Experimental validation of a physically based mathematical model of wheel rolling motion on a solid supporting surface during rectilinear driving

Introduction. High-fidelity simulation of off-road and amphibious vehicle motion relies on accurate wheel-surface interaction models. Although empirical and semi-empirical wheel rolling models (Pacejka, Guo and Lu) are dominant on solid surfaces, their input parameters are often ambiguous and do not have a direct physical interpretation, it is significantly limiting their predictive capabilities under complex, multi-mode driving conditions. Expensive and time-consuming specific sample testing is often required to obtain accurate characteristics.

Materials and Methods. This study presents an experimental validation of a physically based wheel dynamics model for non-deformable supporting surfaces. The mathematical description of the tire model with the use of brush analogy has been previously presented. A laboratory test bench was used as a validation environment to measure wheel kinematics and dynamics under a wide range of vertical loads in both driving and driven modes. Key parameters, including rolling radius, longitudinal slip, and torque have been measured directly on the rig. 

Results. Experimental data were used to validate the developed mathematical model, implemented in MATLAB/ Simulink. The model demonstrated match with experiment results in free-rolling mode, with a normalized root-meansquare error (RMS) below 1.2% for the covered distance. In driving mode, the error increased to approximately 10%, which, according to the analysis, is explained by the risen complexity of torque application and slip dynamics. 

Discussion and Conclusion. Unlike purely empirical models, all parameters of the developed model have a clear physical meaning and can be determined from a limited set of experiments. It makes this model a preferred choice for problems requiring the behavior prediction under various conditions.

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