Frequency Response of Tires Using the Point Contact Theory

The theoretical frequency response of a rolling tire is obtained here for angular oscillations about a vertical axis through the axle in the wheel plane. The point contact theory, also known as the DeCarbon or Moreland theory, is used to describe the side (cornering) force and the torsional (self-aligning) moment as a function of the oscillating frequency. These results are compared to previously published experimental results and found to show reasonable correlation especially when compared to theoretical results obtained using the von Schlippe or stretched string theory. It is noted, both from experimental and theoretical results, that the frequency response is considerably influenced by rolling speed which is contrary to implications given in previous papers. It is also pointed out that an upper limit of the forcing frequency exists above which the empirical data is not likely to represent natural shimmy oscillations. The results indicate that the point contact theory is adequate for use in shimmy analysis over both the tire yaw and structural-torsion shimmy modes of vibration if appropriate tire parameters are used. Nomenclature b = half width of tire footprint or contact area c = tire yaw coefficient CL = tire lateral damping coefficient ct = tire time constant D = tire diameter Airum = drum diameter d = effective tire width F = magnitude of dimensionless, complex lateral force ampli_ tude