Vibration Analysis of Two-Axle Automobiles in Spatial Model with Wheel Separation

This article considers vertical vibration of a two-axle automobile in spatial model (full-car model) where wheel separation and road deformation are taken into account. The automobile with dependent suspensions is modeled as a spatial vibration system with three masses and seven degrees of freedom. The deformed road is modeled as an elastic rectangular plate which has uniform thickness, lies on the Kelvin's visco-elastic ground and is simply supported at all edges. The phenomenon of wheel separation is taken into account by introducing four contact state parameters (each per a wheel) into the differential equations of motion. The change in dimensions of the contact areas is also regarded by generating relations among the contact forces, the wheel geometries and their vertical deformations. The differential equations of motion of the automobile-road coupled system where exists a partial differential equation are transformed into a set of all ordinary differential equations by applying the Bubnov-Galerkin's method. Some illustrating results obtained from consideration are also given in the article. The results confirm the need of regard to the wheel separation. The effect of movement velocity on the dynamic responses and the total time of losing contact in case of taking wheel separation are also considered.