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Lewis, Kemper E.
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Inflation Pressure Effects in the Nondimensional Tire Model

Milliken Research Associates, Inc.-Douglas L. Milliken
University at Buffalo-Edward M. Kasprzak, Kemper E. Lewis
Published 2006-12-05 by SAE International in United States
Inflation pressure affects every aspect of tire performance. Most tire models, including the Radt/Milliken Nondimensional Tire Model, are restricted to modeling a single inflation pressure at a time. This is a reasonable limitation, in that the Nondimensional model forms an input/output relationship between tire operating conditions and force & moment outputs. Traditional operating conditions are normal load, slip angle, inclination angle, slip ratio and road surface friction coefficient.Tire pressure is more like a tire parameter than a tire operating condition. Since the Nondimensional Tire Model is semi-empirical it does not specifically deal with tire parameters like sidewall height or tread compound. Still, tire pressure is the easiest tire parameter to change, and as the air temperature within the tire varies during use so does the inflation pressure. Thus, it is desirable to incorporate inflation pressure into the Nondimensional Tire Model as an input.This paper discusses the effects of tire pressure on tire force and moment output. Effects on lateral force and aligning torque are investigated in detail. Additionally, the effects on cornering stiffness, friction coefficients,…
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Tire Asymmetries and Pressure Variations in the Radt/Milliken Nondimensional Tire Model

Milliken Research Associates, Inc.-Douglas L. Milliken
University at Buffalo, State University at New York-Edward M. Kasprzak, Kemper E. Lewis
Published 2006-02-14 by SAE International in United States
The Nondimensional Tire Model is based on the idea of data compression to load-independent curves. Through the use of appropriate transforms, tire data can be manipulated such that, when plotted in nondimensional coordinates, all data falls on a single curve. This leads to a highly efficient and mathematically consistent tire model.In the past, data for slip angle and slip ratio has been averaged across positive and negative values for use with the transforms. In this paper, techniques to handle tire asymmetries in lateral and longitudinal force are presented. This is an important advance, since in passenger cars driving/braking data is almost always asymmetric and, depending on tire construction, lateral force data may follow likewise.In addition, this paper is the first to explore the inclusion of inflation pressure as an operating variable in the Nondimensional Tire Theory. Inflation pressure affects the shape of the tire curves, notably the linear range stiffness and peak force friction coefficient. With this new variable, the operating conditions addressed by Nondimensional Tire Theory now include slip angle, slip ratio, inclination angle,…
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Steady-State Vehicle Optimization Using Pareto-Minimum Analysis

Milliken Research Associates, Inc.-Douglas L. Milliken
State University of New York at Buffalo-Kemper E. Lewis
Published 1998-11-16 by SAE International in United States
Designing for optimal performance across a variety of situations involves compromise decisions. Through the investigation of a two-variable optimization of a vehicle for two different “races” the importance of this compromise design is underscored. The use of Pareto-minimal solution techniques, borrowed from game theory, aid in the design process by limiting the number of possible compromise designs, highlighting which solution applies for a given situation and providing some insight to the sensitivity of the design.
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