This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Tire Modeling for Low-Speed and High-Speed Calculations
Annotation ability available
Sector:
Language:
English
Abstract
Vehicle dynamics simulations typically use semi-empirical tire models. The input to these models are normal load, sideslip angle and longitudinal slip, and the output are shear forces, aligning moment, and overturning moment.
Since the longitudinal speed is in the denominator of both sideslip angle and longitudinal slip, the calculation of sideslip angle and longitudinal slip at very low longitudinal velocities leads to numerical problems. This has not been a particular stumbling point in the past because vehicle dynamics calculations were largely concerned with high speed analysis. In situations wherein the vehicle was braked to a stop, patchwork techniques sufficed for calculations at low speeds.
Now, however, with the advent of serious attention to driving simulators, low speed tire modelling has become more important. This paper presents a new formulation which differs from previous work in that both longitudinal slip and slip angle become state variables rather than kinematic functions of wheel spin rate and wheel velocity. The result is a model which yields traditional solutions at high speed, and which comes to a stop in a reasonable way without numerical problems. The calculated longitudinal slip and slip angle can be paired with any semi-empirical tire model.
Several challenging examples, including braking-induced spinout ending in a stop on a severely inclined surface, illustrate the power of this new technique.
Recommended Content
Technical Paper | Analysis of the STI Tire Model |
Technical Paper | Lateral Stiffness, Cornering Stiffness and Relaxation Length of the Pneumatic Tire |
Technical Paper | A Robust Lumped-Parameter Tire Model Developed for Real-Time Simulation |
Authors
Citation
Bernard, J. and Clover, C., "Tire Modeling for Low-Speed and High-Speed Calculations," SAE Technical Paper 950311, 1995, https://doi.org/10.4271/950311.Also In
New Developments in Vehicle Dynamics, Simulation, and Suspension Systems
Number: SP-1074; Published: 1995-02-01
Number: SP-1074; Published: 1995-02-01
References
- Segel, L. “An overview of developments in road-vehicle dynamics: past, present, and future” Proceedings of The Institution of Mechanical Engineers Automobile Division 1993
- Bernard, J.E. Winkler, C.B. Fancher, P.S. “A Computer Based Mathematical Method for Predicting the Directional Response of Trucks and Tractor-Trailers (Phase II Technical Report)” June 1973
- Owen, R.H. Bernard, J.E. “Directional Dynamics of a Tractor-Loader-Backhoe” Vehicle System Dynamics 11 December 1982
- Allen, R.W. Rosenthal, T.J. Szostak, H.T. “Analytical Modeling of Driver Response in Crash Avoidance Maneuvering, Volume I: Technical Background” Systems Technology, Inc. April 1988
- Heydinger, G.J. “Improved Simulation and Validation of Road Vehicle Handling Dynamics” Ohio State University Columbus, Ohio 1990
- Allen, R.W. Szostak, H.T. Rosenthal, T.J. et al. “Vehicle Dynamic Stability and Rollover” Systems Technology, Inc
- Shapley, C.G. “The Influence of Tire Modeling in Commercial Vehicle Simulation” Proceedings of a Symposium on Commercial Braking and Handling May 5-7 1975
- Bernard, J.E. Segel, L. Wild, R.E. “Tire Shear Force Generation During Combined Steering and Braking Maneuvers” SAE Transactions SAE Paper No. 770852 1977
- Bernard, J.E. Bhatnagar, A. Clover, C.L. “Evaluation of Select Vehicle Dynamics Models (Phase II)” June 1992
- Szostak, H.T. Allen, R.W. Rosenthal, T.J. “Analytical Modeling of Driver Response in Crash Avoidance Maneuvering, Volume II: An Interactive Tire Model for Driver/Vehicle Simulation” Systems Technology, Inc. April 1988