The Prediction of the Friction Ellipse for Formula SAE Tires

Photo of Raquel Carampatan, Enes Gokkus, Canberk Oztoprak, Matthew Sherbin Students: Raquel Carampatan, Enes Gokkus, Canberk Oztoprak, Matthew Sherbin

Sponsor: The University of Texas Society of Automotive Engineers

Date: Spring 2012

Requirements:
The team was required to obtain car parameters, such as car weight, camber angle, and wheel base height, from UT FSAE so that calculations could be specified for the car itself. Also, all calculations were required to utilize the raw data of the Tire Testing Consortium. This data was used to calculate forces with respect to tire parameters such as slip ratio and slip angle. The project was constrained by both vehicle and model design. Restrictions in camber angle, normal force, slip angle, and slip ratio were all critical to the analysis of the selected tire models. The team was also constrained to the technical computing software at hand: Excel and MATLAB.

Problem:
During competition, The University of Texas at Austin Formula SAE team must choose the best tires for on-track performance. They also must justify this choice to the judges to receive an optimal score. For this project the team used various tire performance models to create a friction ellipse. The friction ellipse provides the force limitations of a tire in the latitudinal and longitudinal directions. The team also developed a MATLAB program that dynamically simulates tire performance.

Solution:
The team evaluated three different tire models: the Pacejka Pure Slip, Pacejka Combined Slip, and MRA Non-Dimensional models. From the analysis, the Pacejka Pure Slip model was deemed to be the most accurate and justifiable tire model due to the amount of literature that has been published and ease of implementation. The MATLAB program presents force graphs as well as the friction ellipse for the TTC tested tires using the Pacejka pure slip equations.

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