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A tire enveloping model is described by a “four-ports network” system. A flexible roller contact (FRC) model is proposed, in which both tire geometric filtering effect and tire flexible filtering effect are taken into account. Furthermore, partial loss of contact and the variation of contact length are also considered effectively in this model. In the modelling of automobile vibration systems, because of the influences of tire enveloping properties, the road input could not be original road profile. So an effective road input is proposed which is filtered by the tire. Under different obstacles, tire loads and inflation pressures, the simulations of the effective road input are carried out based on the FRC model. The simulation results show that FRC model can describe tire enveloping properties more effectively than rigid roller contact (RRC) model.

One of the most essential factors causing automobile and aircraft shimmy is energy import from road to tires due to tire hysteresis characteristic. The magnitudes and direction of the energy import are close to frequency responses of tire cornering properties (TCP), which can be calculated directly according to the presented non-steady state TCP theoretical model. Selfexcited shimmy is the main type of wheel shimmy and behaves as negative equivalent damping characteristic of the tire-road vibration subsystem. The values of energy import or equivalent damping determine the tendency of wheel shimmy. Tire structural parameters have certain effects on frequency response of TCP and thereby result in influences on wheel shimmy. Based on the tire model, some valid ways to decrease shimmy tendency are concluded through proper variations of carcass stiffness, tire-width, kingpin caster, tire pneumatic trail, tire cornering stiffness and so on.