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Research Papers

Physics-Based Flexible Tire Model Integrated With LuGre Tire Friction for Transient Braking and Cornering Analysis

[+] Author and Article Information
Hiroki Yamashita

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
2312 Seamans Center,
Iowa City, IA 52242

Paramsothy Jayakumar

US Army TARDEC,
6501 E. 11 Mile Road,
Warren, MI 48397-5000

Hiroyuki Sugiyama

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
2416C Seamans Center,
Iowa City, IA 52242
e-mail: hiroyuki-sugiyama@uiowa.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 16, 2015; final manuscript received February 9, 2016; published online March 16, 2016. Assoc. Editor: Javier Cuadrado.This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Comput. Nonlinear Dynam 11(3), 031017 (Mar 16, 2016) (17 pages) Paper No: CND-15-1441; doi: 10.1115/1.4032855 History: Received December 16, 2015; Revised February 09, 2016

In transient vehicle maneuvers, structural tire deformation due to the large load transfer causes abrupt change in normal contact pressure and slip distribution over the contact patch, and it has a dominant effect on characterizing the transient braking and cornering forces including the history-dependent friction-induced hysteresis effect. To account for the dynamic coupling of structural tire deformations and the transient tire friction behavior, a physics-based flexible tire model is developed using the laminated composite shell element based on the absolute nodal coordinate formulation and the distributed parameter LuGre tire friction model. In particular, a numerical procedure to integrate the distributed parameter LuGre tire friction model into the finite-element based spatial flexible tire model is proposed. To this end, the spatially discretized form of the LuGre tire friction model is derived and integrated into the finite-element tire model such that change in the normal contact pressure and slip distributions over the contact patch predicted by the deformable tire model enters into the spatially discretized LuGre tire friction model to predict the transient shear contact stress distribution. By doing so, the structural tire deformation and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. The tire model developed is experimentally validated and several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study.

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Figures

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Fig. 1

Kinematics of shear deformable laminated composite shell element

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Fig. 2

Tire model creation procedure: (a) cut section, (b) geometry data points, (c) spline curve, (d) element discretization, (e) 3D tire geometry, and (f) flexible tire model data

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Fig. 3

Physics-based tire model using the laminated composite shell element

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Fig. 4

Connection of flexible tire element i and rigid rim j: (a) spring/damper coordinate system and (b) reference frame defined at spring/damper definition point l on shell element i

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Fig. 5

Integration of LuGre tire friction model in flexible tire model

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Fig. 6

Uniaxial tensile test model

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Fig. 7

Twisting angle and in-plane shear strain of two-layer laminated composite plate subjected to uniaxial tensile load

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Fig. 8

Deformed shape of cantilevered two-layer composite shell subjected to point load

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Fig. 9

Numerical convergence of finite-element solutions

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Fig. 10

Vibration mode shapes of two-layer laminated composite shell

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Fig. 12

Global X-position at the tip point

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Fig. 13

Global Y-position at the tip point

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Fig. 14

Global Z-position at the tip point

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Fig. 15

Deformed shape of tire cross section

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Fig. 16

Lateral deflection of tire for various wheel loads

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Fig. 17

Vertical deflection of tire for various wheel loads

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Fig. 18

Longitudinal contact patch length for various wheel loads

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Fig. 19

Lateral contact patch length for various wheel loads

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Fig. 20

Normal contact pressure distribution in the longitudinal direction (4 kN)

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Fig. 21

Normal contact pressure distribution in the lateral direction (4 kN)

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Fig. 22

In-plane and out-of-plane natural frequencies

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Fig. 23

Tire force characteristics under combined slip condition

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Fig. 24

Transient braking analysis results

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Fig. 25

Shear contact stress distribution in the transient braking analysis

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Fig. 26

Transient cornering analysis results

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Fig. 27

Shear contact stress distribution in the transient cornering analysis

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