (1) an ALE iterative solver for the finite strain poromechanics problem has been formulated with multiplicative kinematics and (2) the ALE finite strain poromechanics has been used to capture the tire-soil-water interaction. Main effects of existing pore water on the tire-soil interaction are demonstrated in the numerical example. The presented research is an essential basis for further developments considering, for example, unsaturated soils and inelastic soil models like the Cam-Clay model for a more realistic representation of off-road rolling tires. APPENDIX Transient Lagrangian formulation of mass balanceThe time derivative of the Jacobian J in the Lagrangian frame is given [6] bẏ J J

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“…In the recent years, FE models of the drum testing had been developed. The rotation system of drum and tire could be modeled by using transient dynamic analysis and steady state rolling (SSR) analysis which was based on the Eulerian and Lagrangian coupling [5]. Tönük [6] used kinematic inversion technique by assigning the drum to move around the fixed tire with same relative motion.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Modeling with Embed Rebar Elements and Steady State Rolling Analysis for Rolling Resistance Test of Pneumatic Tire

Suvanjumrat

Rugsaj

2017

MATEC Web Conf.

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Abstract. Finite element model of tire rolling resistance test on the drum was developed using 3D steady state rolling analysis coupling with pre-inflation of 2D axisymmetric tire analysis. The complex components of the radial tires composing tread, sidewall, ply layers, steel belts, and lead wires were modeled using rebar elements which were embed into the rubber element using the tying equation. The Mooney-Rivlin hyperelastic constitutive model was employed to describe the large deformation behavior of tread and sidewall, while other components such as plies, steel belts and bead wires were assigned the linear isotropic material. The tire rolling resistance system was modeled by inflation of slick tire and compression on the drum for the footprint analysis regarding the rolling resistance test. The tire's steady state characteristics such as footprint contact pressure, rolling resistance force, and time response characteristic of tires were predicted instead the experiment of the prototype.

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Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment

Cited by 62 publications

References 34 publications

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

Finite Element Modeling with Embed Rebar Elements and Steady State Rolling Analysis for Rolling Resistance Test of Pneumatic Tire

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