The present invention relates generally to vehicle simulations for ride, handling, and road load prediction. In particular, the present invention relates to an analytical tire model that is used for vehicle simulations.
The use of simulations has become an important design tool of the automotive industry for predicting vehicle ride and load characteristics. A critical component of these simulations is the tire model used to characterize the interaction between the tire and the ground. Due to the complexity of the tire structure and composition, a range of tire models are used depending on the particular simulation application. The tire models can be divided into three general categories; finite element models, lumped mass models, and analytical tire models.
Finite element tire models can provide highly accurate results for simulations of tire and vehicle interactions. However, finite element models require an excessive amount of computation time as well as requiring a complex and time consuming set-up. In addition, some nonlinear finite element models may not be stable for all operating conditions of the simulation, causing additional lost time determining the source of the instability.
Lumped mass tire models are particularly suited to simulating tire tread bend. This model type can be used to simulate tire local resonance and its interaction with the vehicle. In some cases a lumped mass tire model can be used to directly define the contact between the tread bend and road surface. Unfortunately, the lumped mass tire models are very difficult and costly to create, often requiring special tire tests, programs, and experience to create an accurate model of the physical tire.
Analytical tire models do not require the detailed modeling of the physical tire that the finite element and lumped mass tire models both require. Instead of providing a detailed model of the physical tire, an analytical tire model uses global tire parameters such as tire radial stiffness, radial damping, and tire radius to model a tire. Using global tire parameters simplifies the creation of the tire model and leads to much faster computation times. However, since the physical tire is not modeled, mathematical assumptions must be made in order to simulate the interaction of the tire and the road surface. Determining what assumptions to use and how to mathematically implement those assumptions is generally determinative of the tire model accuracy and computation speed.
The first analytic tire model was created during the ""60s. Since then, numerous types of analytic tire models have been created, each based on different assumptions and having varying limitations in the usage of the particular model. Currently, various mathematical implementations of the radial spring tire model are the most widely used conventional analytical tire models because of the simplicity and accuracy compared with other analytical models. Referring to FIGS. 1A and 1B, radial spring tire models in general rely on the assumption that a tire is formed by a series of radial springs emanating from the center of the tire. At every time step as the tire progresses, the deformed area between the road profile and the tire undeformed envelope is calculated from the deformation of the radial springs. One method that many of the radial spring models employ to determine the magnitude of the resultant force is by hypothetically pressing the tire on a flat surface to deform the same area. Likewise, the angle of the resultant force is determined by summing all of the radial spring forces. Generally speaking, for gradually changing road surfaces conventional radial spring models provide reasonably accurate results. However, suddenly changing surfaces such as a step or pothole road input, may cause conventional radial spring models to provide inaccurate results. Due to the assumptions that were made in mathematically describing conventional radial spring models, the models do not always converge when a step input or pothole input is used as the ground profile for the simulation. In addition, for ground profile inputs similar to a step input, the models generally require excessive computation time in order to complete the numerical iterations that are necessitated for convergence.
Therefore, it is an object of the invention to provide an analytical tire model that can be used in vehicle simulations to accurately predict the tire and vehicle interaction when subjected to a predetermined ground profile. Also, it is desirable for the tire model to minimize the computation time required for the simulation. Additionally, it is an object to provide a tire model that is easily created. Also, it is desirable for the tire model to provide accurate simulation results when subjected to a ground profile describing a sudden change such as a step input.
To achieve the foregoing objectives an analytical tire model is provided for modeling a tire for use in simulating vehicle response to a simulated ground profile. The tire is described by an undeformed envelope that is mathematically characterized. The difference between the tire undeformed envelope and the ground profile is integrated with respect to the horizontal direction in order to determine the tire deformed area. The magnitude of a resultant force vector acting on the tire is calculated from the deformed area. The direction of the resultant force vector is combined with the magnitude of the resultant force vector.
The above described system is only an example. Systems in accordance with the present invention may be implemented in a variety of ways.