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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Pacejka, H. B., 2002, Tire and Vehicle Dynamics, Society of Automotive Engineers (SAE), Warrendale, PA.
Lugner, P., Pacejka, H., and Plochl, M., 2005, “Recent Advances in Tyre Models and Testing Procedures,” Veh. Syst. Dyn., 43(6–7), pp. 413–436. [CrossRef]
Gim, G. H., and Nikravesh, P. E., 1990, “An Analytical Model of Pneumatic Tires for Vehicle Dynamic Simulations—Part 1: Pure Slips,” Int. J. Veh. Des., 11(6), pp. 589–618. [CrossRef]
Clover, C. L., and Bernard, J. E., 1998, “Longitudinal Tire Dynamics,” Veh. Syst. Dyn., 29(4), pp. 231–260. [CrossRef]
Canudas-de-Wit, C., Tsiotras, P., Velenis, E., Basset, M., and Gissinger, G., 2003, “Dynamic Friction Models for Road/Tire Longitudinal Interaction,” Veh. Syst. Dyn., 39(3), pp. 189–226. [CrossRef]
Deur, J., Ivanović, V., Troulis, M., Miano, C., Hrovat, D., and Asgari, J., 2005, “Extensions of the LuGre Tyre Friction Model Related to Variable Slip Speed Along the Contact Patch Length,” Veh. Syst. Dyn., 43(1), pp. 508–524. [CrossRef]
Deur, J., Ivanović, V., Pavković, D., Hrovat, D., Asgari, J., Troulis, M., and Miano, C., 2005, “Experimental Analysis and Modelling of Longitudinal Tyre Friction Dynamics for Abrupt Transients,” Veh. Syst. Dyn., 43(1), pp. 525–539. [CrossRef]
Alvarez, L., Yi, J., Horowitz, R., and Olmos, L., 2005, “Dynamic Friction Model-Based Tire-Road Friction Estimation and Emergency Braking Control,” ASME Dyn. Syst., Meas. Control, 127(1), pp. 22–32. [CrossRef]
Rajapakshe, M. P., Gunaratne, M., and Kaw, A. K., 2010, “Evaluation of LuGre Tire Friction Model With Measured Data on Multiple Pavement Surfaces,” Tire Sci. Technol., 38(3), pp. 213–227. [CrossRef]
Gipser, M., 2005, “FTire: A Physically Based Application-Oriented Tyre Model for Use With Detailed MBS and Finite-Element Suspension Models,” Veh. Syst. Dyn., 43(1), pp. 76–91. [CrossRef]
Lee, C. R., Kim, J. W., Hallquist, J. O., Zhang, Y., and Farahani, A. D., 1997, “Validation of a FEA Tire Model for Vehicle Dynamic Analysis and Full Vehicle Real Time Proving Ground Simulations,” SAE Technical Paper No. 971100.
Koishi, M., Kabe, K., and Shiratori, M., 1998, “Tire Cornering Simulation Using an Explicit Finite Element Analysis Code,” Tire Sci. Technol., 26(2), pp. 109–119. [CrossRef]
Gruber, P., Sharp, R. S., and Crocombe, A. D., 2012, “Normal and Shear Forces in the Contact Patch of a Braked Racing Tyre. Part 2: Development of a Physical Tyre Model,” Veh. Syst. Dyn., 50(3), pp. 339–356. [CrossRef]
Shabana, A. A., 2005, Dynamics of Multibody Systems, 3rd ed., Cambridge University Press, Cambridge, UK.
Belytschko, T., Liu, W. K., and Moran, B., 2000, Nonlinear Finite Elements for Continua and Structures, Wiley, New York.
Sugiyama, H., and Suda, Y., 2009, “Nonlinear Elastic Ring Tire Model Using the Absolute Nodal Coordinate Formulation,” IMechE J. Multi-Body Dyn., 223(3), pp. 211–219. [CrossRef]
Zegelaar, P. W. A., Gong, S., and Pacejka, H. B., 2008, “Tyre Models for the Study of In-Plane Dynamics,” Veh. Syst. Dyn., 23(Suppl.  1), pp. 578–590. [CrossRef]
Kim, S., Nikravesh, P. E., and Gim, G., 2008, “A Two-Dimensional Tire Model on Uneven Roads for Vehicle Dynamic Simulation,” Veh. Syst. Dyn., 46(10), pp. 913–930. [CrossRef]
Sugiyama, H., Koyama, H., and Yamashita, H., 2010, “Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 5(2), p. 021001. [CrossRef]
Chung, J., and Hubert, G. M., 1993, “A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method,” ASME J. Appl. Mech., 60(2), pp. 371–375. [CrossRef]
Deur, J., Asgari, J., and Hrovat, D., 2004, “A 3D Brush-Type Dynamic Tire Friction Model,” Veh. Syst. Dyn., 42(3), pp. 133–173. [CrossRef]


Grahic Jump Location
Fig. 1

LuGre tire friction model

Grahic Jump Location
Fig. 2

Longitudinal tire force on wet surface

Grahic Jump Location
Fig. 3

ANCF elastic ring tire model integrated with LuGre dynamic friction

Grahic Jump Location
Fig. 4

Absolute nodal coordinates of the curved beam

Grahic Jump Location
Fig. 5

Contact model of ANCF-LuGre Tire model

Grahic Jump Location
Fig. 6

Slip-dependent friction coefficient

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

Friction testing of tread rubber

Grahic Jump Location
Fig. 10

Tangential force coefficients for 4 kgf

Grahic Jump Location
Fig. 11

Tangential force coefficients for 5 kgf

Grahic Jump Location
Fig. 12

Tangential force coefficients for 6 kgf

Grahic Jump Location
Fig. 13

Normal contact pressure

Grahic Jump Location
Fig. 14

Circumferential velocity of the tire

Grahic Jump Location
Fig. 15

Tangential force coefficients for various braking torques

Grahic Jump Location
Fig. 16

Normal contact pressure (T = 1000 Nm)

Grahic Jump Location
Fig. 17

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In