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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6924506, 9 pages
Research Article

Nonlinear Research and Efficient Parameter Identification of Magic Formula Tire Model

College of Engineering, Nanjing Agricultural University, Nanjing 210031, China

Correspondence should be addressed to Zhixiong Lu

Received 6 May 2017; Revised 16 August 2017; Accepted 22 August 2017; Published 28 September 2017

Academic Editor: Stefan Balint

Copyright © 2017 Zhun Cheng and Zhixiong Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Magic Formula tire model can describe the mechanical properties of tire accurately and thus is applied in the research field of vehicle dynamics widely. The Magic Formula tire model has the characteristics of a great number of parameters and the high nonlinearity, so it is hard to identify parameters. Researchers generally use different intelligent optimization algorithms for parameter identification. However, in the process of parameter identification, with a few experimental data, parameter identification results generally have the low accuracy, while, in the case of a large number of experimental data, the amount of work done in the experiment will increase and there will be many experimental errors. To solve these problems, this paper researches the longitudinal force of tire and proposes an interpolation method and a method based on the nonlinear research of the tire force. The results of parameter identification experiments on the two kinds of tire data show that both of the two methods can be used for the parameter identification of Magic Formula tire model fast and accurately with only a few experimental data. In addition, this paper proposes a method estimating the maximum longitudinal force and corresponding slip rate.