Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire

A plane problem of controlled rotation of a wheel with a weightless tire is considered. The wheel is placed on a fixed base and is equipped with a shock absorber to damp vertical vibrations. For simplicity, horizontal motions of the rotation axis are not admitted. It is required to maximize the average traction force on a sufficiently long time interval by applying a bounded control torque on the rotation axis. A nonlinear mathematical model of the system is developed, with the tire modeled by a weightless solid hollow cylinder connected to the wheel disk by numerous weightless springs that are in a pretensioned state. Equations of motion are derived with the use of the quasistatic condition. The dynamics of the process and the maximum traction force are analyzed.