Modeling of the motion of automobile elastic wheel in real-time for creation of wheeled vehicles motion control electronic systems

Modeling of the motion of the elastic wheel of the vehicle in real-time is used in the tasks of constructing different models in the creation of wheeled vehicles motion control electronic systems, in the creation of automobile stand-simulators etc. The accuracy and the reliability of simulation of the parameters of the wheel motion in real-time when rolling with a slip within the given road conditions are determined not only by the choice of the model, but also by the inaccuracy and instability of the numerical calculation. It is established that the inaccuracy and instability of the calculation depend on the size of the step of integration and the numerical method being used. The analysis of these inaccuracy and instability when wheel rolling with a slip was made and recommendations for reducing them were developed. It is established that the total allowable range of steps of integration is 0.001..0.005 s; the strongest instability is manifested in the calculation of the angular and linear accelerations of the wheel; the weakest instability is manifested in the calculation of the translational velocity of the wheel and moving of the center of the wheel; the instability is less at large values of slip angle and on more slippery surfaces. A new method of the average acceleration is suggested, which allows to significantly reduce (up to 100%) the manifesting of instability of the solution in the calculation of all parameters of motion of the elastic wheel for different braking conditions and for the entire range of steps of integration. The results of research can be applied to the selection of control algorithms in vehicles motion control electronic systems and in the testing stand-simulators