Wet-Surface Tire Model With Speed-Dependent Cornering Force
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Solution Overview
Problem
Current tire modeling approaches, such as the Magic Formula, fail to accurately predict tire behavior on wet road surfaces, particularly in terms of grip and cornering stiffness, and do not account for the influence of vehicle speed.
Innovation Solution
A computer-implemented tire model that calculates the lateral load-dependent friction coefficient and cornering stiffness based on vertical tire load and longitudinal tire velocity, incorporating linear and non-linear dependencies on vehicle speed, and using pre-calculated dimensionless coefficients from experimental data on wet surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Magic Formula approach is used to model tire behavior, then the model is simple and computationally efficient, but it does not accurately predict tire grip on wet surfaces
Solution Approach 1:
The patent modifies the Magic Formula model by adding velocity-dependent parameters. Specifically, the lateral friction coefficient μy is changed from being load-dependent only to being dependent on both vertical load Fz and longitudinal velocity v, expressed as μy(Fz, v). This parameter expansion allows the model to capture wet surface behavior while retaining the original formula's computational efficiency.
Solution Approach 2:
The patent introduces dynamic velocity dependence into the tire model. The lateral friction coefficient is no longer static but varies with longitudinal velocity v, allowing the model to adapt to changing driving conditions. This dynamic adjustment enables accurate prediction of tire grip degradation at different speeds on wet surfaces.
2Measurement precision
If complex models incorporating hydrodynamic lubrication are used to predict tire forces on low coefficient surfaces, then prediction accuracy improves, but computational complexity and processing time increase significantly
Solution Approach 1:
Instead of using complex hydrodynamic lubrication models, the patent simplifies the approach by introducing velocity as a direct parameter in the friction coefficient calculation. The lateral friction coefficient μy is expressed as a function of vertical load and velocity: μy(Fz, v). This parameter-based approach achieves accurate predictions without the computational burden of solving hydrodynamic equations.
Solution Approach 2:
The patent extracts the essential velocity dependence effect from complex hydrodynamic models and incorporates it directly into the Magic Formula framework. By taking out only the critical velocity-dependent behavior and integrating it into the existing model structure, the patent achieves accurate wet surface prediction while maintaining real-time computational performance.
3Productivity
If the Magic Formula model is used without velocity dependence, then computational efficiency is maintained, but the model fails to capture the influence of vehicle speed on tire grip
Solution Approach 1:
The patent expands the friction coefficient from μy(Fz) to μy(Fz, v) by adding velocity v as a parameter. This minimal parameter addition captures the physical reality that tire grip on wet surfaces decreases with increasing velocity, while maintaining the computational efficiency of the Magic Formula approach.
Solution Approach 2:
The patent introduces dynamic velocity dependence into the lateral friction coefficient calculation. The coefficient μy now varies with longitudinal velocity v, allowing the model to dynamically adjust tire grip predictions based on vehicle speed, thereby improving reliability without sacrificing computational efficiency.
Data Source
AI summary
A computer-implemented method of predicting the behaviour of a vehicle tire on a wet road surface comprises: providing a computer-implemented tire model; inputting a vertical tire load and a longitudinal tire velocity to the tire model; using the computer-implemented tire model to calculate a predicted tire cornering force in terms of the lateral load-dependent friction coefficient and/or cornering stiffness being dependent on the vertical tire load and being dependent on the longitudinal tire velocity; and outputting the predicted tire cornering force from the computer-implemented tire model.