Research Papers

Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model

[+] Author and Article Information
Hiroki Yamashita

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

Yusuke Matsutani

Department of Mechanical Engineering,
Tokyo University of Science,
Tokyo 125-8585, Japan

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 April 23, 2014; final manuscript received August 13, 2014; published online February 11, 2015. Assoc. Editor: Dr. Corina Sandu.

J. Comput. Nonlinear Dynam 10(3), 031003 (May 01, 2015) (11 pages) Paper No: CND-14-1109; doi: 10.1115/1.4028335 History: Received April 23, 2014; Revised August 13, 2014; Online February 11, 2015

In this investigation, the flexible tire model based on the absolute nodal coordinate formulation (ANCF) is integrated with LuGre tire friction model for evaluation of the longitudinal tire dynamics under severe braking scenarios. The ANCF-LuGre tire model developed allows for considering the nonlinear coupling between the dynamic structural deformation of the tire and its transient tire force distribution in the contact patch using general multibody dynamics computer algorithms. To this end, the contact patch obtained by the ANCF elastic ring tire model is discretized into small strips and the state of friction at each strip is defined by the differential equation associated with the discretized LuGre friction parameters. The normal contact pressure distribution predicted by the ANCF elastic ring elements that are in contact with the road surface are mapped onto the LuGre strips in the contact patch to evaluate the tangential tire force distribution and then the tire forces evaluated at LuGre strips are fed back to the generalized tangential contact forces of the ANCF elastic ring tire model. By doing so, the structural deformation of the ANCF elastic ring tire model is dynamically coupled with the LuGre tire friction in the final form of the governing equations. Furthermore, the systematic and automated parameter identification procedure for the LuGre tire force model is developed. It is shown that use of the proposed procedure with the modified friction curve proposed for wet road conditions leads to accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Several numerical examples are presented in order to demonstrate the use of the in-plane ANCF-LuGre tire model for the longitudinal transient dynamics of tires under severe braking scenarios.

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Fig. 1

LuGre tire friction model

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Fig. 2

Longitudinal tire force on wet surface

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Fig. 3

ANCF elastic ring tire model integrated with LuGre dynamic friction

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Fig. 4

Absolute nodal coordinates of the curved beam

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Fig. 5

Contact model of ANCF-LuGre Tire model

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Fig. 6

Slip-dependent friction coefficient

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Fig. 7

Slip-dependent friction coefficient modeled by exiting and modified g(vr)-function

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Fig. 8

Longitudinal tire force with exiting and modified g(vr)-function

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Fig. 9

Friction testing of tread rubber

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Fig. 10

Tangential force coefficients for 4 kgf

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Fig. 11

Tangential force coefficients for 5 kgf

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Fig. 12

Tangential force coefficients for 6 kgf

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Fig. 13

Normal contact pressure

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Fig. 14

Circumferential velocity of the tire

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Fig. 15

Tangential force coefficients for various braking torques

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Fig. 16

Normal contact pressure (T = 1000 Nm)

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Fig. 17

Longitudinal tire forces per unit area (T = 1000 Nm)




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