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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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Race Car Vehicle Dynamics - Problems, Answers and Experiments

Metz Engineering & Racing-L. Daniel Metz
Milliken Research Associates Inc.-Douglas L. Milliken, Edward M. Kasprzak, William F. Milliken
  • Book
  • R-280
Published 2003-05-30 by SAE International in United States

Written for the engineer as well as the race car enthusiast and students, this is a companion workbook to the original classic book, Race Car Vehicle Dynamics, and includes:

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Race Car Vehicle Dynamics Book and Problems, Answers and Experiments Set

Metz Engineering & Racing-L. Daniel Metz
Milliken Research Associates Inc-William F. Milliken, Douglas L. Milliken
  • Book
  • R-146.SET
Published 2003-05-01 by SAE International in United States
This set includes: Race Car Vehicle Dynamics, Race Car Vehicle Dynamics - Problems, Answers and Experiments Purchase both the book and the workbook as a set and save!
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Chassis Design

Milliken Research Associates Inc-William F. Milliken, Douglas L. Milliken
  • Book
  • R-206
Published 2002-02-01 by SAE International in United States

Chassis Design: Principles and Analysis is based on Olley's technical writings, and is the first complete presentation of his life and work. This new book provides insight into the development of chassis technology and its practical application by a master. Many examples are worked out in the text and the analytical developments are grounded by Olley's years of design experience.

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MRA Vehicle Dynamics Simulation-Matlab®/Simulink®

Milliken Research Associates, Inc.-Edward M. Kasprzak, Douglas L. Milliken
Published 2000-05-01 by SAE International in United States
Milliken Research Associates has developed a new simulation tool, named Vehicle Dynamics Simulation-Matlab/Simulink (VD-M/S). Produced for the government's Variable Dynamic Testbed Vehicle (VDTV), VD-M/S is an 18 degree-of-freedom simulation programmed in the Matlab/Simulink environment. It contains a detailed non-linear tire model, kinematic and compliance effects, aerodynamic loadings, etc. as do MRA's other simulation programs. Unique to VD-M/S is its development from Day One as a simulation catered to the inclusion and exploration of active systems within the vehicle.
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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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Analysis and Correlation using Lap Time Simulation-Dodge Stratus for the North American Touring Car Championship

Chrysler Corp.-Dan W. Thomas
Milliken Research Associates, Inc.-David J. Segal, Douglas L. Milliken
Published 1996-12-01 by SAE International in United States
Simulation of race circuit performance had a significant impact on the design and development of the Dodge Stratus North American Touring Car Championship (NATCC) entry. The analysis involved utilization of the Milliken Research Associates, Inc. (MRA) Lap Time Simulation (LTS) program which predicts lap time based on data describing the vehicle, tires, and race track.Input data for the simulation was obtained from several sources. Chrysler Vehicle Engineering provided vehicle design information and engine power data. Tire characteristics were measured at Calspan Corporation. Aerodynamic coefficients were derived from scale model wind tunnel tests performed by Reynard Racing Cars Ltd. at the Houghton Wind Tunnel, Royal Military College of Science Shrivenham, Wiltshire, UK. X-Trac Ltd. provided transaxle specifications and race line data was derived from on-board measurements and circuit maps.Parametric studies of the vehicle variables were performed for various tracks. The results were used, in conjunction with more traditional race car design techniques, to specify the initial vehicle design and the range of setup adjustments required to tune the car for different tracks.The results were correlated with…
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Moment Method - A Comprehensive Tool for Race Car Development

Milliken Research Associates, Inc.-William F. Milliken, Douglas L. Milliken
Team Lotus Ltd.-Peter G. Wright
Published 1994-12-01 by SAE International in United States
The MRA Moment Method computer program automates an original approach to the analysis of race car handling. For a given speed and power/braking condition, the computer solution covers the full maneuvering envelope and presents the results graphically in one figure. The model is based on a comprehensive nonlinear vehicle representation utilizing tire, chassis, and aerodynamic input data as available to race car designers and developers. The paper will first explain and illustrate the Moment Method in general terms, with some graphical examples.The ability of the technique to model the behavior of an F.1 car traversing a small bump in mid-corner on a Grand Prix circuit is then reviewed. The results correlate well with the driver comments relative to changes in directional stability (plow/spin) as the car pitches over the bump. It also correlates well with the lateral acceleration/speed that the driver is willing to use in this corner.
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Race Car Vehicle Dynamics

Milliken Research Associates Inc-Douglas L. Milliken
Milliken Research Associates Inc.-William F. Milliken
  • Book
  • R-146
Published 1994-12-01 by SAE International in United States

Written for the engineer as well as the race car enthusiast, Race Car Vehicle Dynamics includes much information that is not available in any other vehicle dynamics text. Truly comprehensive in its coverage of the fundamental concepts of vehicle dynamics and their application in a racing environment, this book has become the definitive reference on this topic. Although the primary focus is on the race car, the engineering fundamentals detailed are also applicable to passenger car design and engineering.