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Research Papers

A Consistent, Hybrid-Dynamical-System, Lumped-Parameter Model of Tire–Terrain Interactions

[+] Author and Article Information
Pravesh Sanghvi

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Harry Dankowicz

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: danko@illinois.edu

Here, and throughout this paper, text or mathematical symbols enclosed in brackets refer consistently within a sentence to an alternative situation, typically conditions for backward slip.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 10, 2013; final manuscript received September 10, 2013; published online February 11, 2015. Assoc. Editor: Dr. Corina Sandu.

J. Comput. Nonlinear Dynam 10(3), 031002 (May 01, 2015) (9 pages) Paper No: CND-13-1135; doi: 10.1115/1.4025481 History: Received June 10, 2013; Revised September 10, 2013; Online February 11, 2015

This paper establishes the internal mathematical and energetic consistency of a hybrid-dynamical-system, lumped-parameter, planar, physical model for capturing transient interactions between an elastically deformable tire and an elastically deformable terrain as a baseline result for more realistic models that account for permanent deformation, shear failure, and three-dimensional contact conditions. The model accounts for radial and circumferential deformation of the tire as well as normal and tangential deformation of the terrain. It captures the onset and loss of contact as well as localized stick and slip phases for each of the discrete tire elements by a suitable evolution of a collection of associated internal state variables. The analysis characterizes generic transitions between distinct phases of contact uniquely in forward time and proves that all internal state variables remain bounded during compact intervals of contact. The behavior of the model is further illustrated through an analytical and numerical study of two instances of tire-terrain interactions under steady state condition.

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Figures

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Fig. 1

Schematic diagram illustrating the overall body geometry

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Fig. 2

Schematic of the contact geometry for the model of a rigid body on a deformable terrain

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Fig. 3

Schematic of the contact geometry for the model of a deformable body on a rigid terrain

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Fig. 4

Schematic of the contact geometry for the model of a deformable body on a deformable terrain

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Fig. 5

(Left panel) root manifold of Eq. (55) (solid) separating combinations of μ and φi corresponding to stick (white) and slip (shaded) for the parameter values given in the text. Here, the dashed horizontal line corresponds to δ=0.1. (Right panel) the normal load W as a function of the deflection δ for different values of μ. For μ<μ*, the load-deflection curves coincide with that for μ=μ* until the value of δ corresponds to a locus on the root manifold in the upper panel.

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Fig. 6

Gross thrust ratio (left panel) and percentage of the duration of contact corresponding to an initial stick phase (right panel) parameterized by the deflection δ and the slip ratio 1-U/ω for the parameter values given in the text

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